Abstract In this paper, the physics informed neural network (PINN) deep learning method is applied to solve the two dimensional nonlocal equations including partial reverse space y-nonlocal Mel'nikov equation, partial reverse space-time nonlocal Mel'nikov equation and nonlocal two dimensional NLS equation. By PINN method, we successfully derive data-driven two soliton solution, lump solution and rogue wave solution. Numerical simulation results indicate that the error range between the data-driven solution and the exact solution is relatively small, which verifies the effectiveness of the PINN deep learning method for solving high dimensional nonlocal equation.
Moreover, the parameter discovery of the partial reverse space-time nonlocal Mel'nikov equation is analysed in terms of its soliton solution for the first time.