Deforming them is tricky and the deformations must be integrated into the actual model. That is, without something like a non-linear deformation space, as this paper talks about.

Lawrence J. Christiano, Solving the Stochastic Growth Model by Linear-Quadratic Approximation and by Value-Function Iteration, Journal of Business & Economic Statistics, Vol. 8, No. 1 (Jan., 1990), pp ...

A number of statistical techniques to analyze and model coastal morphological evolution over yearly and decadal (i.e., long-term) time scales based on field data are presented. After a general ...