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PaPi: Parallel Picard-Duhamel Integration for Fast Neuro-Spectral Architectures

Arthur Augusto Coutinho Bizzi, Márcio Marques, Kleyton da Costa, Vitor Balestro, Tiago Novello, João M. Pereira, Daniel Yukimura · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.28591 · cited by 0 works (OpenAlex) · open-access PDF

Indonesian

Arsitektur Neuro-spektral (NeuSA) adalah kelas jaringan saraf yang diinformasikan oleh fisika (PINN) yang telah terbukti efektif untuk memecahkan PDEs yang tergantung pada waktu di domain frekuensi. Namun, pelatihan dan inferensi sering bergantung pada integrasi numerik yang mahal dari bidang vektor yang dipelajari, biasanya menggunakan langkah waktu Runge-Kutta berurutan, yang membatasi paralelisme waktu. Kami memperkenalkan PaPi, skema integrasi yang terinspirasi oleh aliran nonlinear yang lemah yang memungkinkan inferensi waktu-paralel melalui integrasi eksponensial dan skema Duhamel-Pardic. Kami menunjukkan bahwa Duhamel-Picarder it converges secara eksponensial untuk semua aliran, dan memberikan batas kesalahan eksplisit yang tergantung pada seberapa dekat aliran ke linear. Eksperimen menunjukkan bahwa PaPi

Machine translation (Meta M2M100); the English original follows.

Abstract

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 exponentially for all flows, and provide explicit error bounds that depend on how close the flow is to linear. Experiments show that PaPi accelerates training and inference by up to two orders of magnitude, achieving training times of under one second for low-dimensional PDE learning problems, while maintaining competitive predictive accuracy.

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Topics: Inference, Computer science, Numerical integration, Nonlinear system, Artificial neural network, Algorithm

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