We introduce Sparse Physics Informed Backpropagation (SPInProp), a new class of methods for accelerating backpropagation for a specialized neural network architecture called Low Rank Neural Representation (LRNR). The approach exploits the low rank structure within LRNR and constructs a reduced neural network approximation that is much smaller in size. We call the smaller network FastLRNR. We show that backpropagation of FastLRNR can be substituted for that of LRNR, enabling a significant reduction in complexity. We apply SPInProp to a physics informed neural networks framework and demonstrate how the solution of parametrized partial differential equations is accelerated.

翻译：本文提出稀疏物理信息反向传播（SPInProp）——一种用于加速特定神经网络架构（称为低秩神经表示，LRNR）反向传播过程的新方法类别。该方法利用LRNR内部的低秩结构，构建了一个规模显著减小的简化神经网络近似模型，我们将其命名为快速低秩神经表示（FastLRNR）。我们证明，可以用FastLRNR的反向传播替代LRNR的反向传播，从而实现计算复杂度的大幅降低。我们将SPInProp应用于物理信息神经网络框架，并展示了参数化偏微分方程求解过程的加速效果。