  The eigenvalue problem of quantum many-body systems is a fundamental and
challenging subject in condensed matter physics, since the dimension of the
Hilbert space (and hence the required computational memory and time) grows
exponentially as the system size increases. A few numerical methods have been
developed for some specific systems, but may not be applicable in others. Here
we propose a general numerical method, Random Sampling Neural Networks (RSNN),
to utilize the pattern recognition technique for the random sampling matrix
elements of an interacting many-body system via a self-supervised learning
approach. Several exactly solvable 1D models, including Ising model with
transverse field, Fermi-Hubbard model, and spin-$1/2$ $XXZ$ model, are used to
test the applicability of RSNN. Pretty high accuracy of energy spectrum,
magnetization and critical exponents etc. can be obtained within the strongly
correlated regime or near the quantum phase transition point, even the
corresponding RSNN models are trained in the weakly interacting regime. The
required computation time scales linearly to the system size. Our results
demonstrate that it is possible to combine the existing numerical methods for
the training process and RSNN to explore quantum many-body problems in a much
wider parameter regime, even for strongly correlated systems.
