Abstract
In this paper, we extend the previous method for solving inverse problems for PDEs using the Generalized Collage Theorem by searching for a set of coefficients that not only minimizes the collage error but also maximizes the entropy. In this extended formulation, the parameter estimation minimization problem can be understood as a multi-criteria problem, with two different and conflicting criteria, the generalized collage error and entropy associated with the unknown parameters. We use the typical approach of scalarization to reduce the multi-criteria program to a single-criteria program by combining all objective functions with different trade-off weights. Numerical examples confirm that the collage method produces good, but sub-optimal, results, and that adding a relatively low-weighted entropy term helps us obtain a better approximation.
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