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Physics-informed Neural Networks (PINNs) often have, in their loss functions,terms based on physical equations and derivatives. In order to evaluate theseterms, the output solution is sampled using a distribution of collocationpoints. However, density-based strategies, in which the number of collocationpoints over the domain increases throughout the training period, do not scalewell to multiple spatial dimensions. To remedy this issue, we present here acurriculum-training-based method for lightweight collocation pointdistributions during network training. We apply this method to a PINN whichrecovers a full two-dimensional magnetohydrodynamic (MHD) solution from apartial sample taken from a baseline MHD simulation. We find that thecurriculum collocation point strategy leads to a significant decrease intraining time and simultaneously enhances the quality of the reconstructedsolution.

A Curriculum-Training-Based Strategy for Distributing Collocation Points during Physics-Informed Neural Network Training