Exctracting Non-Perturbative Ground States from First-Order Perturbation of Monte Carlo Lattice Simulations

We present the application of Parametric Matrix Models (PMMs), a novel machine learning framework designed for scientific computing, to imaginary-time evolution in quantum Monte Carlo (QMC) lattice simulations. PMMs excel at extracting accurate physical predictions from limited or computationally expensive datasets. First, we demonstrat that PMMs trained on synthetic Lattice Effective Field Theory (EFT) data can successfully extrapolate non-perturbative ground-state properties using only first-order perturbative imaginary-time data. The PMM accurately recovers the ground-state energy, its derivative with respect to a coupling constant, other observables in the ground state, and remarkably, even the first excited state. By implicitly learning from early-time data, typically "contaminated" by excited-state contributions, PMMs uniquely extract information about low-lying states. By applying this approach to computationally intensive QMC datasets, we aim to extend ab initio nuclear predictions into regimes currently inaccessible to conventional methods, offering direct comparison with experimental results and advancing the reach of modern nuclear theory to heavier nuclei.