Mask-PINNs: Regulating Feature Distributions in Physics-Informed Neural Networks
Physics-Informed Neural Networks (PINNs) are a class of deep learning models designed to solve partial differential equations by incorporating physical laws directly into the loss function. However, the internal covariate shift, which has been largely overlooked, hinders the effective utilization of neural network capacity in PINNs. To this end, we propose Mask-PINNs, a novel architecture designed to address this issue in PINNs. Unlike traditional normalization methods such as BatchNorm or LayerNorm, we introduce a learnable, nonlinear mask function that constrains the feature distributions without violating underlying physics. The experimental results show that the proposed method significantly improves feature distribution stability, accuracy, and robustness across various activation functions and PDE benchmarks. Furthermore, it enables the stable and efficient training of wider networks a capability that has been largely overlooked in PINNs.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Physics-Informed Neural Networks with Skip Connections for Modeling and Control of Gas-Lifted Oil Wells
Neural networks, while powerful, often lack interpretability. Physics-Informed Neural Networks (PINNs) address this limitation by incorporating physics laws into the loss function, making them applicable to solving Ordin…
Model Predictive ControlSeparable Physics-informed Neural Networks for Solving the BGK Model of the Boltzmann Equation
In this study, we introduce a method based on Separable Physics-Informed Neural Networks (SPINNs) for effectively solving the BGK model of the Boltzmann equation. While the mesh-free nature of PINNs offers significant ad…
Physics-Informed Neural Systems for the Simulation of EUV Electromagnetic Wave Diffraction from a Lithography Mask
Physics-informed neural networks (PINNs) and neural operators (NOs) for solving the problem of diffraction of Extreme Ultraviolet (EUV) electromagnetic waves from contemporary lithography masks are presented. A novel hyb…
Statistical Learning Analysis of Physics-Informed Neural Networks
We study the training and performance of physics-informed learning for initial and boundary value problems (IBVP) with physics-informed neural networks (PINNs) from a statistical learning perspective. Specifically, we re…
Stochastic OptimizationEnhancing Physics-Informed Neural Networks with Domain-aware Fourier Features: Towards Improved Performance and Interpretable Results
Physics-Informed Neural Networks (PINNs) incorporate physics into neural networks by embedding partial differential equations (PDEs) into their loss function. Despite their success in learning the underlying physics, PIN…