Deep learning: Extrapolation tool for ab initio nuclear theory
This work addresses a domain-specific challenge in nuclear physics by providing a novel extrapolation tool for observables like energy and radius, which is incremental as it builds on existing ab initio methods but introduces machine learning for improved handling of uncertainties.
The paper tackles the problem of extrapolating ab initio nuclear theory results from finite to infinite basis spaces, proposing a feed-forward artificial neural network method to predict ground state energy and point-proton root-mean-square radius for $^6$Li with associated uncertainties, achieving results comparable to other extrapolation methods.
Ab initio approaches in nuclear theory, such as the no-core shell model (NCSM), have been developed for approximately solving finite nuclei with realistic strong interactions. The NCSM and other approaches require an extrapolation of the results obtained in a finite basis space to the infinite basis space limit and assessment of the uncertainty of those extrapolations. Each observable requires a separate extrapolation and most observables have no proven extrapolation method. We propose a feed-forward artificial neural network (ANN) method as an extrapolation tool to obtain the ground state energy and the ground state point-proton root-mean-square (rms) radius along with their extrapolation uncertainties. The designed ANNs are sufficient to produce results for these two very different observables in $^6$Li from the ab initio NCSM results in small basis spaces that satisfy the following theoretical physics condition: independence of basis space parameters in the limit of extremely large matrices. Comparisons of the ANN results with other extrapolation methods are also provided.