Theoretical Nuclear Physics and Machine Learning
Coupled-Cluster Calculations of Infinite Nuclear Matter in the Complete Basis Limit Using Bayesian Machine Learning
- Authors: Julie Butler, Morten Hjorth-Jensen, Gustav R. Jansen
- ArXiV pre-print; Submitted to Physical Review C
- Abstract: Infinite nuclear matter provides valuable insights into the behavior of nuclear systems and aids our understanding of atomic nuclei and large-scale stellar objects such as neutron stars. However, partly due to the large basis needed to converge the system’s binding energy, size-extensive methods such as coupled-cluster theory struggle with long computational run times, even using the nation’s largest high-performance computing facilities. This research introduces a novel approach to the problem. We propose using a machine learning method to predict the coupled-cluster energies of infinite matter systems in the complete basis limit, leveraging only data collected using smaller basis sets. This method promises to deliver high-accuracy results with significantly reduced run times. The sequential regression extrapolation (SRE) algorithm, based on Gaussian processes, was created to perform these extrapolations. By combining Bayesian machine learning with a unique method of formatting the training data, we can create a powerful extrapolator that can make accurate predictions given very little data. The SRE algorithm successfully predicted the CCD(T) energies for pure neutron matter across six densities near nuclear saturation density, with an average error of 0.0083 MeV/N. The algorithm achieved an average error of 0.038 MeV/A for symmetric nuclear matter. These predictions were made with a time savings of 83.8 node hours for pure neutron matter and 284 node hours for symmetric nuclear matter. Additionally, the symmetry energy at these six densities was predicted with an average error of 0.031 MeV/A and a total time savings of 368 node hours compared to the traditional converged coupled-cluster calculations performed without the SRE algorithm.
Accelerating the Convergence of Coupled Cluster Calculations of the Homogeneous Electron Gas Using Bayesian Ridge Regression
- Authors: Julie Butler, Morten Hjorth-Jensen, Justin Lietz
- ArXiV pre-print; Accepted for publication in The Journal of Chemical Physics
- Abstract: The homogeneous electron gas is a system which has many applications in chemistry and physics. However, its infinite nature makes studies at the many-body level complicated due to long computational run times. Because it is size extensive, coupled cluster theory is capable of studying the homogeneous electron gas, but it still poses a large computational challenge as the time needed for precise calculations increases in a polynomial manner with the number of particles and single-particle states. Consequently, achieving convergence in energy calculations becomes challenging, if not prohibited, due to long computational run times and high computational resource requirements. This paper develops the sequential regression extrapolation (SRE) to predict the coupled cluster energies of the homogeneous electron gas in the complete basis limit using Bayesian ridge regression to make predictions from calculations at truncated basis sizes. Using the SRE method we were able to predict the coupled cluster doubles energies for the electron gas across a variety of values of N and rₛ, for a total of 70 predictions, with an average error of 4.28x10⁻⁴ Hartrees while saving 88.9 hours of computational time. The SRE method can accurately extrapolate electron gas energies to the complete basis limit, saving both computational time and resources. Additionally, the SRE is a general method that can be applied to a variety of systems, many-body methods, and extrapolations.
Computing in Physics Education