PaPi parallel integrator speeds neuro-spectral PDE learning
Original title: PaPi: Parallel Picard-Duhamel Integration for Fast Neuro-Spectral Architectures
Experiments report up to two orders of magnitude faster training and inference, with some low-dimensional PDE runs under one second.
Researchers introduce PaPi, an integration scheme for neuro-spectral architectures used as physics-informed networks on time-dependent PDEs. It replaces sequential Runge-Kutta stepping with exponential integration and a Duhamel-Picard iteration that supports time-parallel inference. The authors say the iteration converges exponentially for all flows, with error bounds tied to how close a flow is to linear. They report speedups of up to two orders of magnitude and competitive accuracy.
- NeuSA models solve time-dependent PDEs in the frequency domain.
- Existing training often uses sequential Runge-Kutta integration of the learned field.
- Error bounds depend on how close the flow is to linear.
- Reported training times fall under one second on low-dimensional problems.
From the original article
1 min read at arxiv.orgNeuro-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.
By Arthur Bizzi · arxiv.org
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