# Improved physics-informed neural network in mitigating gradient related failures

arXiv: https://arxiv.org/abs/2407.19421 · HTML: https://mlsanity.com/paper/2407.19421/

## Key facts

- Cited by 1 papers in the map (data through 13 Oct 2026).
- Builds on 11 of its 31 references that are in the map.
- First posted on arXiv 28 Jul 2024.

## Builds on (most cited first, 11 of 11)

- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Physics-informed neural networks with hard constraints for inverse design](https://mlsanity.com/paper/2102.04626/) (2021)
- [A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks](https://mlsanity.com/paper/2207.10289/) (2022)
- [Can Physics-Informed Neural Networks beat the Finite Element Method?](https://mlsanity.com/paper/2302.04107/) (2023)
- [A Dual-Dimer Method for Training Physics-Constrained Neural Networks with Minimax Architecture](https://mlsanity.com/paper/2005.00615/) (2020)
- [Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology](https://mlsanity.com/paper/2211.08939/) (2022)
- [Physics and Equality Constrained Artificial Neural Networks: Application to Forward and Inverse Problems with Multi-fidelity Data Fusion](https://mlsanity.com/paper/2109.14860/) (2021)
- [A practical PINN framework for multi-scale problems with multi-magnitude loss terms](https://mlsanity.com/paper/2308.06672/) (2023)
- [Solving Partial Differential Equations with Point Source Based on Physics-Informed Neural Networks](https://mlsanity.com/paper/2111.01394/) (2021)

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

- [Physics-Informed Neural PDE Solvers via Spatio-Temporal MeanFlow](https://mlsanity.com/paper/2605.08915/) (2026)

## Abstract (arXiv)

Physics-informed neural networks (PINNs) integrate fundamental physical principles with advanced data-driven techniques, driving significant advancements in scientific computing. However, PINNs face persistent challenges with stiffness in gradient flow, which limits their predictive capabilities. This paper presents an improved PINN (I-PINN) to mitigate gradient-related failures. The core of I-PINN is to combine the respective strengths of neural networks with an improved architecture and adaptive weights containingupper bounds. The capability to enhance accuracy by at least one order of magnitude and accelerate convergence, without introducing extra computational complexity relative to the baseline model, is achieved by I-PINN. Numerical experiments with a variety of benchmarks illustrate the improved accuracy and generalization of I-PINN. The supporting data and code are accessible at https://github.com/PanChengN/I-PINN.git, enabling broader research engagement.