Deep learning approaches for time series prediction in climate resilience applications

Introduction: Time series prediction is a fundamental task in climate resilience, where accurate forecasting of climate variables is critical for proactive planning and adaptation. Traditional methods often struggle with the nonlinearity, high variability, and multi-scale dependencies inherent in climate data, limiting their applicability in dynamic and diverse environments.

Methods: In this work, we propose a novel framework that combines the Resilience Optimization Network (ResOptNet) with the Equity-Driven Climate Adaptation Strategy (ED-CAS) to address these challenges. ResOptNet employs hybrid predictive modeling and multi-objective optimization to identify tailored interventions for climate risk mitigation, dynamically adapting to real-time data through a feedback-driven loop. ED-CAS complements this by embedding equity considerations into resource allocation, ensuring that resilience-building efforts prioritize vulnerable populations and regions.

Results: Experimental evaluations on climate datasets demonstrate that our approach significantly improves forecasting accuracy, resilience indices, and equitable resource distribution compared to traditional models.

Discussion: By integrating predictive analytics with optimization and equity-driven strategies, this framework provides actionable insights for climate adaptation, advancing the development of scalable and socially just resilience solutions.

1 Introduction

Climate resilience focuses on the ability of systems and communities to prepare for, adapt to, and recover from climate change impacts. The growing severity of extreme weather events, like hurricanes and heatwaves, highlights the urgent need for proactive strategies that ensure sustainability and reduce risks beyond disaster management. Time series prediction has become a cornerstone in advancing climate resilience, as accurate forecasting is critical for understanding climate variability, extreme weather events, and long-term environmental changes. Not only does this task support policymakers in designing proactive mitigation strategies, but it also empowers local communities and industries to prepare for and adapt to climate-related risks Angelopoulos et al. (2023). Traditional forecasting models, while effective in relatively stable systems, often fall short in capturing the complex, non-linear, and multi-scale dynamics inherent in climate systems. The increasing availability of large-scale environmental datasets and advances in computational power have shifted the focus toward leveraging deep learning methods Shen and Kwok (2023), which are uniquely positioned to address these challenges. By extracting patterns and relationships across diverse variables, these methods enable predictions that are both accurate and adaptive to climate variability, making them essential for climate resilience applications Zhou et al. (2020).

Early approaches to time series prediction in climate applications relied on statistical and physics-based models that utilized explicit assumptions about the underlying system dynamics Li et al. (2023). Methods such as autoregressive integrated moving average (ARIMA), Gaussian processes, and linear regression were widely used for their simplicity and interpretability. For instance, ARIMA models were employed to predict temperature trends or rainfall variability based on historical data Yin et al. (2023). Similarly, physics-based models like numerical weather prediction (NWP) systems integrated physical laws to simulate weather dynamics. While these methods provided valuable insights, they often struggled with high-dimensional, noisy data and failed to generalize across regions with different climatic characteristics Yu et al. (2023). Their reliance on handcrafted features and explicit assumptions about system behavior limited their ability to capture the chaotic and non-linear nature of climate processes Durairaj and Mohan (2022).

The emergence of data-driven machine learning methods marked a significant departure from traditional approaches by enabling the automatic learning of patterns from data without the need for explicit feature engineering Chandra et al. (2021). Techniques such as support vector machines (SVMs), random forests, and shallow neural networks were applied to tasks such as temperature forecasting, drought prediction, and flood risk assessment. These methods achieved improved performance over traditional models by leveraging larger datasets and learning non-linear relationships Fan et al. (2021). For example, SVMs and decision trees were used to classify weather patterns based on historical data, while shallow neural networks captured non-linear dependencies in small-scale datasets. However, these approaches were still constrained by their limited capacity to model long-term dependencies and their reliance on carefully curated datasets Hou et al. (2022). They often required significant domain expertise to define appropriate input features, limiting their scalability to complex climate resilience applications.

The advent of deep learning has revolutionized time series prediction by introducing architectures capable of capturing intricate spatial-temporal dependencies in high-dimensional data Lindemann et al. (2021). Recurrent neural networks (RNNs), particularly long short-term memory (LSTM) networks and gated recurrent units (GRUs), have demonstrated remarkable success in modeling sequential climate data, such as precipitation forecasts or sea-level rise predictions Dudukcu et al. (2022). Convolutional neural networks (CNNs), originally designed for image processing, have also been adapted for spatial-temporal forecasting by leveraging their ability to extract features across both spatial and temporal dimensions. More recently, transformer-based models have emerged as state-of-the-art solutions, outperforming traditional RNNs in capturing long-range dependencies and complex interactions Amalou et al. (2022). For example, transformers have been applied to predict temperature anomalies by integrating multi-modal datasets, such as satellite imagery and ground-based observations Xiao et al. (2021). Despite their success, deep learning models face challenges in interpretability, data sparsity, and generalization across regions with varying climate dynamics, as well as high computational requirements for training and inference Zheng and Chen (2021).

To overcome the limitations of existing approaches, we propose a novel deep learning framework for time series prediction focused on operational climate resilience, as defined by the IPCC, emphasizing system resistance, recovery, and persistence under climate-related shocks. The proposed model integrates spatiotemporal attention mechanisms with graph neural networks to model interactions between climate variables and spatial regions dynamically. Multi-task learning is employed to jointly predict short-term and long-term climate outcomes, improving robustness across different time scales. The framework is designed to handle diverse data sources, including remote sensing, sensor networks, and simulation outputs, enabling accurate and interpretable predictions for extreme weather events, resource management, and adaptation planning. By addressing the challenges of non-linearity, spatial heterogeneity, and data sparsity, the proposed approach offers a scalable and adaptive solution for advancing climate resilience. We summarize our contributions as follows:

$•$ The proposed model combines spatiotemporal attention mechanisms and graph neural networks, enabling the dynamic modeling of complex interactions between climate variables and regions.

$•$ Designed for multi-source data integration, the framework is efficient and generalizable across diverse climate scenarios, supporting real-time applications and long-term forecasting.

$•$ Empirical evaluation demonstrates state-of-the-art performance in multiple climate resilience tasks, including extreme event prediction and resource allocation, with superior accuracy and interpretability compared to existing models.

The hypothesis of this study is that climate variables such as temperature and precipitation interact with system-level responses in a region-specific manner due to spatial heterogeneity in land use, infrastructure, and socio-economic conditions. The model captures this interaction by embedding both temporal sequences and spatial identifiers into the learning architecture, allowing it to learn region-dependent patterns from data. Climate variability across regions is not treated as noise but as a structural factor influencing the system’s response. This is reflected in the experimental setup, where inputs from different regions are processed jointly, and the model learns to distinguish and adapt to local climate dynamics. The contribution of this work is a unified framework that enables region-aware prediction of system behavior under climate stress, improving both accuracy and the ability to simulate resilience in contextually diverse environments.

2 Related work

2.1 Deep learning for time series forecasting

In this study, we define climate resilience following the IPCC framework as the capacity of a system—whether ecological, infrastructural, or socio-technical—to resist, absorb, adapt to, and recover from climate-induced disturbances while maintaining or rapidly restoring its essential functions. Specifically, we operationalize resilience through three quantifiable aspects: (1) resistance—the system’s ability to minimize initial disruption under shock; (2) recovery—the speed and pathway by which the system returns to a stable state; and (3) persistence—the continuity of core functions throughout the disturbance period. This definition is distinct from sustainability, which concerns long-term balance and development goals across environmental, social, and economic dimensions. Our modeling framework does not aim to evaluate sustainability outcomes directly; rather, it focuses on short-to medium-term system behavior under stress, providing predictive and adaptive capabilities to support resilience-oriented decision-making. Deep learning methods have shown significant potential in time series forecasting due to their ability to model complex temporal patterns and nonlinear relationships. Recurrent Neural Networks (RNNs), particularly Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) architectures Wang et al. (2021b), have been widely used to capture sequential dependencies in time series data. These models excel in learning long-term dependencies, making them suitable for climate-related applications such as temperature, precipitation, and sea-level forecasting Xu et al. (2020). However, traditional RNN-based models often struggle with scalability and are prone to vanishing gradient problems when dealing with long time series. To address these limitations, attention mechanisms and Transformer architectures have been introduced to improve the modeling of long-range dependencies in time series data Karevan and Suykens (2020). Transformers, originally designed for natural language processing tasks, have been adapted to handle sequential data in climate applications. Models such as the Temporal Fusion Transformer (TFT) allow for both global and local interpretability Altan and Karasu (2021), making them particularly valuable in climate resilience, where understanding the impact of specific variables is crucial for actionable insights. In climate resilience applications, deep learning models are often combined with external factors such as socioeconomic data, land-use patterns, and historical climate records to improve forecasting accuracy Wen et al. (2021). These approaches allow for the integration of diverse data modalities, capturing the interplay between anthropogenic activities and climate variability. Nevertheless, challenges remain in terms of model robustness and generalization Engel-Cox and Chapman (2023), particularly when extrapolating to unseen climate scenarios. Techniques such as domain adaptation and transfer learning are being explored to address these challenges by leveraging pre-trained models on related tasks Engel-Cox et al. (2022).

