Calibration of aquifer models using neural network parameterization with a simple regularization

A parameterization of transmissivity based on neural networks is developed. By defining an appropriate network topology it is possible to express the two-dimensional transmissivity map as a sum of one-dimensional functions similarly to the turning bands method. By selecting appropriate neural activation functions it is possible to get flexible and concise parameterizations that can handle gradual as well as abrupt large-scale changes of the real transmissivity map. A simple regularization is proposed that can dampen the erratic high frequency components in the estimated parameters. Various examples indicate that the proposed parameterization can handle well various types of transmissivity variations and is particularly suited when the true transmissivity map exhibits specific sorts of heterogeneity with large anisotropies or abrupt changes along lines.