Arthur Bizzi, Márcio Marques, Kleyton Da Costa, Vitor Balestro, Tiago Novello, João M. Pereira, Daniel Yukimura · 2026 · arXiv
DOI: 10.48550/arXiv.2610.28591 · open-access PDF
As arquiteturas neuro-espectral (NeuSA) são uma classe de redes neurais informadas pela física (PINNs) que provaram ser eficazes para resolver PDEs dependentes do tempo no domínio de frequência. No entanto, o treinamento e a inferência muitas vezes dependem da integração numérica dispendiosa do campo vetorial aprendido, tipicamente usando o passo do tempo sequencial Runge-Kutta, que limita o paralelismo temporal. Introduzimos PaPi, um esquema de integração inspirado por fluxos fracos não lineares que permite a inferência do tempo paralelo através de integração exponencial e um esquema Duhamel-Pardic.
Machine translation (Meta M2M100); the English original follows.
Neuro-spectral architectures (NeuSA) are a class of physics-informed neural networks (PINNs) that have proven effective for solving time-dependent PDEs in the frequency domain. However, training and inference often rely on costly numerical integration of the learned vector field, typically using sequential Runge-Kutta time stepping, which limits temporal parallelism. We introduce PaPi, an integration scheme inspired by weakly nonlinear flows that enables time-Parallel inference through exponential integration and a Duhamel-Picard scheme. We show that the Duhamel-Picard iteration converges expo
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