NSEM solves Poisson-Nernst-Planck benchmarks to 10^-4 to 10^-7 relative error using two orders of magnitude fewer collocation points than adaptive PINNs by combining spectral differentiation matrices with neural networks and a boundary-layer coordinate map.
Finite basis physics-informed neural networks (fbpinns): a scalable domain decomposition approach for solving differential equations
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PINNs fail on spurious solutions admitted by the residual loss; adaptive pseudo-time stepping with Jacobian-based step selection improves accuracy and robustness on PDE benchmarks.
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Neural Spectral Element Methods for stiff multiphysics PDEs with electrochemical transport benchmarks
NSEM solves Poisson-Nernst-Planck benchmarks to 10^-4 to 10^-7 relative error using two orders of magnitude fewer collocation points than adaptive PINNs by combining spectral differentiation matrices with neural networks and a boundary-layer coordinate map.
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When PINNs Go Wrong: Pseudo-Time Stepping Against Spurious Solutions
PINNs fail on spurious solutions admitted by the residual loss; adaptive pseudo-time stepping with Jacobian-based step selection improves accuracy and robustness on PDE benchmarks.