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Solving the wave equation numerically constitutes the majority of thecomputational cost for applications like seismic imaging and full waveforminversion. An alternative approach is to solve the frequency domain Helmholtzequation, since it offers a reduction in dimensionality as it can be solved perfrequency. However, computational challenges with the classical Helmholtzsolvers such as the need to invert a large stiffness matrix can make theseapproaches computationally infeasible for large 3D models or for modeling highfrequencies. Moreover, these methods do not have a mechanism to transferinformation gained from solving one problem to the next. This becomes abottleneck for applications like full waveform inversion where repeatedmodeling is necessary. Therefore, recently a new approach based on the emergingparadigm of physics informed neural networks (PINNs) has been proposed to solvethe Helmholtz equation. The method has shown promise in addressing severalchallenging associated with the conventional algorithms, including flexibilityto model additional physics and the use of transfer learning to speed upcomputations. However, the approach still needs further developments to befully practicable. Foremost amongst the challenges is the slow convergencespeed and reduced accuracy, especially in presence of sharp heterogeneities inthe velocity model. Therefore, with an eye on exploring how improvedconvergence can be obtained for the PINN Helmholtz solvers, we study differentactivation functions routinely used in the PINN literature, in addition to theswish activation function - a variant of ReLU that has shown improvedperformance on a number of data science problems. Through a comparative study,we find that swish yields superior performance compared to the other activationfunctions routinely used in the PINN literature.

Is it time to swish? Comparing activation functions in solving the Helmholtz equation using physics-informed neural networks