Application of Automatic Differentiation to Groundwater Transport Models

Abstract

Automatic differentiation (AD) is a technique for generating efficient and reliable derivative codes from computer programs with a minimum of human effort. Derivatives of model output with respect to input are obtained exactly. No intrinsic limits to program length or complexity exist for this procedure. Calculation of derivatives of complex numerical models is required in systems optimization, parameter identification, and systems identification. We report on our experiences with the ADIFOR (Automatic Differentiation of Fortran) tool on a two-dimensional groundwater flow and contaminant transport finite-element model, ISOQUAD, and a three-dimensional contaminant transport finite-element model, TLS3D. Derivative values and computational times for the automatic differentiation procedure axe compared with values obtained from the divided differences and handwritten analytic approaches. We found that the derivative codes generated by ADIFOR provided accurate derivatives and ran significantly faster than divided-differences approximations, typically in a tenth of the CPU time required for the imprecise divided-differences method for both codes. We also comment on the impact of automatic differentiation technology with respect to accelerating the transfer of general techniques developed for using water resource computer models, such as optimal design, sensitivity analysis, and inverse modeling problems to field problems.