On the Application of Theory-Trained Neural Networks to Solid and Structural Mechanics

In the expensive operations and challenging implementation of mesh-based and meshless-based solutions in complicated computing domains, it is impossible to address high-dimensional solid and structural mechanics issues (complicated geometric structures, multi-physics boundary conditions, and multi-scale features) governed by parameterized partial differential equations (PDEs). Physics-informed Neural Networks (PINNs), also referred to as Theory-Trained Neural Networks (TTNs) in the machine learning (ML) domain, have recently become a potent paradigm that synergistically combines the advantages of deep neural networks and multi-physics-based modelling to solve PDEs. Raissi et al. first presented the PINNs in 2019, and they have since been acknowledged as successful surrogate solvers for PDEs (while adhering to governing equations and boundary/initial conditions to regularize the solution) in solid and structural mechanics. To alleviate the scarcity of training data, improve the model's broadness, and guarantee the physical validity of the findings, PINNs/TTNs have become a viable strategy. This technique allows for the modelling of complicated physical systems by utilizing neural networks as versatile function approximators (incorporating physical laws into the neural network's loss function). TTNs employ conditional data, such as structural pictures or load circumstances, to produce realistic synthetic output (such as displacement, stress distributions, dynamic behaviour, damage/failure of materials, and material microstructures). The previous physics knowledge can serve as a regularization agent. These TTNs are trained to generate these particular results by learning from labelled datasets gathered from experiments or high-fidelity simulations (such as the Finite Element Method). When experimental or simulation data are scarce, this approach is especially helpful since it may produce reliable outcomes even with comparatively limited training data or even with unlabeled data, which results in more accurate and quicker predictive models for material design, structural analysis, and performance optimization. Furthermore, TTNs demonstrate unique advantages in addressing inverse problems like parameter identification and equation finding, which are frequently ill-posed or challenging to solve using standard approaches. As a result, TTNs have become a valuable tool for researchers working in solid and structural mechanics fields, including heat transfer and coupled fluid-structure interaction predictions, structural acoustics, periodic waveguide structures for wave manipulation, optimization of metamaterial design and prediction of their response characteristics (mechanical, acoustic, and dynamic), continuum mechanics, constitutive modelling of materials, and other related fields. This research topic aims to contribute to the recent advances in computational solid and structural mechanics using TTNs in order to keep up with the most recent advancements.

This topic is intriguing for new potential applications of physics-informed or theory-trained neural networks (PINN/TTNs) for the design and optimization of components in the fields of solid and structural mechanics. These PINN/TTNs can be applied to the associated physical system (static and dynamic) in solid and structural mechanics including heat transmission, fluid flow, acoustics, dynamics, and the electromagnetic. Identification, evaluation, and prediction of mechanical properties of materials, deformation, stress distribution, damage, failure of materials or structures under load, and vibration are all highly dependent on the constitutive, kinetic, and the computational domain's geometric relationships. Periodic waveguide structures (waveguide's repeating unit cells) are used in solid and structural mechanics for wave manipulation (vibration reduction, improved material qualities, acoustic and elastic metamaterials for vibration and noise suppression, phononic crystals for filtering and directing energy flow, unique properties such as band gaps to prevent vibration propagation and control over dynamic responses, frequency ranges in which waves are significantly attenuated by the recursive structure of the unit cells). The potential PINN/TTNs applications for infrastructures, mechanical, geothermal, oil & gas, and aerospace engineering structures enhance the prediction and monitoring of additive manufactured parts, 3D/4D print processes control, design, analysis, and product development of composite structures and materials, and many more. This research topic highlights the state-of-the-art on the growing interest in these fields in academia and industry, as well as the emerging prospects and challenges in future research.

We welcome manuscripts, reviews, and mini-reviews on exploring promising, recent, and novel research trends on topics of interest “On the Application of Physics-Informed Neural Networks to Solid and Structural Mechanics,” including, but not limited to, the following:

1. 1D, 2D, and 3D structural problems such as truss, beam, plate, and shell structures.

2. Constitutive modelling, contact mechanics, and computer-aided structural mechanics.

3. Deformation analysis and structural integrity evaluation.
4. Prediction of fatigue life of material under multi-axial loads.
5. Mechanical properties identification. Capture bidirectional mappings between geometric parameters and mechanical properties.
6. Crack path prediction within materials.
7. Topology optimization.
8. Inverse problems in solid and structural mechanics.
9. Vibration behaviour and analysis of structures; identification of vibration sources, etc.
10. Analysis and design of periodic structures, micro-structured waveguides, acoustic metamaterials/phononic crystals.
11. Design of multilayer electromagnetic absorbers.
12. Heat transfer situations, including thermo-structural analysis, coupled thermal-fluid problems.
13. Potential development of real-time structural response monitoring systems that are useful to various engineering fields.
14. Super-resolution approximation between lower-order and higher-order finite element models; super-resolution capability with the weak form and the strong form of governing equations in static and dynamic systems.
15. Predicting factors like temperature fields, molten pool behaviour, and estimation of residual stress/fatigue life in additive manufacturing and welding processes.