This short note describes the concept of guided training of deep neural networks (DNNs) to learn physically reasonable solutions. DNNs are being widely used to predict phenomena in physics and mechanics. One of the issues of DNNs is that their output does not always satisfy physical equations. One approach to consider physical equations is adding a residual of equations into the loss function; this is called physics-informed neural network (PINN). One feature of PINNs is that the physical equations and corresponding residual must be implemented as part of a neural network model. In addition, the residual does not always converge to a small value. The proposed model is a physics-guided generative adversarial network (PG-GAN) that uses a GAN architecture in which physical equations are used to judge whether the neural network's output is consistent with physics. The proposed method was applied to a simple problem to assess its potential usability.

This has many applications, such as hydrogeology and geologic carbon dioxide sequestration. The imaging portion of the task can be costly because high-resolution images of 3D rocks often must be pieced-together by taking many images of 2D rock slices. You et al. [2021] utilize a machine learning technique called a "progressive growing generative adversarial network" (or PG-GAN) to reduce the cost of producing high-resolution 3D rock images. The PG-GAN learns to generate realistic, high-dimensional rock images from noise in a low-dimensional space. A given rock image can be reconstructed by finding an optimal point in the low-dimensional space.