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arXiv Machine Learning By Pablo Cort\'es Castillo, Wolfgang Dahmen, Jay Gopalakrishnan

DPG loss functions for learning parameter-to-solution maps by neural networks

Read the original on arXiv Machine Learning →

The paper introduces residual-based loss functions derived from Discontinuous Petrov Galerkin (DPG) discretizations for training neural networks to learn parameter-to-solution maps of PDEs. It focuses on rigorous accuracy certification and demonstrates the approach on an elliptic PDE, showing that DPG-based losses outperform simple least-squares losses, especially for high-contrast diffusion problems. The concepts are applicable to any problem with a stable DPG formulation.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

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