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Stiff-PDEs and Physics-Informed Neural Networks

Prakhar Sharma Orcid Logo, Llion Evans Orcid Logo, Michelle Tindall, Perumal Nithiarasu Orcid Logo

Archives of Computational Methods in Engineering

Swansea University Authors: Prakhar Sharma Orcid Logo, Llion Evans Orcid Logo, Perumal Nithiarasu Orcid Logo

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Abstract

In recent years, Physics-Informed Neural Networks (PINN) have been used to solve stiff-PDEs mostly in the 1D and 2D spatial domain. PINNs still experience issues solving 3D problems, especially, problemswith conflicting boundary conditions at adjacent edges and corners. These problems have discontin...

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Published in: Archives of Computational Methods in Engineering
ISSN: 1134-3060 1886-1784
Published: Springer Science and Business Media LLC 2023
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa62396
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Abstract: In recent years, Physics-Informed Neural Networks (PINN) have been used to solve stiff-PDEs mostly in the 1D and 2D spatial domain. PINNs still experience issues solving 3D problems, especially, problemswith conflicting boundary conditions at adjacent edges and corners. These problems have discontinuous solutions at edges and corners that are difficult to learn for neural networks with a continuous activation function. In this review paper, we have investigated various PINN frameworks that are designed to solve stiff-PDEs. We took two heat conduction problems (2D and 3D) with a discontinuous solution at corners as test cases. We investigated these problems with a numberof PINN frameworks, discussed and analysed the results against the FEM solution. It appears that PINNs provide a more general platform for parameterisation compared to conventional solvers. Thus, we have investigated the 2D heat conduction problem with parametric conductivity and geometry separately. We also discuss the challenges associated with PINNs and identify areas for further investigation.
Keywords: Physics-informed neural networks, stiff-PDEs, Parametric PDEs, thermal problems
College: Faculty of Science and Engineering
Funders: This work is funded by the United Kingdom Atomic Energy Authority (UKAEA) and the Engineering and Physical Sciences Research Council (EPSRC) under the Grant Agreement Numbers EP/T517987/1 and EP/R012091/1. We acknowledge the support of Supercomputing Wales and AccelerateAI projects, which is part-funded by the European Regional Development Fund (ERDF) via the Welsh Government for giving us access to NVIDIA A100 40 GB GPUs for batch training. We also acknowledge the support of NVIDIA for donating us a NVIDIA RTX A5000 24 GB for local testing.