RANG: A Residual-based Adaptive Node Generation Method for Physics-Informed Neural Networks
Learning solutions of partial differential equations (PDEs) with Physics-Informed Neural Networks (PINNs) is an attractive alternative approach to traditional solvers due to its flexibility and ease of incorporating observed data. Despite the success of PINNs in accurately solving a wide variety of PDEs, the method still requires improvements in terms of computational efficiency. One possible improvement idea is to optimize the generation of training point sets. Residual-based adaptive sampling and quasi-uniform sampling approaches have been each applied to improve the training effects of PINNs, respectively. To benefit from both methods, we propose the Residual-based Adaptive Node Generation (RANG) approach for efficient training of PINNs, which is based on a variable density nodal distribution method for RBF-FD. The method is also enhanced by a memory mechanism to further improve training stability. We conduct experiments on three linear PDEs and three nonlinear PDEs with various node generation methods, through which the accuracy and efficiency of the proposed method compared to the predominant uniform sampling approach is verified numerically.
Code (1)
Tasks
Computational EfficiencySimilar Papers 제목 키워드 기반
Do We Really Need Adaptive Global Spatial Attention for Traffic Forecasting?
Existing traffic forecasting models commonly focus on extracting spatial dependencies, particularly global spatial information, which characterizes the representations obtained through interactions between each node and …
Information ExtractionGradient-enhanced physics-informed neural networks for forward and inverse PDE problems
Deep learning has been shown to be an effective tool in solving partial differential equations (PDEs) through physics-informed neural networks (PINNs). PINNs embed the PDE residual into the loss function of the neural ne…
Self-adaptive weights based on balanced residual decay rate for physics-informed neural networks and deep operator networks
Physics-informed deep learning has emerged as a promising alternative for solving partial differential equations. However, for complex problems, training these networks can still be challenging, often resulting in unsati…
Stabilized Adaptive Loss and Residual-Based Collocation for Physics-Informed Neural Networks
Physics-Informed Neural Networks (PINNs) have been recognized as a mesh-free alternative to solve partial differential equations where physics information is incorporated. However, in dealing with problems characterized …
Physics-Informed Residual Neural Ordinary Differential Equations for Enhanced Tropical Cyclone Intensity Forecasting
Accurate tropical cyclone (TC) intensity prediction is crucial for mitigating storm hazards, yet its complex dynamics pose challenges to traditional methods. Here, we introduce a Physics-Informed Residual Neural Ordinary…
Deep LearningTropical Cyclone Intensity Forecasting