论文标题
ADCME：使用深神经网络学习空间变化的物理领域
ADCME: Learning Spatially-varying Physical Fields using Deep Neural Networks
论文作者
论文摘要
ADCME是一个新的计算框架，可解决涉及物理模拟和深神经网络（DNN）的反问题。本文基于使用DNN学习空间变化的物理领域的能力。我们证明，与在线性或非线性，静态或动态的各种问题上的离散化方法相比，我们的方法具有较高的精度。从技术上讲，我们将逆问题提出为PDE受限的优化问题。我们使用计算图同时表达数值模拟和DNN，因此，我们可以使用反向模式自动分化来计算梯度。我们应用了一个受约束的学习算法（PCL），通过迭代求解器的非线性方程有效地向后渐变。随附本文附带的开源软件可以在https://github.com/kailaix/adcme.jl上找到。
ADCME is a novel computational framework to solve inverse problems involving physical simulations and deep neural networks (DNNs). This paper benchmarks its capability to learn spatially-varying physical fields using DNNs. We demonstrate that our approach has superior accuracy compared to the discretization approach on a variety of problems, linear or nonlinear, static or dynamic. Technically, we formulate our inverse problem as a PDE-constrained optimization problem. We express both the numerical simulations and DNNs using computational graphs and therefore, we can calculate the gradients using reverse-mode automatic differentiation. We apply a physics constrained learning algorithm (PCL) to efficiently back-propagate gradients through iterative solvers for nonlinear equations. The open-source software which accompanies the present paper can be found at https://github.com/kailaix/ADCME.jl.
