Estimating scattering potentials in inverse problems with Volterra series and neural networks

Abstract

Inverse problems often occur in nuclear physics, when an unknown potential has to be determined from the measured cross sections, phase shifts or other observables. In this paper, a data-driven numerical method is proposed to estimate the scattering potentials, using data, that can be measured in scattering experiments. The inversion method is based on the Volterra series representation, and is extended by a neural network structure to describe problems, which require a more robust estimation. The Volterra series method is first used to describe the one-dimensional scattering problem, where the transmission coefficients, and the phase shifts are used as inputs to determine the unknown potentials in the Fourier domain. In the second example the scattering process described by the radial Schrödinger equation is used to estimate the scattering potentials from the energy dependence of the phase shifts, where neural networks are used to describe the scattering problem. At the end, to show the capabilities of the proposed models, real-life data is used to estimate the $${}_{}^3 S_1$$ 3 S 1 NN potential with the neural network approach from measured phase shifts, where a few percent relative match is obtained between the measured values and the model calculations.

Constructing Inverse Scattering Potentials for α-α System using Physics Informed Machine Learning

“…This is akin to physics informed machine learning [16] wherein one obtains the inherent model from available data, either using a global optimisation algorithm [17] or neural networks [18], which is guided by the governing physical laws. Even though physics informed neural networks (PINNs) are increasingly becoming popular to address both forward and inverse problems in order to understand the hidden physics principles [19,20], there is a need to constantly evolve in terms of new frameworks as well as new mathematics for obtaining robust and rigorous next generation physics driven machine learning. Our work is inspired by inverse scattering theory which, inspite of being mathematically rigorous, has not been extensively applied to obtaining physical models due to non-availability of large amounts of data and inherent complexity in solving the underlying equations.…”