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

Practical Tips

Practical tips and how-to guidance will be added by our editorial team.

中文解读

中文解读待补充：本站将优先为睡眠改善、失眠治疗、助眠方法等高价值文章补充中文说明。

Article Summary

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.

Sources & References

• Original source
• Full article (PDF)

Comments