Neural Network Extrapolation of Many Body Methods on Infinite Matter Systems

Computational methods for many-body nuclear theory such as many body perturbation theory (MBPT) and the coupled cluster theory (CC)are useful for exploring concrete properties of many body systems, such as the energy or the correlation energy. However, due to the scaling computational cost of these methods, it is often prohibitively time-consuming to execute these methods on larger systems of interest to a convergent value with respect to single particle states. MBPT and CC correlation energies were generated for the pairing model, as a simple test case, and for the infinite electron gas, as the two models have analytical results of their energies. Trained using this data from converged systems, various neural network routines were created to find the convergent value given only the first several results of these computational methods and basic properties of the many body systems. With these routines, it will be possible to estimate properties such as the energy of a many body system that is of a scale beyond what can be reasonably computationally modeled. Comparisons to the runtime for the true calculation versus generating the calculated convergent methods will also be presented to justify the use of neural network. With these infinite systems, we hope to extrapolate to the thermodynamic limit.