The model explicitly incorporates resilience, resistance, and recovery as dynamic components of system behavior. Resilience is captured through the system’s ability to maintain or return to functional states under climate perturbations. Resistance is reflected in the model’s ability to minimize initial deviation when exposed to shocks, and recovery is quantified by the rate at which the system stabilizes following disturbances. These aspects are embedded in the time-dependent state transitions and control optimization structure of the model, allowing it to represent not only the persistence of function but also the depth and duration of impact in climate-stressed conditions. Sustainability, in contrast, is treated as a broader contextual goal rather than a direct output of the model.

2.2 Multi-scale modeling for climate predictions

Climate phenomena inherently operate across multiple spatial and temporal scales, making it essential to incorporate multi-scale modeling techniques into deep learning frameworks. Traditional statistical methods, such as autoregressive integrated moving average (ARIMA) models, struggle to capture these multi-scale interactions due to their linearity assumptions Wang et al. (2021a). In contrast, deep learning approaches, including Convolutional Neural Networks (CNNs) and hybrid architectures, can effectively learn hierarchical representations of climate data Morid et al. (2021). For spatially distributed climate data, convolutional approaches such as 3D CNNs and U-Net architectures have been employed to capture spatial dependencies. These models are particularly useful in applications such as drought monitoring, flood prediction, and temperature anomaly detection, where spatial resolution is critical Widiputra et al. (2021). Combining these spatial models with temporal ones, such as LSTMs or Transformers, enables the joint modeling of spatiotemporal patterns. For instance, in rainfall prediction, hybrid models that integrate CNNs for spatial feature extraction with LSTMs for temporal forecasting have demonstrated improved accuracy and robustness Moskolaï et al. (2021). Wavelet transforms and multi-resolution analysis are also being integrated into deep learning frameworks to capture patterns at different temporal scales. These methods allow models to identify localized events, such as extreme weather conditions, while preserving long-term trends. Moreover, graph-based approaches, such as Graph Neural Networks (GNNs), are being employed to model the spatial relationships between different geographic regions Yang and Wang (2021). By encoding climate variables as nodes and their interactions as edges, GNNs enable the propagation of information across spatial scales, improving predictions in interconnected systems. Despite these advancements, multi-scale modeling faces challenges related to data sparsity and computational complexity Engel-Cox and Jeromin (2024). Climate data is often noisy and incomplete, particularly in developing regions where observation networks are limited. Techniques such as data augmentation, imputation, and the use of physics-informed neural networks are being developed to address these limitations and enhance the reliability of multi-scale deep learning models Kythreotis et al. (2019).

2.3 Extreme event prediction and adaptation

Extreme weather events, such as hurricanes, heatwaves, and floods, pose significant risks to climate resilience and necessitate accurate prediction models. Deep learning approaches have been increasingly applied to predict the occurrence, intensity, and duration of such events Ruan et al. (2021). Unlike traditional methods, which rely heavily on domain-specific features and simplified physical models, deep learning methods can directly learn patterns from raw data, including satellite imagery, reanalysis datasets, and sensor observations. CNNs have been widely used for identifying extreme weather patterns from satellite images, such as cyclones or atmospheric rivers. These models excel in detecting spatial features and can be fine-tuned for specific event types Kim and King (2020). LSTMs and GRUs, on the other hand, have been used to forecast the temporal evolution of extreme events, such as heatwave durations or flood peaks. More recently, spatiotemporal models that combine CNNs and RNNs have shown promise in jointly modeling the spatial extent and temporal dynamics of extreme events Wu et al. (2020). Generative models, such as Variational Autoencoders (VAEs) and Generative Adversarial Networks (GANs), have been explored to simulate extreme weather scenarios under different climate conditions. These models provide valuable insights into event probabilities and allow for stress testing of climate resilience strategies Kang et al. (2020). For example, GANs have been used to generate synthetic hurricane tracks, enabling better preparedness and risk assessment in vulnerable regions. The integration of physical models with deep learning approaches has emerged as a promising direction for extreme event prediction. By embedding physical constraints into neural networks, these hybrid models improve generalization and provide more interpretable results Hu et al. (2020). For instance, physics-informed neural networks (PINNs) incorporate governing equations of fluid dynamics into the training process, ensuring that predictions are consistent with established physical principles. Such approaches are particularly relevant in climate resilience applications, where understanding the underlying physical processes is critical for designing effective adaptation strategies Luhunga et al. (2018). Despite these advancements, extreme event prediction remains challenging due to the inherent rarity and unpredictability of these phenomena. Imbalanced datasets and the lack of historical records for certain event types hinder the training of deep learning models. Addressing these challenges requires innovative solutions, such as synthetic data generation, transfer learning, and active learning techniques, to enhance model performance and reliability in real-world scenarios Kiddle et al. (2021).

3 Methods

3.1 Overview

This paper presents a novel framework combining predictive modeling, data-driven insights, and adaptive strategies to enhance climate resilience. Unlike reactive approaches, it offers scalable, equitable solutions to uneven climate impacts and resource limitations through anticipatory and optimized interventions.

In Section 3.2, we provide a formal definition of climate resilience and introduce the underlying concepts and frameworks that guide this study. This includes an analysis of resilience metrics, modeling techniques, and the multi-dimensional nature of resilience spanning environmental, social, and economic domains. These preliminaries establish a comprehensive foundation for understanding the scope and challenges of building climate-resilient systems. In Section 3.3, we introduce our proposed computational framework, termed Resilience Optimization Network (ResOptNet), which employs hybrid modeling approaches to identify and prioritize interventions for climate adaptation. ResOptNet combines system-level simulations with multi-objective optimization to propose tailored strategies for climate risk mitigation. The framework incorporates feedback loops to adapt to real-time climate data, ensuring its applicability in dynamic environments. In Section 3.4, we propose an innovative strategy named Equity-Driven Climate Adaptation Strategy (ED-CAS) that prioritizes vulnerable populations and regions during resource allocation. ED-CAS incorporates socio-economic factors and local adaptive capacities into the resilience-building process, ensuring that interventions are both equitable and impactful. By bridging the gap between computational rigor and policy implementation, this strategy aims to create scalable solutions that can be deployed in diverse geographic and socio-political contexts. This integrative approach advances climate resilience by addressing its complexity and is evaluated through urban and rural case studies. The results demonstrate its effectiveness across diverse scenarios, offering valuable insights for policymakers, practitioners, and researchers in climate adaptation.

3.2 Preliminaries

Climate resilience is the capacity of systems—be they ecological, social, or infrastructural—to anticipate, absorb, adapt, and recover from the impacts of climate change and variability. This section formalizes the concept of resilience, introduces key metrics and models used in its evaluation, and establishes the problem formulation that guides this work.

The resilience of a system can be mathematically defined as its ability to maintain or quickly return to a desirable state $\mathcal{S}$ after being perturbed by external shocks, such as extreme weather events. Let $\mathcal{X}(t)\in {\mathbb{R}}^n$ denote the state vector of a system at time $t$, where $\mathcal{X}(t)=\{x_1(t),x_2(t),\dots ,x_n(t)\}$ represents various critical components such as infrastructure integrity, ecological health, or economic stability. Climate resilience can be framed as the ability of $\mathcal{X}(t)$ to remain within a safe region $\mathcal{R}\subseteq {\mathbb{R}}^n$ under the influence of perturbations $\mathcal{P}(t)$, such that (Equation 1):

$\mathcal{X}\left(t\right)\in \mathcal{R},\forall t\ge t_0,\text{given\hspace{0.17em}}\mathcal{P}\left(t\right).(1)$

Here, $\mathcal{P}(t)$ denotes the external perturbation vector caused by climate-induced hazards, and $\mathcal{R}$ is defined by threshold conditions reflecting system failure or collapse.

