  Recently, Physics-Informed Neural Networks (PINNs) have gained significant
attention for their versatile interpolation capabilities in solving partial
differential equations (PDEs). Despite their potential, the training can be
computationally demanding, especially for intricate functions like wavefields.
This is primarily due to the neural-based (learned) basis functions, biased
toward low frequencies, as they are dominated by polynomial calculations, which
are not inherently wavefield-friendly. In response, we propose an approach to
enhance the efficiency and accuracy of neural network wavefield solutions by
modeling them as linear combinations of Gabor basis functions that satisfy the
wave equation. Specifically, for the Helmholtz equation, we augment the fully
connected neural network model with an adaptable Gabor layer constituting the
final hidden layer, employing a weighted summation of these Gabor neurons to
compute the predictions (output). These weights/coefficients of the Gabor
functions are learned from the previous hidden layers that include nonlinear
activation functions. To ensure the Gabor layer's utilization across the model
space, we incorporate a smaller auxiliary network to forecast the center of
each Gabor function based on input coordinates. Realistic assessments showcase
the efficacy of this novel implementation compared to the vanilla PINN,
particularly in scenarios involving high-frequencies and realistic models that
are often challenging for PINNs.
