论文标题
Cophy-PGNN:学习物理引导的神经网络具有竞争性损失功能,以解决特征值问题
CoPhy-PGNN: Learning Physics-guided Neural Networks with Competing Loss Functions for Solving Eigenvalue Problems
论文作者
论文摘要
物理学指导的神经网络(PGNN)代表了一类新兴的神经网络,这些神经网络经过物理引导(PG)损失功能(在具有已知物理学的网络输出中捕获违规),以及数据中包含的监督。 PGNN中的现有工作证明了使用恒定的权衡参数在神经网络目标中添加单个PG损失函数的功效,以确保更好的推广性。但是,在具有竞争性梯度方向的多个PG功能的情况下,需要在培训过程中适应不同的PG损失功能的贡献,以达到可推广的解决方案。我们证明了在通用神经网络问题中存在竞争性PG损失的存在,该问题是在基于物理学的特征值方程的最低(或最高)特征向量解决的,这在许多科学问题中通常遇到。我们提出了一种处理竞争性PG损失的新方法,并证明了其在两种激励量子力学和电磁传播的激励应用中学习概括的解决方案的功效。这项工作中使用的所有代码和数据均可在https://github.com/jayroxis/cophy-pgnn上获得。
Physics-guided Neural Networks (PGNNs) represent an emerging class of neural networks that are trained using physics-guided (PG) loss functions (capturing violations in network outputs with known physics), along with the supervision contained in data. Existing work in PGNNs has demonstrated the efficacy of adding single PG loss functions in the neural network objectives, using constant trade-off parameters, to ensure better generalizability. However, in the presence of multiple PG functions with competing gradient directions, there is a need to adaptively tune the contribution of different PG loss functions during the course of training to arrive at generalizable solutions. We demonstrate the presence of competing PG losses in the generic neural network problem of solving for the lowest (or highest) eigenvector of a physics-based eigenvalue equation, which is commonly encountered in many scientific problems. We present a novel approach to handle competing PG losses and demonstrate its efficacy in learning generalizable solutions in two motivating applications of quantum mechanics and electromagnetic propagation. All the code and data used in this work is available at https://github.com/jayroxis/Cophy-PGNN.