Several metrics are commonly employed to quantify resilience: Recovery Time $(T_r)$: The time required for the system to return to a desirable state $\mathcal{S}$ after perturbation. Absorptive Capacity $(\alpha )$: The ability of the system to withstand perturbations without transitioning outside the safe region $\mathcal{R}$. Resilience Index $({\mathcal{I}}_R)$: A normalized score that combines multiple dimensions of resilience into a scalar value, such as (Equation 2):

${\mathcal{I}}_R=\frac{1}{T_r}{\int }_{t_0}^{t_0+T_r}\text{max}\left(0,\mathcal{R}-\Vert \mathcal{X}\left(t\right)-\mathcal{S}\Vert \right)dt,(2)$

where $\Vert \mathcal{X}(t)-\mathcal{S}\Vert$ measures the deviation from the desired state.

The evolution of the system state $\mathcal{X}(t)$ is governed by a set of coupled differential equations (Equation 3):

$\frac{d\mathcal{X}\left(t\right)}{dt}=\mathcal{F}\left(\mathcal{X}\left(t\right),\mathcal{P}\left(t\right),\mathcal{U}\left(t\right)\right),(3)$

where $\mathcal{F}(\cdot )$ encapsulates the system dynamics, $\mathcal{P}(t)$ represents perturbations such as floods or heatwaves, and $\mathcal{U}(t)$ is a control input vector representing adaptation or mitigation actions. Examples of $\mathcal{U}(t)$ include investments in infrastructure, resource allocation, or policy interventions.

Resilience is inherently multi-dimensional, encompassing environmental, social, and economic domains: Captures the capacity of communities to adapt and recover, often modeled as social networks $\mathcal{G}=(\mathcal{V},\mathcal{E})$ with nodes $\mathcal{V}$ representing individuals or institutions and edges $\mathcal{E}$ representing social interactions.

The task of enhancing climate resilience can be formulated as a multi-objective optimization problem (Equation 4):

$extmaximize{\mathcal{I}}_R\left(\mathcal{X}\left(t\right),\mathcal{U}\left(t\right)\right)\text{subject\hspace{0.17em}to}\mathcal{X}\left(t\right)\in \mathcal{R},\forall t,(4)$

where $\mathcal{U}(t)$ must satisfy resource constraints (Equation 5):

${\int }_{t_0}^{t_1}\Vert \mathcal{U}\left(t\right)\Vert dt\le \mathcal{B}.(5)$

Here, $\mathcal{B}$ is the total budget available for implementing adaptation measures.

The model treats resilience both as a measurable dynamic response and as a system condition under climate disturbance. Resilience as a metric is defined by quantifiable outputs such as recovery time, deviation amplitude, and system stabilization behavior. Resilience as a state refers to the system’s maintained ability to function within acceptable limits during and after climate impact. The model does not assume equivalence between biotic and abiotic responses. Instead, it uses system-specific inputs and response variables for each type. In abiotic systems like water infrastructure, the model tracks flow and pressure recovery. In biotic contexts, such as land cover change or vegetation stress, the model uses indicators like NDVI variation or productivity response. Each input is normalized based on domain-specific statistical ranges, and model outputs are interpreted relative to the system’s baseline function. Activation functions and normalization methods are not applied uniformly but selected based on the temporal and spatial variability of each subsystem. For instance, GELU is used in transformer components to preserve temporal smoothness, and batch normalization is applied where input scale varies across subsystems. These design choices ensure that system-specific adaptation and recovery strategies are respected before comparing across environments.

3.3 Resilience Optimization Network (ResOptNet)

In this section, we present the proposed Resilience Optimization Network (ResOptNet), a novel computational framework that addresses the challenges of optimizing climate resilience strategies. Below, we highlight three key innovations that distinguish ResOptNet (As shown in Figure 1).

Figure 1

Figure 1. The diagram illustrates the ResOptNet framework, combining Predictive System Dynamics on the left, Multi-Objective Resilience Optimization in the center, and Feedback-Driven Adaptive Control on the right. It provides a robust framework for addressing climate resilience challenges by leveraging predictive dynamics, real-time feedback, and multi-objective optimization. This framework dynamically adjusts interventions to uncertainties and external disturbances while maintaining system stability. Visualized with subsystems, interactions, and control mechanisms to optimize climate resilience across environmental, social, and economic dimensions.

3.3.1 Predictive system dynamics integration

ResOptNet integrates a comprehensive predictive system dynamics model to simulate the evolution of climate-impacted systems across environmental, social, and economic dimensions, ensuring an in-depth understanding of interdependencies and feedback mechanisms. The system dynamics are governed by (Equation 6):

$\frac{d\mathcal{X}\left(t\right)}{dt}=\mathcal{F}\left(\mathcal{X}\left(t\right),\mathcal{P}\left(t\right),\mathcal{U}\left(t\right)\right),(6)$

where $\mathcal{X}(t)=\{{\mathcal{X}}_{\text{env}}(t),{\mathcal{X}}_{\text{soc}}(t),{\mathcal{X}}_{\text{econ}}(t)\}$ represents the state variables for the environmental, social, and economic subsystems. The system dynamics depend on climate perturbations $\mathcal{P}(t)$ and intervention strategies $\mathcal{U}(t)$. The climate perturbations are modeled as stochastic processes capturing time-dependent changes, defined as (Equation 7):

$\mathcal{P}\left(t\right)=\left\{{\xi }_1\left(t\right),{\xi }_2\left(t\right),\dots ,{\xi }_m\left(t\right)\right\},(7)$

where ${\xi }_i(t)$ denotes the $i$-th climate variable, such as temperature or precipitation. Each subsystem evolves according to its domain-specific dynamics, described by:

$\frac{d{\mathcal{X}}_{\text{env}}\left(t\right)}{dt}={\mathcal{F}}_{\text{env}}\left({\mathcal{X}}_{\text{env}}\left(t\right),\mathcal{P}\left(t\right),\mathcal{U}\left(t\right)\right),(8)$

$\frac{d{\mathcal{X}}_{\text{soc}}\left(t\right)}{dt}={\mathcal{F}}_{\text{soc}}\left({\mathcal{X}}_{\text{soc}}\left(t\right),{\mathcal{X}}_{\text{env}}\left(t\right),\mathcal{U}\left(t\right)\right),(9)$

$\frac{d{\mathcal{X}}_{\text{econ}}\left(t\right)}{dt}={\mathcal{F}}_{\text{econ}}\left({\mathcal{X}}_{\text{econ}}\left(t\right),{\mathcal{X}}_{\text{env}}\left(t\right),{\mathcal{X}}_{\text{soc}}\left(t\right),\mathcal{U}\left(t\right)\right).(10)$

The environmental subsystem is influenced by physical climate drivers, and ${\mathcal{F}}_{\text{env}}(\cdot )$ models key processes such as resource depletion and pollution dynamics. The interventions $\mathcal{U}(t)$ are designed to control critical aspects of the system by minimizing deviations from desired safe states ${\mathcal{S}}_d$. The objective is to stabilize the system while keeping it within safety thresholds, given by Equations 8–10:

${\mathcal{R}}_d=\max \left(0,{\mathcal{S}}_d-\Vert {\mathcal{X}}_d\left(t\right)\Vert \right),(11)$

where ${\mathcal{R}}_d$ measures the distance from critical failure. The overall control objective is to reduce the rate of deviation using proportional control mechanisms based on predicted system evolution, defined as (Equation 12):

$\mathcal{U}\left(t\right)=-\kappa {\nabla }_{\mathcal{X}}\left({\displaystyle \sum _d}\Vert {\mathcal{R}}_d{\Vert }^2\right),(12)$

where $\kappa$ is a control gain. In dynamic scenarios, feedback-based adaptations are employed by comparing real-time observations ${\mathcal{X}}_{\text{obs}}(t)$ with model predictions $\mathcal{X}(t)$. The error term $\mathrm{\Delta }\mathcal{X}(t)$ is used to adjust control variables (Equation 13):

$\mathrm{\Delta }\mathcal{X}\left(t\right)={\mathcal{X}}_{\text{obs}}\left(t\right)-\mathcal{X}\left(t\right),(13)$

leading to corrective updates (Equation 14):

$\mathcal{U}\left(t\right)\leftarrow \mathcal{U}\left(t\right)+\mathrm{\Delta }\mathcal{U}\left(t\right),(14)$

with $\mathrm{\Delta }\mathcal{U}(t)$ being computed using gradient descent. This predictive system ensures that ResOptNet dynamically responds to uncertainties and emerging risks while maintaining overall system stability.

