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Nonlinear physics models can't be learned accurately with current methods, even with lots of data. This research proves a gap in how we formulate these problems. It affects anyone using physics-informed neural networks for complex simulations.
“arXiv:2607.15702v1 Announce Type: cross Abstract: We prove a finite-sample formulation gap for physics-informed learning of nonlinear multiscale elliptic equations. For a uniformly monotone divergence-form class with coefficients oscillatin…”
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arXiv:2607.15702v1, physics-informed neural networks
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Aug 6, 2026