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Physics-Informed Neural Networks

techniqueactiveprovisionalphysics-informed-neural-networks-24780f8a·1 events·first seen 4d ago

Aliases: Physics-Informed Neural Networks

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5arXiv · cs.LG·4d ago·source ↗

Global convergence proof for DGM and PINN algorithms on semi-linear PDEs

A new arXiv preprint establishes global convergence guarantees for the Deep Galerkin Method (DGM) and Physics-Informed Neural Networks (PINNs) when trained via gradient descent to minimize PDE residuals. The result applies to a class of semi-linear PDEs (nonlinear in the solution and its first derivative), resolving a longstanding open question about whether gradient descent can get stuck at non-solution local minima. This provides formal mathematical foundations for two of the most widely used neural PDE solvers in scientific machine learning.

Deep Galerkin Method Physics-Informed Neural Networks