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

arXiv: https://arxiv.org/abs/2211.11396 · HTML: https://mlsanity.com/paper/2211.11396/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 30 references that are in the map.
- First posted on arXiv 21 Nov 2022.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Curriculum Learning: A Survey](https://mlsanity.com/paper/2101.10382/) (2021)
- [Efficient training of physics-informed neural networks via importance sampling](https://mlsanity.com/paper/2104.12325/) (2021)
- [CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Method](https://mlsanity.com/paper/2110.15832/) (2021)
- [Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learning](https://mlsanity.com/paper/2008.13333/) (2020)
- [NVIDIA SimNet^{TM}: an AI-accelerated multi-physics simulation framework](https://mlsanity.com/paper/2012.07938/) (2020)
- [Student-Teacher Curriculum Learning via Reinforcement Learning: Predicting Hospital Inpatient Admission Location](https://mlsanity.com/paper/2007.01135/) (2020)
- [Prediction of soft proton intensities in the near-Earth space using machine learning](https://mlsanity.com/paper/2105.15108/) (2021)

## Built on by (most cited first, 5 of 5)

- [Localized Physics-informed Gaussian Processes with Curriculum Training for Topology Optimization](https://mlsanity.com/paper/2503.15561/) (2025)
- [Learning Transient Convective Heat Transfer with Geometry Aware World Models](https://mlsanity.com/paper/2601.22086/) (2026)
- [(Un)supervised Learning of Maximal Lyapunov Functions](https://mlsanity.com/paper/2408.17246/) (2024)
- [Enhancing PINN Accuracy for the RLW Equation: Adaptive and Conservative Approaches](https://mlsanity.com/paper/2511.11638/) (2025)
- [Curriculum Learning of Physics-Informed Neural Networks based on Spatial Correlation](https://mlsanity.com/paper/2605.15254/) (2026)

## Abstract (arXiv)

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.