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arXiv Machine Learning By M\'arcio Marques, Leonardo Mendon\c{c}a, Leonardo M. Moreira, Christian J\'unior de Oliveira, Vitor Balestro, Tiago Novello, Daniel Yukimura, Pavel Petrov, Lucas Nissenbaum

NEXT: Physics-Informed Neuro-Spectral Exponential Time Differencing Architectures

Read the original on arXiv Machine Learning →

The paper introduces NEXT, a new physics-informed neural architecture that combines Neuro‑Spectral Architectures with high‑order exponential time‑differencing integrators. NEXT integrates the stiff linear part of PDEs exactly via matrix exponentials while a neural network models the remaining nonlinear dynamics, thereby overcoming spectral bias, causality issues, and numerical instability seen in previous PINNs and NeuSAs. Benchmark tests on stiff PDEs show NEXT remains stable and accurate, and it can also solve inverse problems by learning unknown parameters or boundary conditions from sparse data.

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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