SVD-Assist is powerful new model calibration methodology unique to PEST. SVD-Assist embodies a hybrid regularization methodology that combines the strengths of subspace and Tikhonov regularization methodologies. PEST can implement both subspace and Tikhonov methods independently or combine them together in a new hybrid technique that combines the advantages of both. This is described below. SVD-Assist can provide:

Here’s what you get with SVD-Assist.

• Ability to employ hundreds, even thousands, of parameters in the calibration process.
  This provides the ability to capture information from your hard-won dataset.

• Numerical stability. Even though hundreds of parameters may be featured in the inverse problem, the combined use of subspace and Tikhonov regularization techniques ensures the problem is tractable.

• Improved fits. The stability of the hybrid methodology ensures that different data types in different parts of the model domain can be fit equally well without the deleterious effects of high condition numbers that often degrade the applicability of highly-parameterized inversion schemes.

• Pleasing parameters. The use of Tikhonov schemes with reference to a preferred system condition guarantees that estimated parameter fields are physically, or otherwise, reasonable.

• Efficiency. You may be estimating hundreds of parameters – but the hybrid methodology ensures you may need as few as 50 model runs per iteration to estimate these parameters.

Parameter parsimony is often employed in environmental models due to the numerical instability and computational burden that comes with estimating a large number of parameters. However - in many other modeling applications, such as geophysical data analysis, petroleum well field simulation, medical image processing, regularized inversion of highly parameterized models is the norm, not the exception. This is because when model inversion is undertaken using an effective regularization scheme, the calibration process can be stabilized, and reasonable parameter values are estimated. Regularized inversion provides the ability to achieve a level of fit determined by the modeler, to ensure there is no over-fitting.

Furthermore, regularized inversion using the hybrid methodology allows the solution of the inverse problem to possess as many degrees of freedom as the data can sustain. This ensures that the gains inherent in parsimonious approaches are retained, without basing the inverse model on a-priori parameterizations that may artificially over-constrain the solution to a very limited volume within parameter space. The result is:

• flexibility of the calibration process to respond to information contained within the calibration dataset pertaining to system complexity

• the ability of the inverse process to automatically include heterogeneity in response to information contained in the calibration dataset

• reduced error variance of model predictions - because the calibrated parameter set occupies maximum sustainable degrees of freedom in parameter space. Put simply, predictions made with models calibrated through regularized inversion are likely to be
  more accurate.

SVD-assist is a breakthrough in calibration technology. When the efficiency gains of the method are combined with the execution speed of Parallel PEST, the result is that high-end, state-of-the-art calibration and predictive analysis can be applied to complex models with high run times.