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

arXiv: https://arxiv.org/abs/2602.15883 · HTML: https://mlsanity.com/paper/2602.15883/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 43 references that are in the map.
- First posted on arXiv 5 Feb 2026.

## Builds on (most cited first, 10 of 10)

- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction](https://mlsanity.com/paper/2211.14680/) (2022)
- [PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs](https://mlsanity.com/paper/1909.10145/) (2019)
- [Parallel Physics-Informed Neural Networks via Domain Decomposition](https://mlsanity.com/paper/2104.10013/) (2021)
- [Physics-informed deep learning for incompressible laminar flows](https://mlsanity.com/paper/2002.10558/) (2020)
- [Reconstruction of turbulent data with deep generative models for semantic inpainting from TURB-Rot database](https://mlsanity.com/paper/2006.09179/) (2020)
- [PiRD: Physics-informed Residual Diffusion for Flow Field Reconstruction](https://mlsanity.com/paper/2404.08412/) (2024)
- [Frequency-compensated PINNs for Fluid-dynamic Design Problems](https://mlsanity.com/paper/2011.01456/) (2020)
- [A unified method of data assimilation and turbulence modeling for separated flows at high Reynolds numbers](https://mlsanity.com/paper/2211.00601/) (2022)

## Built on by (most cited first, 1 of 1)

- [Inferring physical fields in coupled systems with unknown parameters from incomplete observations using physics-constrained attentive neural operators](https://mlsanity.com/paper/2610.05723/) (2026)

## Abstract (arXiv)

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.