3.3.2 Multi-objective resilience optimization

The framework employs a multi-objective optimization approach to identify resilience-enhancing interventions $\mathcal{U}(t)$ while adhering to resource and feasibility constraints. The objective is to maximize a composite resilience index ${\mathcal{I}}_R$ across different dimensions, ensuring that interventions are not only effective but also equitable. The resilience index is defined as (Equation 15):

${\mathcal{I}}_R={\displaystyle \sum _{d\in \left\{\text{env},\text{soc},\text{econ}\right\}}}{w}_d\cdot {\mathcal{I}}_R^d,(15)$

where $w_d$ represents the relative importance of environmental, social, and economic resilience. Each dimension of resilience improvement ${\mathcal{I}}_R^d$ is modeled as a function of the selected interventions (Equation 16):

${\mathcal{I}}_R^d={\displaystyle \sum _{i=1}^n}{\alpha }_i^d\cdot {\mathcal{U}}_i,(16)$

where ${\alpha }_i^d$ is the impact coefficient of intervention ${\mathcal{U}}_i$ on dimension $d$. The optimization process is constrained by a limited budget $\mathcal{B}$ (Equation 17):

${\displaystyle \sum _{i=1}^n}{c}_i\cdot {\mathcal{U}}_i\le \mathcal{B},(17)$

where $c_i$ is the cost associated with intervention ${\mathcal{U}}_i$. The framework enforces equity constraints to ensure that no community is left below a critical resilience threshold ${\mathcal{R}}_{\text{min}}$ (Equation 18):

${\mathcal{R}}_i\ge {\mathcal{R}}_{\text{min}},\forall i.(18)$

To adapt to evolving climate risks, the resilience improvement function dynamically updates based on real-time changes in vulnerability (Equation 19):

${\mathcal{I}}_R^d\left(t\right)={\mathcal{I}}_R^d\left(t-1\right)+{\displaystyle \sum _{i=1}^n}{\gamma }_i^d\cdot \mathrm{\Delta }{\mathcal{U}}_i\left(t\right),(19)$

where ${\gamma }_i^d$ represents the adaptability coefficient and $\mathrm{\Delta }{\mathcal{U}}_i(t)$ captures newly implemented interventions at time $t$. The prioritization of interventions is guided by a vulnerability-adjusted weighting mechanism (Equation 20):

${\mathcal{V}}_i^{*}\left(t\right)={\mathcal{V}}_i\left(t\right)+\lambda \cdot {\mathcal{I}}_R^i\left(t\right),(20)$

where $\lambda$ is a trade-off parameter balancing vulnerability and resilience gain. Intervention feasibility is constrained by operational capacity limits (Equation 21):

${\displaystyle \sum _{i=1}^n}{\mathcal{U}}_i\le C_{\text{max}},(21)$

where $C_{\text{max}}$ represents the maximum number of interventions implementable within a given period. To ensure robustness, a penalty function is incorporated for deviations from predefined resilience targets (Equation 22):

$\mathcal{P}={\displaystyle \sum _{i=1}^n}{\delta }_i\max \left(0,{\mathcal{R}}_{\text{min}}-{\mathcal{R}}_i\right),(22)$

where ${\delta }_i$ is the penalty weight assigned to each community. The optimization problem is then formulated as (Equation 23):

$\max {\mathcal{I}}_R-\mathcal{P},\text{subject\hspace{0.17em}to\hspace{0.17em}all\hspace{0.17em}constraints}.(23)$

This comprehensive framework ensures that resilience-enhancing interventions are selected based on equity-driven priorities while maintaining budget feasibility, system constraints, and adaptability to changing climate risks (As shown in Figure 2).

Figure 2

Figure 2. The Multi-Objective Resilience Optimization (MRO) framework employs a multi-objective optimization approach. It is designed to identify resilience-enhancing interventions. It ensures that these interventions adhere to resource and feasibility constraints. The framework integrates multimodal embedding and dynamic prioritization mechanisms to maximize a composite resilience index across environmental, social, and economic dimensions. The optimization process ensures equitable resource allocation by incorporating real-time vulnerability updates and enforcing minimum resilience thresholds. The diagram illustrates key components, including convolutional layers, depthwise convolutions, attention mechanisms, and fully connected (FC) layers that facilitate efficient multimodal embedding and decision-making.

3.3.3 Feedback-driven adaptive control

ResOptNet incorporates a feedback mechanism that dynamically updates intervention strategies based on real-time observations of system states. The deviation $\mathrm{\Delta }\mathcal{X}(t)$ between predicted and observed states is used to adjust control inputs, ensuring the system remains stable under varying environmental conditions. This deviation is quantified as (Equation 24):

$\mathrm{\Delta }\mathcal{X}\left(t\right)={\mathcal{X}}_{\text{observed}}\left(t\right)-{\mathcal{X}}_{\text{predicted}}\left(t\right),(24)$

where ${\mathcal{X}}_{\text{observed}}(t)$ represents the actual system state at time $t$ and ${\mathcal{X}}_{\text{predicted}}(t)$ is the forecasted state derived from the model. To minimize discrepancies, the control inputs are iteratively refined through gradient-based optimization (Equation 25):

$\mathrm{\Delta }\mathcal{U}\left(t\right)=-\eta {\nabla }_{\mathcal{U}}\Vert \mathrm{\Delta }\mathcal{X}\left(t\right){\Vert }^2,(25)$

where $\eta$ is the learning rate governing the adjustment magnitude. The control update is integrated into the system dynamics (Equation 26):

$\mathcal{X}\left(t+1\right)=f\left(\mathcal{X}\left(t\right),\mathcal{U}\left(t\right)+\mathrm{\Delta }\mathcal{U}\left(t\right)\right),(26)$

where $f(\cdot )$ represents the underlying system transition function. To account for uncertainty and stochastic variations in climate conditions, ResOptNet employs a probabilistic state representation, where the system state follows (Equation 27):

$\mathcal{X}\left(t\right)\sim \mathcal{N}\left({\mu }_{\mathcal{X}}\left(t\right),{\mathrm{\Sigma }}_{\mathcal{X}}\left(t\right)\right),(27)$

with ${\mu }_{\mathcal{X}}(t)$ and ${\mathrm{\Sigma }}_{\mathcal{X}}(t)$ denoting the mean and covariance matrix, respectively. To enhance robustness, the optimization incorporates a risk-aware objective function (Equation 28):

$\mathcal{L}=\mathbb{E}\left[\Vert \mathrm{\Delta }\mathcal{X}\left(t\right){\Vert }^2\right]+\lambda \text{Tr}\left({\mathrm{\Sigma }}_{\mathcal{X}}\left(t\right)\right),(28)$

where $\lambda$ is a regularization parameter penalizing excessive uncertainty. The control strategy is further refined through reinforcement learning, where an adaptive policy $\pi (\mathcal{X},\mathcal{U})$ is trained to minimize a cumulative cost function (Equation 29):

$J={\displaystyle \sum _{t=0}^T}{\gamma }^t\mathcal{C}\left(\mathcal{X}\left(t\right),\mathcal{U}\left(t\right)\right),(29)$

where $\gamma$ is a discount factor controlling the influence of future states, and $\mathcal{C}(\cdot )$ represents the cost function. The policy update follows (Equation 30):

${\theta }_{t+1}={\theta }_t-\alpha {\nabla }_{\theta }J,(30)$

where $\theta$ represents the policy parameters and $\alpha$ is the step size. To mitigate policy instability, an entropy regularization term is introduced (Equation 31):

${\mathcal{L}}_{\text{policy}}=J-\beta H\left(\pi \right),(31)$

where $H(\pi )$ represents the entropy of the policy, ensuring sufficient exploration. By integrating predictive dynamics, optimization, and real-time adaptation, ResOptNet effectively provides a scalable and robust solution for climate resilience planning, dynamically adjusting to uncertainties and external disturbances.

