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
Neuro-Spektralarchitekturen (NeuSA) sind eine Klasse von physikalisch informierten neuronalen Netzwerken (PINNs), die sich als wirksam erwiesen haben, um zeitabhängige PDEs im Frequenzbereich zu lösen. Allerdings verlassen sich Ausbildung und Schlussfolgerung oft auf kostspielige numerische Integration des erlernten Vektorfelds, typischerweise mithilfe sequentieller Runge-Kutta-Zeitschritte, die zeitliche Parallelismus einschränken. Wir führen PaPi ein, ein von schwach nichtlinearen Flüssen inspiriertes Integrations-Schema, das zeitparallel-Inferenz durch exponentielle Integration und ein Duhamel-Pardic-Schema ermöglicht. Wir zeigen, dass die Duhamel-Picarderation es für alle Flüsse ex
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 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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