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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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.