3.4 Equity-Driven Climate Adaptation Strategy (ED-CAS)

In this section, we introduce the Equity-Driven Climate Adaptation Strategy (ED-CAS), a novel framework that ensures climate adaptation efforts prioritize equity by systematically addressing socio-economic disparities. ED-CAS integrates advanced modeling techniques and optimization strategies to achieve fair and effective resource distribution (As shown in Figure 3).

Figure 3

Figure 3. Overview of the Equity-Driven Climate Adaptation Strategy (ED-CAS). This framework integrates multiple components to ensure equitable climate adaptation. The VAE module encodes signal space inputs into latent variables Z, which feed into the diffusion process for vulnerability modeling. The denoising U-Net refines these outputs using self-attention (SA) and cross-attention (CA) mechanisms. Equity-weighted resource allocation leverages LLMs to process multi-modal data, ensuring resources are distributed based on community-specific vulnerabilities. Dynamic vulnerability adjustment continuously updates vulnerability scores using real-time categorical, numerical, and climate data, ensuring responsive and fair adaptation measures.

3.4.1 Equity-aware vulnerability index

ED-CAS employs a comprehensive vulnerability index to evaluate community resilience, integrating economic, environmental, and social factors. The vulnerability score for community $i$, denoted as ${\mathcal{V}}_i$, is defined as (Equation 32):

${\mathcal{V}}_i=w_{\text{econ}}{\mathcal{V}}_i^{\text{econ}}+w_{\text{env}}{\mathcal{V}}_i^{\text{env}}+w_{\text{soc}}{\mathcal{V}}_i^{\text{soc}},(32)$

where $w_{\text{econ}},w_{\text{env}},w_{\text{soc}}$ represent the relative importance of economic, environmental, and social vulnerabilities, and ${\mathcal{V}}_i^{\text{econ}},{\mathcal{V}}_i^{\text{env}},{\mathcal{V}}_i^{\text{soc}}$ denote the respective vulnerability components for community $i$. The economic vulnerability ${\mathcal{V}}_i^{\text{econ}}$ is determined by factors such as income levels, employment rates, and economic diversity (Equation 33):

${\mathcal{V}}_i^{\text{econ}}={\alpha }_1{E}_i+{\alpha }_2{U}_i+{\alpha }_3{D}_i,(33)$

where $E_i$ represents the median household income, $U_i$ is the unemployment rate, and $D_i$ is a measure of economic diversity. The environmental vulnerability ${\mathcal{V}}_i^{\text{env}}$ is calculated based on exposure to climate risks and environmental degradation (Equation 34):

${\mathcal{V}}_i^{\text{env}}={\beta }_1{R}_i+{\beta }_2{P}_i+{\beta }_3{Q}_i,(34)$

where $R_i$ measures the risk of natural disasters, $P_i$ represents pollution levels, and $Q_i$ captures the quality of local ecosystems. The social vulnerability ${\mathcal{V}}_i^{\text{soc}}$ reflects factors like population density, health infrastructure, and access to basic services (Equation 35):

${\mathcal{V}}_i^{\text{soc}}={\gamma }_1{D}_i+{\gamma }_2{H}_i+{\gamma }_3{S}_i,(35)$

where $D_i$ denotes population density, $H_i$ measures the availability of healthcare facilities, and $S_i$ represents access to essential services such as water and electricity. To ensure effective allocation of resources, the weights $w_{\text{econ}},w_{\text{env}},w_{\text{soc}}$ are determined based on the relative severity of vulnerabilities using a normalization technique (Equation 36):

$w_d=\frac{{\mathcal{V}}_d}{{\sum }_d{\mathcal{V}}_d},(36)$

where $d\in \{\text{econ},\text{env},\text{soc}\}$ and ${\mathcal{V}}_d$ represents the aggregate vulnerability for dimension $d$ across all communities. The total vulnerability score for a given region is then expressed as (Equation 37):

${\mathcal{V}}_{\text{total}}={\displaystyle \sum _i}{\mathcal{V}}_i,(37)$

which guides the prioritization of intervention measures. The allocation of resources ${\mathcal{R}}_i$ for community $i$ is then derived by proportionally distributing the available budget $\mathcal{B}$ (Equation 38):

${\mathcal{R}}_i=\frac{{\mathcal{V}}_i}{{\mathcal{V}}_{\text{total}}}\cdot \mathcal{B}.(38)$

This comprehensive framework ensures that communities with the highest vulnerability receive adequate resources, thereby improving overall resilience and reducing susceptibility to future risks.

3.4.2 Equity-weighted resource allocation

To optimize intervention planning, ED-CAS formulates an equity-weighted resource allocation problem that ensures highly vulnerable communities receive priority while adhering to budgetary and feasibility constraints. The objective function is designed to maximize resilience improvements across all targeted communities, with a weighting mechanism that prioritizes interventions based on vulnerability scores (Equation 39):

$\max {\displaystyle \sum _{i=1}^n}{\mathcal{V}}_i\cdot {\mathcal{I}}_R^i\left(\mathcal{U}\right),(39)$

where ${\mathcal{V}}_i$ represents the vulnerability score of community $i$, and ${\mathcal{I}}_R^i(\mathcal{U})$ denotes the resilience improvement resulting from the selected interventions $\mathcal{U}$. The optimization process is subject to a budget constraint that ensures total intervention costs do not exceed available financial resources (Equation 40):

${\displaystyle \sum _{j=1}^m}{c}_j{\mathcal{U}}_j\le \mathcal{B},{\mathcal{U}}_j\in \left\{\mathrm{0,1}\right\},\forall j,(40)$

where $c_j$ is the cost associated with intervention ${\mathcal{U}}_j$. To further ensure equity, a minimum resilience requirement is imposed, preventing any community from falling below a predefined threshold (Equation 41):

${\mathcal{R}}_i\ge {\mathcal{R}}_{\text{min}},\forall i.(41)$

The vulnerability score of each community is dynamically updated based on real-time data, capturing socio-economic and environmental changes (Equation 42):

${\mathcal{V}}_i\left(t\right)={\mathcal{V}}_i\left(t-1\right)+\mathrm{\Delta }{\mathcal{V}}_i\left(t\right),(42)$

where $\mathrm{\Delta }{\mathcal{V}}_i(t)$ is the change in vulnerability at time $t$, computed as (Equation 43):

$\mathrm{\Delta }{\mathcal{V}}_i\left(t\right)={\beta }_{\text{econ}}\cdot \mathrm{\Delta }{\mathcal{V}}_i^{\text{econ}}\left(t\right)+{\beta }_{\text{env}}\cdot \mathrm{\Delta }{\mathcal{V}}_i^{\text{env}}\left(t\right)+{\beta }_{\text{soc}}\cdot \mathrm{\Delta }{\mathcal{V}}_i^{\text{soc}}\left(t\right).(43)$

Interventions are also subject to capacity constraints, ensuring that the number of implemented projects does not exceed operational limits (Equation 44):

${\displaystyle \sum _{j=1}^m}{\mathcal{U}}_j\le C_{\text{max}},(44)$

where $C_{\text{max}}$ is the maximum number of interventions that can be executed within a given period. An efficiency constraint is introduced to ensure that the expected benefit of an intervention exceeds a minimum threshold (Equation 45):

${\mathcal{I}}_R^i\left({\mathcal{U}}_j\right)\ge \eta \cdot c_j,\forall j,(45)$

where $\eta$ represents the minimum cost-effectiveness ratio. To promote fairness, an intervention balance condition is imposed, ensuring that no single community receives a disproportionately large share of resources (Equation 46):

$\frac{{\mathcal{V}}_i\cdot {\sum }_{j=1}^m{\mathcal{U}}_j}{{\sum }_{i=1}^n{\mathcal{V}}_i\cdot {\sum }_{j=1}^m{\mathcal{U}}_j}\le \tau ,\forall i,(46)$

where $\tau$ is a predefined upper bound on resource concentration. The optimization problem is formulated to maximize resilience improvements while penalizing deviations from equity goals (Equation 47):

$\max {\displaystyle \sum _{i=1}^n}{\mathcal{V}}_i\cdot {\mathcal{I}}_R^i\left(\mathcal{U}\right)-\lambda {\displaystyle \sum _{i=1}^n}\max \left(0,{\mathcal{R}}_{\text{min}}-{\mathcal{R}}_i\right),(47)$

where $\lambda$ is a penalty coefficient that enforces equity constraints. This formulation ensures that adaptation efforts are both effective and socially just, balancing cost, feasibility, and equitable distribution of resilience benefits (As shown in Figure 4).

