论文标题
PDE-NETGEN 1.0：从物理过程的符号PDE表示到可训练的神经网络表示
PDE-NetGen 1.0: from symbolic PDE representations of physical processes to trainable neural network representations
论文作者
论文摘要
桥接物理和深度学习是一个局部挑战。虽然深度学习框架开放了物理科学的途径，但物理上一致的深神经网络体系结构的设计是一个开放的问题。本着物理知识的NNS的精神，PDE-NETGEN软件包提供了新的手段，可以将作为PDE的物理方程自动转换为神经网络体系结构。 PDE-NETGEN结合了符号演算和神经网络发生器。后来利用KERAS利用基于NN的PDE求解器实现。有了一些问题，PDE-NETGEN是生成物理知识的NN体系结构的插件工具。它们提供计算效率却紧凑的表示，以解决各种问题，包括伴随推导，模型校准，预测，数据同化以及不确定性量化。作为例证，首先为2D扩散方程式提供了工作流程，然后将其应用于汉堡方程的不确定性动力学的数据驱动和物理信息识别。
Bridging physics and deep learning is a topical challenge. While deep learning frameworks open avenues in physical science, the design of physically-consistent deep neural network architectures is an open issue. In the spirit of physics-informed NNs, PDE-NetGen package provides new means to automatically translate physical equations, given as PDEs, into neural network architectures. PDE-NetGen combines symbolic calculus and a neural network generator. The later exploits NN-based implementations of PDE solvers using Keras. With some knowledge of a problem, PDE-NetGen is a plug-and-play tool to generate physics-informed NN architectures. They provide computationally-efficient yet compact representations to address a variety of issues, including among others adjoint derivation, model calibration, forecasting, data assimilation as well as uncertainty quantification. As an illustration, the workflow is first presented for the 2D diffusion equation, then applied to the data-driven and physics-informed identification of uncertainty dynamics for the Burgers equation.
