Gradient-regularized physics informed neural networks for acoustic wave simulation Available to Purchase

Physics-informed neural networks (PINNs) are being extensively studied for their capabilities of solving complex partial differential equations (PDEs), including the acoustic wave equation. PINNs are capable of simulating seismic wave propagation without the need for discretization and can be modified to be resolution invariant, making them ideal tools for surrogate modeling in inverse problems. Despite the promise, PINNs often fail to converge and struggle with accuracy when solving multidimensional PDEs. We seek to address these shortcomings by implementing gradient-enhanced physicsinformed neural networks (termed g-PINNs). The enhancement involves augmenting the loss function of PINNs with regularization terms that involve the gradient of the governing equation with respect to the independent variables. We demonstrate that g-PINNs lead to a considerable improvement in convergence and accuracy for the acoustic wave equation with numerical examples.