# Distributed physics informed neural network for data-efficient solution to partial differential equations

arXiv: https://arxiv.org/abs/1907.08967 · HTML: https://mlsanity.com/paper/1907.08967/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jul 2019.

## Built on by (most cited first, 26 of 26)

- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equations](https://mlsanity.com/paper/2107.07871/) (2021)
- [Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology](https://mlsanity.com/paper/2211.08939/) (2022)
- [Physics Informed Kolmogorov-Arnold Neural Networks for Dynamical Analysis via Efficent-KAN and WAV-KAN](https://mlsanity.com/paper/2407.18373/) (2024)
- [Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing](https://mlsanity.com/paper/2211.07377/) (2022)
- [Enhancing training of physics-informed neural networks using domain-decomposition based preconditioning strategies](https://mlsanity.com/paper/2306.17648/) (2023)
- [A Method for Computing Inverse Parametric PDE Problems with Random-Weight Neural Networks](https://mlsanity.com/paper/2210.04338/) (2022)
- [Fourier neural operator for learning solutions to macroscopic traffic flow models: Application to the forward and inverse problems](https://mlsanity.com/paper/2308.07051/) (2023)
- [Bayesian Physics-Informed Extreme Learning Machine for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2205.06948/) (2022)
- [A composable machine-learning approach for steady-state simulations on high-resolution grids](https://mlsanity.com/paper/2210.05837/) (2022)
- [Curriculum Learning-Driven PIELMs for Fluid Flow Simulations](https://mlsanity.com/paper/2503.06347/) (2025)
- [Deep Physics Corrector: A physics enhanced deep learning architecture for solving stochastic differential equations](https://mlsanity.com/paper/2209.09750/) (2022)
- [Physics-informed time series analysis with Kolmogorov-Arnold Networks under Ehrenfest constraints](https://mlsanity.com/paper/2509.18483/) (2025)
- [A composable autoencoder-based iterative algorithm for accelerating numerical simulations](https://mlsanity.com/paper/2110.03780/) (2021)
- [Breaking Boundaries: Distributed Domain Decomposition with Scalable Physics-Informed Neural PDE Solvers](https://mlsanity.com/paper/2308.14258/) (2023)
- [PICS in Pics: Physics Informed Contour Selection for Rapid Image Segmentation](https://mlsanity.com/paper/2311.07002/) (2023)
- [Sequential learning based PINNs to overcome temporal domain complexities in unsteady flow past flapping wings](https://mlsanity.com/paper/2503.15679/) (2025)
- [PINN - a Domain Decomposition Method for Bayesian Physics-Informed Neural Networks](https://mlsanity.com/paper/2504.19013/) (2025)
- [Gated X-TFC: Soft Domain Decomposition for Forward and Inverse Problems in Sharp-Gradient PDEs](https://mlsanity.com/paper/2510.01039/) (2025)
- [Geometry-aware PINNs for Turbulent Flow Prediction](https://mlsanity.com/paper/2412.01954/) (2024)
- [Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks](https://mlsanity.com/paper/2506.17726/) (2025)
- [Soft Partition-based KAPI-ELM for Multi-Scale PDEs](https://mlsanity.com/paper/2601.08719/) (2026)
- [Exact Constraint Enforcement in Physics-Informed Extreme Learning Machines using Null-Space Projection Framework](https://mlsanity.com/paper/2601.10999/) (2026)
- [Multiscale Physics-Informed Neural Network for Complex Fluid Flows with Long-Range Dependencies](https://mlsanity.com/paper/2604.05652/) (2026)
- [Geometric Kolmogorov--Arnold Network (GeoKAN)](https://mlsanity.com/paper/2605.06740/) (2026)
- [Frequency Shift Physics-Informed Extreme Learning Machine for Solving High-Frequency Partial Differential Equations](https://mlsanity.com/paper/2607.01694/) (2026)

## Abstract (arXiv)

The physics informed neural network (PINN) is evolving as a viable method to solve partial differential equations. In the recent past PINNs have been successfully tested and validated to find solutions to both linear and non-linear partial differential equations (PDEs). However, the literature lacks detailed investigation of PINNs in terms of their representation capability. In this work, we first test the original PINN method in terms of its capability to represent a complicated function. Further, to address the shortcomings of the PINN architecture, we propose a novel distributed PINN, named DPINN. We first perform a direct comparison of the proposed DPINN approach against PINN to solve a non-linear PDE (Burgers' equation). We show that DPINN not only yields a more accurate solution to the Burgers' equation, but it is found to be more data-efficient as well. At last, we employ our novel DPINN to two-dimensional steady-state Navier-Stokes equation, which is a system of non-linear PDEs. To the best of the authors' knowledge, this is the first such attempt to directly solve the Navier-Stokes equation using a physics informed neural network.