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

Key points

• 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.1
• 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.1
• 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.1
• 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.1

Sources (1)

• [1]PaPi: Parallel Picard-Duhamel Integration for Fast Neuro-Spectral Architectures
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 20, 05:42 PM

  We introduce PaPi, an integration scheme inspired by weakly nonlinear flows that enables time-Parallel inference through exponential integration and a Duhamel-Picard scheme.

  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.

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