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We have introduced a general method, dubbed self-learning Monte Carlo (SLMC), which speeds up the MC simulation by designing and training a model to propose efficient global updates. We have developed the SLMC in various kinds of systems for electrons[1], spins[2], atoms[3], and quarks and gluons[4].

For example, we proposed an efficient approach called self-learning hybrid Monte Carlo (SLHMC) method, which is a general method to make use of machine learning (ML) potentials to accelerate the statistical sampling of first principles density-functional-theory (DFT) simulations[3]. In the SLHMC simulation, the statistical ensemble is sampled exactly at the DFT level for a given thermodynamic condition. Meanwhile, the ML potential is improved on the fly by training to enhance the sampling, whereby the training dataset, which is sampled from the exact ensemble, is created automatically.

In this talk, I will show the basic concept of SLMC and various kinds of applications.

[1] YN, H. Shen, Y. Qi, J. Liu, and L. Fu, Self-Learning Monte Carlo Method: Continuous-Time Algorithm, Phys. Rev. B 96, 161102 (2017).; YN, M. Okumura, K. Kobayashi, and M. Shiga, Self-Learning Hybrid Monte Carlo: A First-Principles Approach, Phys. Rev. B 102, 041124 (2020).
[2] H. Kohshiro and YN, Effective Ruderman–Kittel–Kasuya–Yosida-like Interaction in Diluted Double-Exchange Model: Self-Learning Monte Carlo Approach, J. Phys. Soc. Jpn. 90, 034711 (2021).;YN and A. Tomiya, Self-Learning Monte Carlo with Equivariant Transformer, http://arxiv.org/abs/2306.11527.
[3] YN, M. Okumura, K. Kobayashi, and M. Shiga, Self-Learning Hybrid Monte Carlo: A First-Principles Approach, Phys. Rev. B 102, 041124 (2020).;K. Kobayashi, YN, M. Itakura, and M. Shiga, Self-Learning Hybrid Monte Carlo Method for Isothermal-Isobaric Ensemble: Application to Liquid Silica, J. Chem. Phys. 155, 034106 (2021).
[4] YN, A. Tanaka, and A. Tomiya, Self-Learning Monte Carlo for Non-Abelian Gauge Theory with Dynamical Fermions, Phys. Rev. D (2023).;Y. Nagai and A. Tomiya, Gauge Covariant Neural Network for 4 Dimensional Non-Abelian Gauge Theory, http://arxiv.org/abs/2103.11965.

Please access here for the registration.

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