Deep Probabilistic Surrogate Modelling for Uncertainty Quantification in Mangrove Hydro-morphodynamics

Majdi Fanous¹Hannah Al Ali²Amin Hosseinian-Far³Omid Chatrabgoun⁴Tabassom Sedighi⁵Alireza Daneshkhah^6*

• ¹Centre for Computational Science and Mathematical Modeling, Coventry University, Coventry, United Kingdom
• ²Emirates Aviation University, Dubai, United Arab Emirates
• ³Department of Business Analytics and Systems, University of Hertfordshire, Hatfield, United Kingdom
• ⁴School of Computing, Mathematics and Data Science, Coventry University,, Coventry, United Kingdom
• ⁵International Policing and Public Protection Research Institute, Anglia Ruskin University, Cambridge, United Kingdom
• ⁶Faculty of Mathematics and Data Science, Emirates Aviation University, Dubai, United Arab Emirates

Mangrove ecosystems are increasingly recognised as essential nature-based solutions (NbS) for enhancing coastal resilience against {sea level rise and climate-induced extreme events}. However, achieving robust uncertainty quantification (UQ) for hydro-morphodynamic models of mangrove systems remains a critical and unresolved challenge. The inherent complexity of physical processes, coupled with the computational demands of solving Navier–Stokes partial differential equations (PDEs), complicates conventional UQ approaches. Traditional surrogate models, such as Gaussian Processes (GPs), often {fall short in capturing} the non-Gaussian behaviour and high-dimensional interactions {characteristic of coastal dynamics}, while physics-informed neural networks (PINNs), though promising, {face scalability issues that limit their application in large-scale uncertainty quantification (UQ)}. \textcolor{red}{To overcome these limitations, we introduce an efficient and scalable probabilistic framework based on Deep Gaussian Processes (Deep GPs), which hierarchically stack multiple GP layers to capture complex, multi-scale, and non-Gaussian dependencies that conventional surrogate models fail to represent.} The proposed Deep GP model significantly reduces computational cost by over three orders of magnitude, (\textcolor{red}{$\approx 5 \times 10^3$ times faster; $\approx$ 1.4~min vs $>$~5~days for the full numerical solver}) while maintaining high predictive accuracy (\textcolor{red}{fivefold improvement; RMSE = 0.0095 m vs 0.0465 m for standard GP}), enabling reliable propagation of uncertainty across complex, nonlinear system dynamics. Through application to a high-resolution mangrove model, we demonstrate the framework’s potential to support evidence-based planning for climate adaptation and ecosystem-based coastal resilience. This work offers a novel pathway to integrate advanced UQ into operational decision-making for sustainable coastal management.