Physics-Informed Machine Learning for the Inverse Design of Wave Scattering Clusters

Clusters of wave-scattering oscillators offer the ability to passivelycontrol wave energy in elastic continua. However, designing such clusters toachieve a desired wave energy pattern is a highly nontrivial task. While theforward scattering problem may be readily analyzed, the inverse problem is verychallenging as it is ill-posed, high-dimensional, and known to admit non-uniquesolutions. Therefore, the inverse design of multiple scattering fields andremote sensing of scattering elements remains a topic of great interest.Motivated by recent advances in physics-informed machine learning, we develop adeep neural network that is capable of predicting the locations of scatterersby evaluating the patterns of a target wavefield. We present a modeling andtraining formulation to optimize the multi-functional nature of our network inthe context of inverse design, remote sensing, and wavefield engineering.Namely, we develop a multi-stage training routine with customized physics-basedloss functions to optimize models to detect the locations of scatterers andpredict cluster configurations that are physically consistent with the targetwavefield. We demonstrate the efficacy of our model as a remote sensing andinverse design tool for three scattering problem types, and we subsequentlyapplicability for designing clusters that direct waves along preferred paths orlocalize wave energy. Hence, we present an effective model for multiplescattering inverse design which may have diverse applications such as wavefieldimaging or passive wave energy control.