A Curriculum-Training-Based Strategy for Distributing Collocation Points during Physics-Informed Neural Network Training
Physics-informed Neural Networks (PINNs) often have, in their loss functions, terms based on physical equations and derivatives. In order to evaluate these terms, the output solution is sampled using a distribution of collocation points. However, density-based strategies, in which the number of collocation points over the domain increases throughout the training period, do not scale well to multiple spatial dimensions. To remedy this issue, we present here a curriculum-training-based method for lightweight collocation point distributions during network training. We apply this method to a PINN which recovers a full two-dimensional magnetohydrodynamic (MHD) solution from a partial sample taken from a baseline MHD simulation. We find that the curriculum collocation point strategy leads to a significant decrease in training time and simultaneously enhances the quality of the reconstructed solution.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Less Emphasis on Difficult Layer Regions: Curriculum Learning for Singularly Perturbed Convection-Diffusion-Reaction Problems
Although Physics-Informed Neural Networks (PINNs) have been successfully applied in a wide variety of science and engineering fields, they can fail to accurately predict the underlying solution in slightly challenging co…
Scalable h-adaptive probabilistic solver for time-independent and time-dependent systems
Solving partial differential equations (PDEs) within the framework of probabilistic numerics offers a principled approach to quantifying epistemic uncertainty arising from discretization. By leveraging Gaussian process r…
Active LearningPINNACLE: PINN Adaptive ColLocation and Experimental points selection
Physics-Informed Neural Networks (PINNs), which incorporate PDEs as soft constraints, train with a composite loss function that contains multiple training point types: different types of collocation points chosen during …
Transfer LearningAn Adaptive Collocation Point Strategy For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method
Physics-informed neural networks (PINNs) have gained significant attention for solving forward and inverse problems related to partial differential equations (PDEs). While advancements in loss functions and network archi…
Adaptive Self-supervision Algorithms for Physics-informed Neural Networks
Physics-informed neural networks (PINNs) incorporate physical knowledge from the problem domain as a soft constraint on the loss function, but recent work has shown that this can lead to optimization difficulties. Here, …