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PINNs can fail to learn correct Hamilton-Jacobi solutions

By PulseAugur Editorial · [1 sources] ·

A new research paper explores the limitations of physics-informed neural networks (PINNs) when solving Hamilton-Jacobi-Isaacs equations. The study found that PINNs, which typically judge solutions by the size of their sampled PDE residual, can converge to incorrect "viscosity solutions" that satisfy the equation on sets of measure zero but are fundamentally wrong. Researchers identified specific parameterizations and structural diagnostics that are essential for ensuring PINNs learn the correct viscosity solution, particularly in complex geometries and higher dimensions. AI

IMPACT Highlights potential pitfalls in using neural networks for complex scientific modeling, emphasizing the need for robust validation methods.

RANK_REASON Research paper detailing limitations of a specific machine learning technique for solving mathematical equations. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

PINNs can fail to learn correct Hamilton-Jacobi solutions

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Research paper detailing limitations of a specific machine learning technique for solving mathematical equations. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Raul Jimenez, Pablo Tejerina-P\'erez, Leonid Sarieddine, Pedro Taranc\'on-\'Alvarez, Marisol Traforetti, Pau Sol\'e-Vilar\'o, Oleksii Ignatenko, Nazar Tkach, Pavlos Protopapas ·

    Low Residuals, Wrong Value: Learning the Viscosity Solution of Hamilton-Jacobi-Isaacs Equations with PINNs

    arXiv:2610.27193v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) and other residual-trained solvers judge a candidate solution by the size of its sampled PDE residual. For first-order Hamilton-Jacobi equations this is not sufficient: the same equation an…

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