A mixed formulation for physics-informed neural networks as a potential solver for engineering problems in heterogeneous domains: Comparison with finite element method

Transfer-learning Enhanced Physics Informed- Neural-Networks for Burgers’ Equation with High Reynolds’ Number

“…In this case, tackling various kinds of boundary conditions and parameters can be done through this technique. Despite many of the works highlighting the importance of transfer learning in this context [11], this area has been relatively underexplored in literature. We attempt to investigate the effects of transfer learning on the convergence of models with differing parameters and ICs/BCs, taking into consideration a well-known benchmark of the PINNs: Burger's equation.…”

The Application of Physics-Informed Machine Learning in Multiphysics Modeling in Chemical Engineering

“…A recent development that exemplifies this learning paradigm is the emergence of physics-informed machine learning (PIML). , This approach seamlessly integrates data and abstract mathematical operators, allowing for the incorporation of PDEs with or without missing physics. The integration of prior knowledge and physics-based constraints into the model architecture (that is, physics-informed neural network, PINN) can improve the generalization performance, interpretability, and scalability of the ML model, reducing the reliance on labeled data. , Due to these advantages, PIML created new possibilities for tackling complex scientific and engineering challenges, making them a focal point of research in the emerging interdisciplinary field of scientific ML (SciML). , Recent literature statistics have indicated it has been successfully applied to over 10 different discipline branches, including but not limited to fluid mechanics, − heat transfer, − chemical reactions, , biomedicine, , materials science, − solid mechanics, , and fracture mechanics. , …”

Physics-aware deep learning framework for linear elasticity

“…In this regard, (Haghighat et al, 2020(Haghighat et al, , 2021b have been the breakthrough works geared towards developing a DL-based solver for inversion and surrogate modeling in solid mechanics for the first time utilizing PINNs theory. Additionally, PINNs have been successfully applied to the solution and discovery in linear elastic solid mechanics (Zhang et al, 2020;Samaniego et al, 2020;Haghighat et al, 2021a;Guo and Haghighat, 2020;Vahab et al, 2021;Rezaei et al, 2022;Zhang et al, 2022), elastic-viscoplastic solids (Frankel et al, 2020;Goswami et al, 2022;Arora et al, 2022;Roy and Guha, 2022), brittle fracture (Goswami et al, 2020) and computational elastodynamics (Rao et al, 2021) etc. The solution of PDEs corresponding to elasticity problems can be obtained by minimizing the network's loss function that comprises the residual error of governing PDEs and the initial/boundary conditions.…”