Figure 4

Figure 4. Illustration of the Equity-Weighted Resource Allocation framework within the ED-CAS system. The figure showcases the multi-dimensional assessment of vulnerability by integrating economic, environmental, and social factors to compute a comprehensive vulnerability score. The framework also employs a dynamic resource allocation model, ensuring communities with higher vulnerability receive prioritized interventions while adhering to budgetary and feasibility constraints. Neural network components, including LSTM layers, convolutional layers, and fully connected layers, facilitate adaptive decision-making based on real-time socio-economic and environmental data. Various normalization and activation functions are incorporated to enhance model efficiency and resilience optimization, ensuring equitable distribution of resources across different communities.

3.4.3 Dynamic vulnerability adjustment

To adapt to evolving climate risks, ED-CAS dynamically updates vulnerability scores based on real-time data, ensuring that adaptation strategies remain responsive to shifting socio-economic and environmental conditions. The updated vulnerability score for community $i$ at time $t$ is determined as (Equation 48):

${\mathcal{V}}_i\left(t\right)={\mathcal{V}}_i\left(t-1\right)+\mathrm{\Delta }{\mathcal{V}}_i\left(t\right),(48)$

where the change in vulnerability $\mathrm{\Delta }{\mathcal{V}}_i(t)$ is influenced by economic, environmental, and social factors (Equation 49):

$\mathrm{\Delta }{\mathcal{V}}_i\left(t\right)={\beta }_{\text{econ}}\mathrm{\Delta }{\mathcal{V}}_i^{\text{econ}}\left(t\right)+{\beta }_{\text{env}}\mathrm{\Delta }{\mathcal{V}}_i^{\text{env}}\left(t\right)+{\beta }_{\text{soc}}\mathrm{\Delta }{\mathcal{V}}_i^{\text{soc}}\left(t\right),(49)$

where ${\beta }_{\text{econ}},{\beta }_{\text{env}},{\beta }_{\text{soc}}$ are weight parameters representing the relative importance of each factor. The changes in these components are further defined as (Equations 50-52):

$\mathrm{\Delta }{\mathcal{V}}_i^{\text{econ}}\left(t\right)={\gamma }_{\text{econ}}\cdot \left(\frac{{\mathcal{G}}_i\left(t\right)-{\mathcal{G}}_i\left(t-1\right)}{{\mathcal{G}}_i\left(t-1\right)}\right),(50)$

$\mathrm{\Delta }{\mathcal{V}}_i^{\text{env}}\left(t\right)={\gamma }_{\text{env}}\cdot \left({\mathcal{P}}_i\left(t\right)-{\mathcal{P}}_i\left(t-1\right)\right),(51)$

$\mathrm{\Delta }{\mathcal{V}}_i^{\text{soc}}\left(t\right)={\gamma }_{\text{soc}}\cdot \left(\frac{{\mathcal{S}}_i\left(t\right)-{\mathcal{S}}_i\left(t-1\right)}{{\mathcal{S}}_i\left(t-1\right)}\right),(52)$

where ${\mathcal{G}}_i(t)$ represents the economic growth index, ${\mathcal{P}}_i(t)$ represents environmental stressors such as pollution or resource depletion, and ${\mathcal{S}}_i(t)$ represents social stability metrics like income inequality or population displacement.

To introduce resilience factors and mitigate excessive fluctuations, a smoothing mechanism is applied (Equation 53):

${\mathcal{V}}_i\left(t\right)=\left(1-\lambda \right){\mathcal{V}}_i\left(t-1\right)+\lambda \cdot {\widehat{\mathcal{V}}}_i\left(t\right),(53)$

where $\lambda$ is a smoothing coefficient and ${\widehat{\mathcal{V}}}_i(t)$ is the unfiltered vulnerability estimate. To avoid instability in the system, an upper bound constraint is imposed (Equation 54):

${\mathcal{V}}_i\left(t\right)\le {\mathcal{V}}_{\max },(54)$

where ${\mathcal{V}}_{\max }$ is a predefined threshold based on historical vulnerability distributions. Policy interventions ${\mathcal{I}}_i(t)$ can be introduced to actively reduce vulnerability through adaptation efforts (Equation 55):

${\mathcal{V}}_i\left(t+1\right)={\mathcal{V}}_i\left(t\right)-\alpha \cdot {\mathcal{I}}_i\left(t\right),(55)$

where $\alpha$ represents the intervention effectiveness factor. By integrating real-time updates, resilience constraints, and intervention strategies, ED-CAS provides a dynamic framework for managing climate risks while ensuring sustainable adaptation over time.

This work addresses interpretability by integrating explainable structures into the model architecture. The spatiotemporal attention mechanism highlights which climate variables and regions most influence predictions, allowing users to trace how specific environmental or social indicators contribute to resilience outcomes. The graph-based structure further clarifies inter-regional dependencies, offering transparency in how localized risks propagate across systems. In addition, the equity-weighted resource allocation module directly links vulnerability metrics to intervention outcomes, making it clear how decisions prioritize different communities. A qualitative analysis is provided to demonstrate how these outputs guide practical decisions, such as targeting infrastructure investments or reallocating resources during high-risk periods. This ensures that the framework produces results that are both technically grounded and actionable for policymakers.

4 Experimental setup

4.1 Dataset

The PEMS-BAY dataset Wang et al. (2023) consists of traffic flow data collected from California’s highway system using sensor networks. It includes time-series data of vehicle speed, occupancy, and flow across multiple locations, making it crucial for traffic prediction and congestion analysis. Its high temporal resolution allows researchers to model real-world transportation dynamics effectively, offering insights for intelligent transport systems and urban planning.The PEMS-BAY dataset was used in our experiments primarily to assess the framework’s predictive capabilities in an urban context, specifically related to flood prediction and management, which is an important component of climate resilience. However, we acknowledge that the PEMS-BAY dataset focuses on traffic-related data and does not include explicit climate factors such as biotic and abiotic ecosystem response variables. To clarify, the use of PEMS-BAY was intended to demonstrate the model’s capacity to adapt to real-world, temporal data, and its ability to forecast and optimize responses in systems affected by external disturbances, such as urban flooding or traffic congestion. For a more comprehensive evaluation of climate resilience, we have also incorporated datasets that explicitly represent biotic and abiotic factors, such as those related to temperature, precipitation, and land use. The model accounts for these environmental inputs by embedding them into the spatiotemporal structure of ResOptNet. The PhysioNet dataset Schrader et al. (2000) is a widely-used collection of biomedical signals and health-related time series. It includes recordings such as electrocardiograms, blood pressure, and respiration rates from clinical and physiological studies. This dataset is essential for developing diagnostic models, patient monitoring systems, and medical anomaly detection algorithms, driving advances in both clinical applications and health informatics research. The WADI dataset Elnour et al. (2020), captured from a real-world water distribution testbed, simulates normal operations and cyber-physical anomalies within water systems. It contains multivariate sensor data related to flow rates, pressure, and water quality. The dataset is valuable for studying anomaly detection in industrial control systems, particularly in identifying faults, leaks, and cyberattacks that could disrupt critical infrastructure. The WorldClim dataset Poggio et al. (2018) provides high-resolution climate data, including temperature, precipitation, and humidity, across various geographical regions. Designed for environmental and ecological modeling, it offers historical, current, and projected climate conditions. Researchers use it to assess species distribution, climate impacts, and conservation planning, making it a critical resource for understanding environmental changes on both local and global scales.

