On-the-fly machine learning algorithm for accelerating Monte Carlo sampling: Application to the stochastic analytical continuation

We present a new Monte Carlo method whose sampling is assisted by modern machine learning (ML) technique. In order to improve the MC sampling efficiency in high dimensional problems, we suggest ML generative model as being a part of MC sampler. We apply this ML+MC method to a long-standing numerical problem in quantum many-body physics, namely, analytic continuation. In our scheme, ML sampler naturally satisfies physical constraints such as detailed balance because it is combined with the conventional Markov chain MC procedure. Furthermore, massive data sets generated by MC procedure provides the on-the-fly ‘learnings’ for ML sampler. Remarkable improvement has been achieved in terms of both convergence speed and the quality of continuation result. The same approach can be applicable to various other problems for which MC algorithm has been used.