NEXT: Physics-Informed Neuro-Spectral Exponential Time Differencing Architectures
Abstract
Physics-Informed Neural Networks (PINNs) build neural representations of time-dependent PDE solutions, naturally incorporating physics knowledge and observational data, which makes them well suited to both forward and inverse PDE problems. PINNs, however, are known to suffer from spectral bias and lack of causality. Neuro-Spectral Architectures (NeuSA), a recently proposed alternative to PINNs, mitigate both issues, but their numerical integration becomes unstable for stiff differential equations arising in many relevant physical problems. This study proposes Neuro-Spectral Exponential Time Differencing Architectures (NEXT), which combines the spectral representation of the PDE solution in NeuSA with high-order exponential integrators. Within this approach, the linear stiff part of the vector field induced by the PDE is integrated exactly through matrix exponentials, while the possibly nonlinear remainder is modeled by a neural network. The effectiveness of NEXT is verified through benchmark experiments on a set of stiff PDEs, in which NEXT is stable and accurate while NeuSA diverges numerically. It is also shown that NEXT can be applied to inverse problems, where the model has to learn unknown parameters or boundary conditions from sparse data. All code used in this work is publicly available at: https://github.com/marcioh2m/next.git .
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BibTeX
@misc{marques2026next,
title = {{NEXT: Physics-Informed Neuro-Spectral Exponential Time Differencing Architectures}},
author = {Márcio Marques and Leonardo Mendonça and Leonardo M. Moreira and Christian Júnior de Oliveira and Vitor Balestro and Tiago Novello and Daniel Yukimura and Pavel Petrov and Lucas Nissenbaum},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31539},
eprint = {2609.31539},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31539},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - NEXT: Physics-Informed Neuro-Spectral Exponential Time Differencing Architectures
AU - Márcio Marques
AU - Leonardo Mendonça
AU - Leonardo M. Moreira
AU - Christian Júnior de Oliveira
AU - Vitor Balestro
AU - Tiago Novello
AU - Daniel Yukimura
AU - Pavel Petrov
AU - Lucas Nissenbaum
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31539
UR - https://arxiv.org/abs/2609.31539
AB - Physics-Informed Neural Networks (PINNs) build neural representations of time-dependent PDE solutions, naturally incorporating physics knowledge and observational data, which makes them well suited to both forward and inverse PDE problems. PINNs, however, are known to suffer from spectral bias and lack of causality. Neuro-Spectral Architectures (NeuSA), a recently proposed alternative to PINNs, mitigate both issues, but their numerical integration becomes unstable for stiff differential equations arising in many relevant physical problems. This study proposes Neuro-Spectral Exponential Time Differencing Architectures (NEXT), which combines the spectral representation of the PDE solution in NeuSA with high-order exponential integrators. Within this approach, the linear stiff part of the vector field induced by the PDE is integrated exactly through matrix exponentials, while the possibly nonlinear remainder is modeled by a neural network. The effectiveness of NEXT is verified through benchmark experiments on a set of stiff PDEs, in which NEXT is stable and accurate while NeuSA diverges numerically. It is also shown that NEXT can be applied to inverse problems, where the model has to learn unknown parameters or boundary conditions from sparse data. All code used in this work is publicly available at: https://github.com/marcioh2m/next.git .
ER -