Imposing physical constraints on neural networks as a method of knowledge
embedding has achieved great progress in solving physical problems described by
governing equations. However, for many engineering problems, governing
equations often have complex forms, including complex partial derivatives or
stochastic physical fields, which results in significant inconveniences from
the perspective of implementation. In this paper, a scientific machine learning
framework, called AutoKE, is proposed, and a reservoir flow problem is taken as
an instance to demonstrate that this framework can effectively automate the
process of embedding physical knowledge. In AutoKE, an emulator comprised of
deep neural networks (DNNs) is built for predicting the physical variables of
interest. An arbitrarily complex equation can be parsed and automatically
converted into a computational graph through the equation parser module, and
the fitness of the emulator to the governing equation is evaluated via
automatic differentiation. Furthermore, the fixed weights in the loss function
are substituted with adaptive weights by incorporating the Lagrangian dual
method. Neural architecture search (NAS) is also introduced into the AutoKE to
select an optimal network architecture of the emulator according to the
specific problem. Finally, we apply transfer learning to enhance the
scalability of the emulator. In experiments, the framework is verified by a
series of physical problems in which it can automatically embed physical
knowledge into an emulator without heavy hand-coding. The results demonstrate
that the emulator can not only make accurate predictions, but also be applied
to similar problems with high efficiency via transfer learning.

提出一种名为 AutoKE 的科学机器学习框架，利用神经网络、方程解析器、神经结构搜索和迁移学习等技术，实现了将物理知识嵌入预测模型的自动化，解决了应用物理方程问题中的编程难题。