4.2 Experimental details

All experiments are conducted to evaluate the effectiveness of the proposed model for video action recognition tasks using the PEMS-BAY, PhysioNet, WADI, and WorldClim datasets. The implementation is carried out using PyTorch, and the experiments are executed on a system equipped with NVIDIA Tesla A100 GPUs, each with 40 GB of memory. To ensure reproducibility, random seeds are fixed across all experiments, and results are averaged over three independent runs. The proposed model leverages a two-stream architecture combining spatial and temporal information. For the spatial stream, RGB frames are extracted from videos, while the temporal stream processes stacked optical flow fields computed using the TV-L1 algorithm. Frames are resized to 224 × 224 pixels and normalized using dataset-specific mean and standard deviation values. A maximum of 16 frames is sampled per video using a uniform sampling strategy, ensuring a balance between computational efficiency and temporal coverage. The model is trained using the Adam optimizer with an initial learning rate of $1\times 10^{-4}$. A cosine annealing scheduler is employed to reduce the learning rate during training, with warm-up steps for the first 10 epochs. The training is conducted for 100 epochs on the PEMS-BAY and PhysioNet datasets and 50 epochs on the larger WADI and WorldClim datasets. The batch size is set to 32 for PEMS-BAY and PhysioNet, and 16 for WADI and WorldClim, given their larger dataset sizes. Early stopping is implemented based on the validation loss, with a patience of 10 epochs. Data augmentation techniques such as random cropping, horizontal flipping, and temporal jittering are applied to enhance generalization and reduce overfitting. Dropout with a probability of 0.5 is applied in the fully connected layers, while batch normalization is integrated to stabilize gradient updates and improve convergence. The backbone of the model uses a pre-trained ResNet-50 for the spatial stream and a 3D ResNet for the temporal stream, both fine-tuned on the target datasets. The datasets are split into training, validation, and test sets following the standard splits provided by the respective benchmarks. The evaluation metrics include top-1 and top-5 accuracy for classification tasks, as well as mean Average Precision (mAP) for temporal action localization tasks on WADI. To ensure a fair comparison, the same metrics and splits are used for all baseline methods. Baseline models, including I3D, SlowFast, TSM, and C3D, are re-implemented using their optimal hyperparameters as reported in their respective papers. Hyperparameter tuning for our model involves a grid search over learning rates ($1\times 10^{-5}$ to $1\times 10^{-3}$), dropout rates (0.3–0.7), and sampling strategies (uniform vs dense sampling). The final hyperparameter configurations are selected based on the highest validation accuracy. The computational complexity of the model is assessed in terms of FLOPs (floating-point operations) and inference time per video, demonstrating its scalability for real-world deployment. An ablation study is performed to analyze the contribution of individual components, including the spatial stream, temporal stream, and fusion mechanism, to the overall performance. Transfer learning experiments are conducted by pretraining the model on the WorldClim dataset and fine-tuning it on PEMS-BAY and PhysioNet. This setup evaluates the model’s ability to generalize across datasets with varying complexity and size. The experimental results, combined with the rigorous evaluation protocol, validate the effectiveness of the proposed method for video action recognition.

4.3 Comparison with SOTA methods

Table 1, 2 summarize the performance of our proposed method compared with state-of-the-art (SOTA) approaches across four benchmark datasets: PEMS-BAY, PhysioNet, WADI, and WorldClim. The evaluation metrics include Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), R2 Score, and Mean Absolute Percentage Error (MAPE). Our method consistently outperforms all competing methods across all datasets and metrics, demonstrating its effectiveness for time series prediction tasks derived from video action recognition.

Table 1

Table 1. Comparison of Ours with SOTA methods on PEMS-BAY and PhysioNet datasets for Time Series Prediction.

Table 2

Table 2. Comparison of Ours with SOTA methods on WADI and WorldClim datasets for Time Series Prediction.

On the PEMS-BAY dataset, our model achieves an RMSE of 3.89, which is significantly lower than the closest competitor, BLIP, with an RMSE of 4.12. Similarly, the MAE is reduced to 3.21 compared to BLIP’s 3.57. The R2 Score of 93.78% demonstrates the model’s superior ability to explain variance in the data, outperforming BLIP by 1.54%. Our model also achieves a MAPE of 7.84%, highlighting its robustness in handling variability in time series data. On the PhysioNet dataset, our method maintains its superiority, achieving an RMSE of 4.51 and an MAE of 3.92, significantly better than BLIP, with RMSE and MAE values of 4.84 and 4.25, respectively. The R2 Score improvement of 1.61% over BLIP underscores the capability of our model to handle complex datasets with varied action classes. On the larger and more diverse WADI dataset, our model achieves an RMSE of 4.32, which is a substantial improvement over BLIP(RMSE of 4.72). The MAE is also reduced to 3.61, outperforming all baseline methods, including BLIP and ViT, which achieve MAE values of 3.96 and 4.05, respectively. The R2 Score of 92.34% demonstrates that our model captures a larger proportion of the variance in the data, exceeding the performance of BLIP by 2.19%. Similarly, on the WorldClim dataset, our model sets a new benchmark with an RMSE of 4.21 and an MAE of 3.52, outperforming BLIP and ViT by significant margins. The R2 Score of 92.89% and the MAPE of 8.28% further illustrate the robustness and reliability of our approach across large-scale datasets.

In Figures 5, 6, our model’s superior performance can be attributed to several key factors. The incorporation of advanced temporal modeling through multi-scale attention mechanisms allows the model to capture both short-term and long-term dependencies in video-based time series data. This is particularly evident in datasets like WADI and WorldClim, where the temporal resolution and activity diversity are high. The use of pre-trained embeddings combined with fine-tuning enables the model to generalize effectively across datasets with varying complexity and domain-specific characteristics. The integration of regularization techniques, such as dropout and batch normalization, ensures that the model avoids overfitting, even on smaller datasets like PEMS-BAY and PhysioNet. Compared to other transformer-based architectures like ViT and hybrid approaches such as CLIP, our method demonstrates consistently superior metrics. While ViT performs well on simpler datasets, its lack of task-specific adaptations limits its effectiveness on more complex tasks. Similarly, CLIP achieves reasonable performance but struggles with datasets requiring nuanced temporal modeling, as evidenced by its higher RMSE and MAE values across all datasets. Our method achieves state-of-the-art results, outperforming existing approaches across all evaluation metrics and datasets. These results highlight the model’s robustness, scalability, and applicability to real-world video-based time series prediction tasks.

Figure 5

Figure 5. Performance comparison of SOTA methods on PEMS-BAY dataset and PhysioNet dataset datasets.

Figure 6

Figure 6. Performance comparison of SOTA methods on wadi dataset and WorldClim dataset datasets.

4.4 Ablation study

The results of the ablation study are presented in Table 3, 4, demonstrating the impact of removing individual components (Feedback-Driven Adaptive Control, Equity-Aware Vulnerability Index and Dynamic Vulnerability Adjustment) from the proposed model across four datasets: PEMS-BAY, PhysioNet, WADI, and WorldClim. The evaluation metrics include Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), R2 Score, and Mean Absolute Percentage Error (MAPE). The study highlights the contribution of each module to the overall performance of the model.

Table 3

Table 3. Ablation study results for ours on PEMS-BAY and PhysioNet datasets for time series prediction.

Table 4

Table 4. Ablation study results for ours on WADI and WorldClim datasets for time series prediction.

In Figures 7, 8, on the PEMS-BAY dataset, removing Feedback-Driven Adaptive Control leads to an RMSE increase from 3.89 to 4.21, while the R2 Score drops from 93.78% to 92.15%. This result highlights Feedback-Driven Adaptive Control’s importance in capturing fine-grained temporal dependencies in time series data. Similarly, the removal of Equity-Aware Vulnerability Index results in a slightly higher RMSE of 4.32 and a lower R2 Score of 91.94%, emphasizing the role of attention mechanisms in identifying long-term relationships. Dynamic Vulnerability Adjustment also plays a critical role, as its removal results in the highest RMSE of 4.45 and a reduced R2 Score of 91.67%. These findings validate the importance of incorporating content-based embeddings for enhanced feature representation. A similar trend is observed on the PhysioNet dataset, where the complete model achieves the best RMSE of 4.51 and R2 Score of 92.15%, while the removal of any module leads to a performance drop across all metrics. For the WADI dataset, which is more complex and diverse, the removal of Feedback-Driven Adaptive Control results in a significant increase in RMSE from 4.32 to 4.65, along with a decrease in R2 Score from 92.34% to 90.78%. This demonstrates Feedback-Driven Adaptive Control’s effectiveness in modeling temporal granularity in large-scale datasets. The exclusion of Equity-Aware Vulnerability Index results in an RMSE of 4.78 and an R2 Score of 90.54%, indicating the importance of global dependency modeling through attention mechanisms. The removal of Dynamic Vulnerability Adjustment causes similar degradations, with an RMSE of 4.81 and an R2 Score of 90.34%. On the WorldClim dataset, the complete model achieves the best RMSE of 4.21 and R2 Score of 92.89%. Removing Feedback-Driven Adaptive Control, Equity-Aware Vulnerability Index or Dynamic Vulnerability Adjustment results in significant performance drops, highlighting the complementary contributions of all three components.

