Distributed physics-informed neural networks via domain decomposition for fast flow reconstruction

TL;DR

This paper introduces a scalable distributed PINNs framework with domain decomposition and normalization strategies, enabling efficient and accurate flow reconstruction across large spatiotemporal domains while addressing pressure indeterminacy.

Contribution

It presents a novel distributed PINNs approach with domain decomposition, anchor normalization, and GPU acceleration to improve scalability and pressure consistency in flow reconstruction.

Findings

Achieves near-linear strong scaling on complex flow benchmarks.

Provides high-fidelity flow and pressure field reconstructions.

Addresses pressure indeterminacy through anchor normalization and asymmetric weighting.

Abstract

Physics-Informed Neural Networks (PINNs) offer a powerful paradigm for flow reconstruction, seamlessly integrating sparse velocity measurements with the governing Navier-Stokes equations to recover complete velocity and latent pressure fields. However, scaling such models to large spatiotemporal domains is hindered by computational bottlenecks and optimization instabilities. In this work, we propose a robust distributed PINNs framework designed for efficient flow reconstruction via spatiotemporal domain decomposition. A critical challenge in such distributed solvers is pressure indeterminacy, where independent sub-networks drift into inconsistent local pressure baselines. We address this issue through a reference anchor normalization strategy coupled with decoupled asymmetric weighting. By enforcing a unidirectional information flow from designated master ranks where the anchor point lies to neighboring ranks, our approach eliminates gauge freedom and guarantees global pressure uniqueness while preserving temporal continuity. Furthermore, to mitigate the Python interpreter overhead associated with computing high-order physics residuals, we implement a high-performance training pipeline accelerated by CUDA graphs and JIT compilation. Extensive validation on complex flow benchmarks demonstrates that our method achieves near-linear strong scaling and high-fidelity reconstruction, establishing a scalable and physically rigorous pathway for flow reconstruction and understanding of complex hydrodynamics.