# Initialization-enhanced Physics-Informed Neural Network with Domain Decomposition (IDPINN)

arXiv: https://arxiv.org/abs/2406.03172 · HTML: https://mlsanity.com/paper/2406.03172/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 49 references that are in the map.
- First posted on arXiv 5 Jun 2024.

## Builds on (most cited first, 24 of 24)

- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition](https://mlsanity.com/paper/2003.05385/) (2020)
- [A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks](https://mlsanity.com/paper/2207.10289/) (2022)
- [Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems](https://mlsanity.com/paper/2111.02801/) (2021)
- [Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equations](https://mlsanity.com/paper/2107.07871/) (2021)
- [Transfer learning enhanced physics informed neural network for phase-field modeling of fracture](https://mlsanity.com/paper/1907.02531/) (2019)
- [Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEs](https://mlsanity.com/paper/2006.16144/) (2020)
- [Residual-based attention in physics-informed neural networks](https://mlsanity.com/paper/2307.00379/) (2023)
- [Physics-informed neural network for ultrasound nondestructive quantification of surface breaking cracks](https://mlsanity.com/paper/2005.03596/) (2020)
- [Transfer learning based multi-fidelity physics informed deep neural network](https://mlsanity.com/paper/2005.10614/) (2020)
- [Failure-informed adaptive sampling for PINNs](https://mlsanity.com/paper/2210.00279/) (2022)
- [When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?](https://mlsanity.com/paper/2109.09444/) (2021)
- [Physics-informed deep learning for incompressible laminar flows](https://mlsanity.com/paper/2002.10558/) (2020)
- [Bayesian Physics-Informed Neural Networks for real-world nonlinear dynamical systems](https://mlsanity.com/paper/2205.08304/) (2022)
- [Physics-Informed Multi-LSTM Networks for Metamodeling of Nonlinear Structures](https://mlsanity.com/paper/2002.10253/) (2020)
- [One-Shot Transfer Learning of Physics-Informed Neural Networks](https://mlsanity.com/paper/2110.11286/) (2021)
- [Physics informed neural networks for continuum micromechanics](https://mlsanity.com/paper/2110.07374/) (2021)
- [Transfer learning based physics-informed neural networks for solving inverse problems in engineering structures under different loading scenarios](https://mlsanity.com/paper/2205.07731/) (2022)
- [Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology](https://mlsanity.com/paper/2211.08939/) (2022)
- [Enhancing training of physics-informed neural networks using domain-decomposition based preconditioning strategies](https://mlsanity.com/paper/2306.17648/) (2023)
- [SeismicNet: Physics-informed neural networks for seismic wave modeling in semi-infinite domain](https://mlsanity.com/paper/2210.14044/) (2022)
- [Gradient-Enhanced Physics-Informed Neural Networks for Power Systems Operational Support](https://mlsanity.com/paper/2206.10579/) (2022)
- [Physics-informed neural networks in the recreation of hydrodynamic simulations from dark matter](https://mlsanity.com/paper/2303.14090/) (2023)

## Built on by (most cited first, 9 of 9)

- [Complex Physics-Informed Neural Network](https://mlsanity.com/paper/2502.04917/) (2025)
- [Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective](https://mlsanity.com/paper/2506.19805/) (2025)
- [Quantifying Training Difficulty and Accelerating Convergence in Neural Network-Based PDE Solvers](https://mlsanity.com/paper/2410.06308/) (2024)
- [BO-SA-PINNs: Self-adaptive physics-informed neural networks based on Bayesian optimization for automatically designing PDE solvers](https://mlsanity.com/paper/2504.09804/) (2025)
- [Plug-and-Play Physics-informed Learning using Uncertainty Quantified Port-Hamiltonian Models](https://mlsanity.com/paper/2504.17966/) (2025)
- [Lightweight Geometric Adaptation for Training Physics-Informed Neural Networks](https://mlsanity.com/paper/2604.15392/) (2026)
- [Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks](https://mlsanity.com/paper/2508.19410/) (2025)
- [AutoBalance: An Automatic Balancing Framework for Training Physics-Informed Neural Networks](https://mlsanity.com/paper/2510.06684/) (2025)
- [From Non-Convex Self-Concordant Regularization to Scalable Quasi-Newton Training of PINNs](https://mlsanity.com/paper/2608.04206/) (2026)

## Abstract (arXiv)

We propose a new physics-informed neural network framework, IDPINN, based on the enhancement of initialization and domain decomposition to improve prediction accuracy. We train a PINN using a small dataset to obtain an initial network structure, including the weighted matrix and bias, which initializes the PINN for each subdomain. Moreover, we leverage the smoothness condition on the interface to enhance the prediction performance. We numerically evaluated it on several forward problems and demonstrated the benefits of IDPINN in terms of accuracy.