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Inverse problems involve for example reconstruction of an object based on physical measurements and finding a best model/parameters out of a family given observed data. Typically the corresponding "forward" problems are well-posed and can be solved straightforwardly, while the inverse problems are often ill-posed. Not to be confused with the (inverse) tag.
2
votes
Can one hear the shape of a drum for operators?
I think this question is ill-posed, because you cannot consider the same operator on different domains (i.e. on different $L^2(\Omega)$ spaces). Hence you would have to require a certain "functorialit …