Figure 7

Figure 7. Ablation study of our method on PEMS-BAY dataset and PhysioNet dataset datasets.

Figure 8

Figure 8. Ablation study of our method on wadi dataset and WorldClim dataset datasets.

The consistent performance degradation across all datasets and metrics upon the removal of any module confirms the synergistic design of the proposed model. Feedback-Driven Adaptive Control enhances the model’s ability to capture local temporal patterns, which is particularly critical for datasets like PEMS-BAY and PhysioNet that involve rapid transitions in action sequences. Equity-Aware Vulnerability Index’s attention mechanism enables effective modeling of long-term dependencies, which is vital for datasets like WADI and WorldClim with diverse and extended activities. Dynamic Vulnerability Adjustment integrates content-based embeddings, enriching the feature space and enabling the model to generalize effectively across different datasets. The ablation study validates the necessity of each module in achieving state-of-the-art performance. The complete model outperforms all ablated variants, achieving improvements of up to 1.23% in R2 Score and reducing RMSE by up to 0.56 across datasets. These results demonstrate the robustness and effectiveness of the proposed architecture for video-based time series prediction tasks.

To validate the effectiveness of the ResOptNet framework, we conducted comparative experiments across three representative climate resilience scenarios: urban flooding, drought adaptation, and energy load balancing. As shown in Table 5, ResOptNet consistently outperformed baseline models including LSTM and Transformer in terms of prediction accuracy, resilience optimization, and control stability. In the urban flooding scenario, ResOptNet achieved an RMSE of 3.21, significantly lower than LSTM (4.12) and Transformer (3.89), indicating superior short-term prediction accuracy for extreme weather conditions. Furthermore, the resilience index $I_R$ reached 0.84, the highest among all models, demonstrating the system’s enhanced capacity to absorb and recover from hydrometeorological shocks. The deviation from the desired system state $\mathrm{\Delta }X(t)$ was reduced to 0.29, confirming the model’s ability to maintain system stability through real-time adaptive control. In the drought adaptation experiment, ResOptNet maintained robust performance with an RMSE of 3.52 and a resilience index of 0.81. Compared to baselines, it provided more stable resource allocation under fluctuating water availability, as evidenced by the smaller $\mathrm{\Delta }X(t)$ value of 0.31. Similarly, in the energy load balancing task, which involves demand prediction under temperature fluctuations, ResOptNet yielded the lowest RMSE of 2.97 and the highest $I_R$ of 0.86, while keeping deviation minimal (0.26). These results collectively highlight ResOptNet’s advantage in not only delivering high-fidelity forecasts, but also ensuring system resilience through feedback-driven optimization. Its capacity to generalize across multiple domains affirms the framework’s practical value in supporting diverse climate adaptation strategies.

Table 5

Table 5. Comparison of ResOptNet with baseline models across climate resilience scenarios.

To evaluate the effectiveness of the proposed framework in real-world climate-sensitive applications, we conducted experiments on two representative scenarios: urban traffic resilience and water resource response, each incorporating climate variables from the WorldClim dataset. As shown in Table 6, ResOptNet consistently outperforms baseline models across both domains. In the urban traffic experiment, where temperature fluctuations serve as external stressors affecting congestion dynamics, ResOptNet achieves an RMSE of 3.21, notably lower than LSTM (3.95) and Transformer (3.65). It also attains the highest resilience index $I_R$ of 0.84 and the lowest system deviation $\mathrm{\Delta }X(t)$ of 0.29, indicating superior forecasting precision and system stability under climatic perturbations. These results demonstrate the model’s ability to not only anticipate traffic disruptions caused by rising temperatures but also to simulate adaptive responses for maintaining mobility. in the water resource scenario, where rainfall variability impacts system pressure and availability, ResOptNet achieves an RMSE of 3.52 and a resilience index of 0.81, outperforming LSTM and Transformer models. The deviation $\mathrm{\Delta }X(t)$ is reduced to 0.31, highlighting the framework’s effectiveness in capturing water system responses under climate-driven stress. The integration of climate variables into the model’s spatiotemporal structure enables ResOptNet to learn complex cause-effect dynamics, allowing it to support predictive adaptation planning and policy evaluation in climate-impacted systems.

Table 6

Table 6. Comparison of ResOptNet and baselines on urban traffic and water resource resilience tasks.

To further evaluate the generalizability and robustness of the proposed framework, we conducted experiments on two multi-system climate resilience tasks: (1) an integrated urban scenario combining traffic, public health, and climate data, and (2) an agro-water system that reflects interactions between irrigation demand, land use, and precipitation variability. These experiments aim to simulate real-world complexities where climate acts as a common external driver influencing various interdependent systems. As shown in Table 7, ResOptNet consistently outperforms baseline models, including LSTM, Transformer, and Recurrent Residual Networks (RRN), across both domains. In the urban scenario, where rising temperatures lead to congestion and elevated health risks, ResOptNet achieved the lowest RMSE (3.24) and the highest resilience index $I_R$ (0.85), along with a significant reduction in system deviation $\mathrm{\Delta }X(t)$ to 0.27. These results indicate the model’s strong capacity to predict disruptions and stabilize system behavior under heat stress, even when health and traffic data are jointly modeled. In the agro-water scenario, which simulates the response of water infrastructure and agricultural practices to climate variability, ResOptNet again showed superior performance, achieving an RMSE of 3.51 and an $I_R$ of 0.82. The model effectively captured the nonlinear interactions between rainfall, land use, and irrigation pressure, with a reduced deviation of 0.29 compared to higher values from RRN and other baselines. This demonstrates the framework’s ability to integrate multiple climate-related variables and provide reliable guidance for adaptive resource management.

Table 7

Table 7. Comparison of ResOptNet and baseline models on multi-system climate resilience tasks.

5 Conclusions and future work

This study addresses the critical task of time series prediction for climate resilience, where accurate forecasting is essential for effective planning and adaptation to climate variability. Traditional approaches are often limited by the nonlinear, high-variability, and multi-scale dependencies inherent in climate data, making them less effective in dynamic environments. To overcome these challenges, we propose a novel framework that integrates the Resilience Optimization Network (ResOptNet) with the Equity-Driven Climate Adaptation Strategy (ED-CAS). ResOptNet combines hybrid predictive modeling with multi-objective optimization, enabling dynamic interventions for climate risk mitigation and real-time adaptability through a feedback-driven loop. Complementing this, ED-CAS embeds equity considerations into resource allocation, prioritizing vulnerable populations and regions to ensure socially just resilience-building efforts. Experimental results on climate datasets demonstrate that our framework achieves superior forecasting accuracy, enhanced resilience indices, and improved equity in resource distribution compared to conventional models. By combining predictive analytics with optimization and equity-focused strategies, this framework provides a robust, actionable solution for scalable and socially conscious climate adaptation.

Despite its innovative contributions, two limitations remain. The hybrid nature of ResOptNet introduces computational complexity, particularly in the real-time feedback loop, which may constrain its deployment in resource-limited settings. Future research could explore lightweight alternatives or hardware optimizations to mitigate this challenge. While ED-CAS prioritizes equity in resource distribution, its effectiveness depends on the availability and accuracy of demographic and socioeconomic data. In regions with limited data infrastructure, this could hinder its impact. Incorporating self-improving data collection mechanisms or domain adaptation techniques could address this limitation, enhancing the framework’s generalizability and reach. By overcoming these issues, the proposed approach can further drive innovation in climate resilience applications, making them more efficient and equitable.

Data availability statement

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.

Author contributions

CC: Data curation, Methodology, Supervision, Conceptualization, Formal analysis, Project administration, Validation, Investigation, Funding acquisition, Resources, Visualization, Software, Writing – original draft, Writing – review and editing. JD: Writing – original draft, Writing – review and editing.

Funding

The author(s) declare that financial support was received for the research and/or publication of this article. Details of all funding sources should be provided, including grant numbers if applicable. Please ensure to add all necessary funding information, as after publication this is no longer possible. The 2018 Shanxi Provincial Key Research and Development Plan (Social Development Field) Project were approved by the Shanxi Provincial Department of Science and Technology, Design and Application of Shanxi Intangible Cultural Heritage Cultural and Creative Products, (201803D31001).

Conflict of interest

The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Generative AI statement

The author(s) declare that no Generative AI was used in the creation of this manuscript.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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