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A two-way parabolic equation (2W-PE) method based on machine learning is proposed to predict the spatial field strength of radio waves propagating over undulating terrain. The method first performs longitudinal domain decomposition on a step distance, and uses different algorithms to solve the 2W-PE in each subdomain. Then, a simple obstacle model (SOM) containing three stepping units of different heights is introduced. A variety of undulating terrains can be approximated using the overlay combinations and lateral extensions of multiple SOMs, and combined with machine learning method, the boundary condition coefficients in different environments can be determined. The simulation results show that the proposed 2W-PE method is in good agreement with the method of moments (MoM), which verifies its accuracy and superiority.

Predicting Spatial Field Values Under Undulating Terrain With 2W-PE Based on Machine Learning