  High-frequency issues have been remarkably challenges in numerical methods
for partial differential equations. In this paper, a learning based numerical
method (LbNM) is proposed for Helmholtz equation with high frequency. The main
novelty is using Tikhonov regularization method to stably learn the solution
operator by utilizing relevant information especially the fundamental
solutions. Then applying the solution operator to a new boundary input could
quickly update the solution. Based on the method of fundamental solutions and
the quantitative Runge approximation, we give the error estimate. This
indicates interpretability and generalizability of the present method.
Numerical results validates the error analysis and demonstrates the
high-precision and high-efficiency features.
