Physical Symmetries Embedded in Neural Networks

Artificial neural networks (ANNs) have become indispensable tools in many machine learning applications and in recent years, ANNs have become an active area of research in the physical sciences. An important consideration for building ANNs for scientific applications is how to incorporate non-negotiable physical constraints. We propose ANNs with embedded physical symmetries including even-odd symmetry, time-reversibility, positivity, energy-momentum conservation, and Galilean invariance. We constrain the weights of the NN so that the physical properties are exactly satisfied by the neural network output. Furthermore, embedding constraints into the NN can drastically reduce the search space thereby providing an efficient deep learning architecture.