Modeling of wave propagation in space-time dependent materials using physics-informed neural networks

Physics-informed neural networks (PINNs) are neural networks whose training is regularized to (approximately) satisfy the governing partial-differential equations (PDEs). The coordinates and number of points in the solution domain at which the underlying PDEs should be satisfied can be freely chosen, making it possible to train a network to learn a solution well outside the range of the input data. I show that it is feasible to model waves in space-time dependent materials using PINNs. For the general case of wave propagation in space-time dependent materials, additional field quantities must be considered in the equation of motion and the stress–strain relation, and the system of first-order partial differential equations must be complemented by constitutive equations. These constitutive equations relations relate the additional field quantities to the usual field quantities through the space-time dependent material properties. The consitutive equations are implemented as additional, higher-weight loss terms in the PINN. For space-time materials with continuously varying properties, no boundary conditions are needed to supplement the equations. Furthermore, no solution direction or causality conditions are imposed when training the PINN. I show that the PINN recovers known solutions for space- and time-dependent media and unknown solutions for general space-time dependent media.