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Abstract

We are interested in exploring the laws of interaction between atoms and molecules. In this thesis, we construct a model to predict the many-body interaction potential between atoms, given the averaged total potentials in an atomic cluster. This is an inverse problem because we are fitting against averaged observations of energy between many-body interactions. In a simplified setting with identically and independently distributed data, and defining an averaged basis that has the appropriate orthogonal property, the inverse problem is well-posed and can be solved with the least squares approximations in a numerically stable way. We perform numerical analysis to estimate the parameters and study the convergence of the approximation. Two-body and three-body interactions potential are studied as a motivation to generalize the framework for higher-order many-body interaction potentials with tensor product bases in the future.