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

• URL: http://arxiv.org/abs/2306.17648v2
• Date: Thu, 28 Dec 2023 02:34:37 GMT
• Title: Enhancing training of physics-informed neural networks using domain-decomposition based preconditioning strategies
• Authors: Alena Kopani\v{c}\'akov\'a and Hardik Kothari and George Em Karniadakis and Rolf Krause
• Abstract summary: We introduce additive and multiplicative preconditioning strategies for the widely used L-BFGS. We demonstrate that both additive and multiplicative preconditioners significantly improve the convergence of the standard L-BFGS.
• Score: 1.8434042562191815
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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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