PDE-NetGen 1.0：从物理过程的符号PDE表示到可训练神经网络表示
PDE-NetGen 1.0: from symbolic PDE representations of physical processes to trainable neural network representations
摘要：
将物理学和深度学习联系起来是一个热门的挑战。虽然深度学习框架为物理科学开辟了道路，但物理上一致的深度神经网络架构的设计仍然是一个悬而未决的问题。在物理学知识的神经网络的精神，PDE-NetGen包提供了新的方法来自动转换物理方程，作为PDE，到神经网络架构。PDE-NetGen结合了符号演算和神经网络生成器。后者利用了使用Keras的PDE求解器的基于NN的实现。通过对问题的一些了解，PDE-NetGen是一个即插即用的工具，可以生成物理信息的NN架构。它们提供了计算效率高但紧凑的表示，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等。作为一个例子，工作流程首先提出了二维扩散方程，然后应用到数据驱动和物理信息的不确定性动力学的伯格斯方程的识别。
英文摘要：
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.
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