论文标题
神经Schrödinger方程：作为神经网络的物理定律
Neural Schrödinger Equation:Physical Law as Neural Network
论文作者
论文摘要
我们根据Schrödinger方程（SE-NET）展示了一个新的神经网络家族。以此类比，神经网络的可训练权重对应于Schrödinger方程的物理量。这些物理量可以使用复杂值的伴随法训练。由于可以通过物理系统的演变来描述SE-NET的传播，因此可以使用物理求解器计算其输出。作为演示，我们使用有限差方法实现了SE-NET。训练有素的网络可转移到实际的光学系统。基于这个概念，我们通过光前端展示了端到端机器学习的数值演示。我们的结果将机器学习的应用领域扩展到混合物理数字优化。
We show a new family of neural networks based on the Schrödinger equation (SE-NET). In this analogy, the trainable weights of the neural networks correspond to the physical quantities of the Schrödinger equation. These physical quantities can be trained using the complex-valued adjoint method. Since the propagation of the SE-NET can be described by the evolution of physical systems, its outputs can be computed by using a physical solver. As a demonstration, we implemented the SE-NET using the finite difference method. The trained network is transferable to actual optical systems. Based on this concept, we show a numerical demonstration of end-to-end machine learning with an optical frontend. Our results extend the application field of machine learning to hybrid physical-digital optimizations.
