Abstract
<jats:p>This paper investigates the feasibility of using Kolmogorov–Arnold neural networks (KANs) to solve the two-dimensional Helmholtz equation for an inhomogeneous medium in the frequency domain. The formulation is constructed for a scattered field, which allows us to analytically isolate the singular part associated with a point source and approximate only the smooth component of the background solution using the neural network. The background field is chosen as the fundamental solution via the Hankel function of the second kind, and a consistent Sommerfeld boundary condition is imposed at the outer boundary. The complex solution is represented by two network outputs, corresponding to the real and imaginary parts. The loss function includes the equation residual in the domain, the boundary condition residual, and a stabilizing contribution in the vicinity of the source. The first- and second-order derivatives are calculated using automatic differentiation. Numerical experiments were performed for the Marmousi geological model. High-quality agreement was achieved between the predicted and reference solutions, as assessed using two-dimensional field maps. Training one model for a fixed setup took approximately two hours on an RTX 5070 Ti GPU. The results demonstrate the fundamental feasibility of applying the KAN approach to frequency-domain wave field modeling.</jats:p>