Improved physics-informed neural network in mitigating gradient related failures
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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.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 11 of its 31 references that are in the map. First posted on arXiv 28 Jul 2024.
Builds on
11 of 31 references.
References · 11
- 2017Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semanticscited by 1,345
- 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 629
- 2019DeepXDE: A deep learning library for solving differential equationscited by 617
- 2021Physics-informed neural networks with hard constraints for inverse designcited by 277
- 2022A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networkscited by 233
- 2023Can Physics-Informed Neural Networks beat the Finite Element Method?cited by 68
- 2020A Dual-Dimer Method for Training Physics-Constrained Neural Networks with Minimax Architecturecited by 50
- 2022Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodologycited by 43
- 2021Physics and Equality Constrained Artificial Neural Networks: Application to Forward and Inverse Problems with Multi-fidelity Data Fusioncited by 38
- 2023A practical PINN framework for multi-scale problems with multi-magnitude loss termscited by 15
- 2021Solving Partial Differential Equations with Point Source Based on Physics-Informed Neural Networkscited by 14
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