The Old and the New: Can Physics-Informed Deep-Learning Replace Traditional Linear Solvers?

Understand

Physics-Informed Neural Networks (PINN) are neural networks encoding the problem governing equations, such as Partial Differential Equations (PDE), as a part of the neural network.

• PINNs have emerged as a new essential tool to solve various challenging problems, including computing linear systems arising from PDEs, a task for which several traditional methods exist.
• In this work, we focus first on evaluating the potential of PINNs as linear solvers in the case of the Poisson equation, an omnipresent equation in scientific computing.
• We characterize PINN linear solvers in terms of accuracy and performance under different network configurations (depth, activation functions, input data set distribution).