论文标题
基于课程培训的策略，用于分发物理知识的神经网络培训期间的搭配点
A Curriculum-Training-Based Strategy for Distributing Collocation Points during Physics-Informed Neural Network Training
论文作者
论文摘要
物理知识的神经网络（PINN）通常具有基于物理方程式和衍生物的损失功能。为了评估这些术语，使用搭配点的分布对输出解决方案进行采样。但是，基于密度的策略，在整个训练期间，绑架点的数量增加，并不能很好地扩展到多个空间维度。为了解决这个问题，我们在这里提出了一种基于课程培训的方法，用于网络培训期间的轻质搭配点分布。我们将此方法应用于PINN，该方法从基线MHD模拟中采集的部分样品中恢复了完整的二维磁性水力动力学（MHD）溶液。我们发现，课程搭配点策略会导致训练时间大大减少，并同时提高了重建解决方案的质量。
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.
