Machine learning-based inversion of nuclear responses

TL;DR

This paper introduces a physics-informed neural network approach to invert Laplace transforms of nuclear response functions, improving accuracy over traditional methods for better understanding of nuclear electroweak interactions.

Contribution

The work develops a novel neural network architecture that effectively inverts Laplace transforms of nuclear responses, outperforming maximum entropy techniques.

Findings

Neural network outperforms maximum entropy in low-energy transfer regions.

Enables robust calculations of electron and neutrino scattering on nuclei.

Improves interpretation of neutrino oscillation experiments.

Abstract

A microscopic description of the interaction of atomic nuclei with external electroweak probes is required for elucidating aspects of short-range nuclear dynamics and for the correct interpretation of neutrino oscillation experiments. Nuclear quantum Monte Carlo methods infer the nuclear electroweak response functions from their Laplace transforms. Inverting the Laplace transform is a notoriously ill-posed problem; and Bayesian techniques, such as maximum entropy, are typically used to reconstruct the original response functions in the quasielastic region. In this work, we present a physics-informed artificial neural network architecture suitable for approximating the inverse of the Laplace transform. Utilizing simulated, albeit realistic, electromagnetic response functions, we show that this physics-informed artificial neural network outperforms maximum entropy in both the low-energy transfer and the quasielastic regions, thereby allowing for robust calculations of electron scattering and neutrino scattering on nuclei and inclusive muon capture rates.