Self-organizing maps with multiple input-output option for modeling the Richards equation and its inverse solution

Inverse solutions of the Richards equation, either for evaluating soil hydraulic parameters from experimental data or for optimizing irrigation parameters, require considerable numerical effort. We present an alternative methodology based on self‐organizing maps (SOM) which was further developed in order to include multiple input‐output (MIO) relationships. The resulting SOM‐MIO network approximates the Richards equation and its inverse solution with an outstanding accuracy, and both tasks can be performed by the same network. No additional training is required for solving the different tasks, which represents a significant advantage over conventional networks. An application of the SOM‐MIO simulating a laboratory irrigation experiment in a Monte Carlo–based framework shows a much improved computational efficiency compared to the used numerical simulation model. The high consistency of the results predicted by the artificial neural network and by the numerical model demonstrates the excellent suitability of the SOM‐MIO for dealing with such kinds of stochastic simulation or for solving inverse problems.