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arXiv · 2306.17648

Enhancing training of physics-informed neural networks using domain-decomposition based preconditioning strategies

Alena Kopaničáková·Hardik Kothari·George Em Karniadakis·Rolf Krause
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Abstract

We propose to enhance the training of physics-informed neural networks (PINNs). To this aim, we introduce nonlinear additive and multiplicative preconditioning strategies for the widely used L-BFGS optimizer. The nonlinear preconditioners are constructed by utilizing the Schwarz domain-decomposition framework, where the parameters of the network are decomposed in a layer-wise manner. Through a series of numerical experiments, we demonstrate that both, additive and multiplicative preconditioners significantly improve the convergence of the standard L-BFGS optimizer, while providing more accurate solutions of the underlying partial differential equations. Moreover, the additive preconditioner is inherently parallel, thus giving rise to a novel approach to model parallelism.

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Alena Kopaničáková, Hardik Kothari, George Em Karniadakis, Rolf Krause. 2023-06-30. Enhancing training of physics-informed neural networks using domain-decomposition based preconditioning strategies. https://doi.org/10.1137/23m1583375

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