Matrix Model Emulators

Presenting a novel approach to a pervasive issue in quantum physics: the determination of extremal eigenvalues of an excessively large Hamiltonian matrix. Existing techniques, ranging from Monte Carlo simulations to variational methods, often fail when a control parameter in the Hamiltonian matrix reach beyond certain limits. The focus of this study is on a new class of implicit deep learning algorithms, termed Matrix Model Emulators (MMEs). Emulators have the potential of bypassing the computational burdens of complex scientific calculations without compromising accuracy. MMEs is a form of Machine Learning that originally was designed to leverage the structure of eigenvector continuation, enabling the calculation of extremal eigenvalues and other observables without the explicit formation of norm and Hamiltonian matrices. However, MME can be seen as a new implicit deep learning architecture. Showcasing a subset of MMEs known as Matrix Eigenvalue Emulators (MEEs) on an array of nuclear physics Hamiltonians and MMEs on a selection of challenging interpolation problems. Furthermore, reveal MMEs/MEEs effectiveness in identifying branch points in the complex plane. The results offer valuable insights for further development and potential applications of MMEs in nuclear physics and beyond.