Machine learning augmented Tikhonov regularization with iterative approach for stable neutron spectrum unfolding

A hybrid multi-stage algorithm is developed for solving the ill-posed inverse problem of unfolding the neutron energy spectrum from multi-sphere Bonner spectrometer measurements. Traditional approaches, such as Tikhonov regularization and iterative methods, have significant limitations due to the subjective choice of the regularization parameter or initial approximation, which compromises the solution's stability and accuracy. In the proposed method, the first stage automated machine learning (autoML) is used to find the optimal model to predict the global spectral shape. The second stage applies Tikhonov regularization, where regularization parameter is objectively optimized based on a similarity metric relative to the autoML prediction. The smoothing functional is minimized using convex optimization techniques. The third stage utilizes the obtained solution as the initial guess for an iterative refinement procedure. Physical prior knowledge is incorporated both through a parametrically generated training dataset (weighted sums of fission, evaporation, Gaussian, and high-energy spectral components). The hybrid approach demonstrates superior robustness to noisy input data compared to methods using solely Tikhonov regularization or machine learning. The developed methodology is applicable to neutron dosimetry at high-energy nuclear facilities and for solving a broad class of inverse problems described by Fredholm integral equations of the first kind.