arXiv:2610.20622v1 Announce Type: new Abstract: Physical experiments frequently result in inverse problems, where the recorded response is used to deduce information about the sample, typically yielding only partial recovery. This work presents a reverse Monte Carlo modeling method for solving such problems involving statistical averaging, e.g. at the nanoscale. The proposed algorithm operates in an input subspace of the forward problem, with dimensions reduced from those of the original input space. The dimensionality reduction focuses on features that influence the response, as irrelevant information is lost in the process. We first study the performance of the method in tailored test cases that also reveal information loss when several input characteristics produce similar responses. Finally, we apply the method to a previously published simulated dataset of X-ray absorption, X-ray emission, and X-ray photoelectron spectra of the water molecule.