A versatile framework to solve the Helmholtz equation using physics-informed neural networks

SUMMARY Solving the wave equation to obtain wavefield solutions is an essential step in illuminating subsurface using seismic imaging and waveform inversion methods. Here, we utilize a recently introduced machine-learning based framework called physics-informed neural networks (PINNs) solve frequency-domain equation, which also referred as Helmholtz for isotropic anisotropic media. Like functions, PINNs are formed by fully connected network (NN) provide solution at spatial points domain of interest, coordinates point form input network. We train such backpropagating misfit output values their derivatives many model space. Generally, hyperbolic tangent activation used with PINNs, however, use adaptive sinusoidal function optimize training process. Numerical results show that functions able generate satisfy equations. flexibility versatility proposed method various media, including anisotropy, models strong irregular topography.