PEST

PEST, by John Doherty of Watermark Numerical Computing, is the tool that made rigorous calibration routine in groundwater practice. It treats any model as a black box — communicating through the model's own input and output files — and performs gradient-based parameter estimation, regularised inversion with pilot points, and predictive uncertainty analysis.

Its concepts (Tikhonov regularisation, highly parameterised inversion) define how the industry thinks about calibration, and its file protocols are supported by every serious groundwater GUI. The newer PEST++ suite reimplements and extends the ideas with iterative-ensemble methods; both remain free.