Self-learning Monte Carlo (SLMC) method is a general-purpose numerical method to simulate many-body systems. SLMC can efficiently cure the critical slowing down in both bosonic and fermionic systems. Moreover, for fermionic systems, SLMC can generally reduce the computational complexity and speed up simulations even away from the critical points. For example, SLMC is more than 1000 times faster than the conventional method for the double exchange model in 8*8*8 cubic lattice. In addition, SLMC also provides a general framework to naturally integrate the advanced machine learning techniques into Monte Carlo. In this talk, I will give an introduction about the background, basic idea and the design principle of SLMC. Later, I will explicitly show how to use SLMC and its great accelerations in classic systems, free fermions coupled with classical spins systems, and interacting fermion systems. At the end, I will talk our recent developed all optical neural networks, which can realize the intrinsic parallel calculations at the speed of light and are expected outperform the electronic neural networks with large system size.

References:

[1] Self-Learning Monte Carlo Method, PRB 95, 041101(R) (2017) 

[2] Accelerated Monte Carlo simulations with restricted Boltzmann machines, PRB 95, 035105 (2017)

[3] Self-Learning Monte Carlo Method in Fermion Systems, PRB 95, 241104(R) (2017)

[4] Self-learning Monte Carlo with Deep Neural Networks, PRB 97, 205140 (2018)

[5] All optical neural network with nonlinear activation functions, Optica 6, 1132-1137 (2019)