Self-learning Monte Carlo method

By Junwei Liu, Yang Qi, Z. Meng, Liang Fu. 2016

200 citations recorded by the source corpus.

Monte Carlo simulation is an unbiased numerical tool for studying classical and quantum many-body systems. One of its bottlenecks is the lack of a general and efficient update algorithm for large size systems close to the phase transition, for which local updates perform badly. In this Rapid Communication, we propose a general-purpose Monte Carlo method, dubbed self-learning Monte Carlo (SLMC), in which an efficient update algorithm is first learned from the training data generated in trial simulations and then used to speed up the actual simulation. We demonstrate the efficiency of SLMC in a spin model at the phase transition point, achieving a 10\char21{}20 times speedup.

Subfields: Artificial Intelligence, Condensed Matter Physics, Materials Chemistry, Probabilistic & Bayesian Methods, AI for Physical Sciences

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. E. Weinan
2. Linfeng Zhang
3. Lei Wang
4. Xiaopeng Li
5. Dong-Ling Deng
6. Giuseppe Carleo
7. Matthias Troyer
8. Juan Felipe Carrasquilla

In Condensed Matter Physics

1. E. Weinan
2. Linfeng Zhang
3. Lei Wang
4. Giuseppe Carleo
5. Matthias Troyer
6. Roger G. Melko
7. Juan Felipe Carrasquilla
8. Xiaopeng Li

In Materials Chemistry

1. Giuseppe Carleo
2. Xiaopeng Li
3. Dong-Ling Deng
4. Linfeng Zhang
5. Matthias Troyer
6. E. Weinan
7. Roger G. Melko
8. Juan Felipe Carrasquilla

In Probabilistic & Bayesian Methods

1. Iván Díaz de León Rodríguez
2. Matthias Troyer
3. E. Weinan
4. Shuo-Hui Li
5. Linfeng Zhang
6. Lei Wang
7. Xiaopeng Li
8. Moritz August

In AI for Physical Sciences

1. Matthias Troyer
2. E. Weinan
3. Linfeng Zhang
4. Lei Wang

Citations in the corpus

• All-optical neural network with nonlinear activation functions (2019, background): “They may be used to solve some problems which are intractable in conventional appraches [13–20].”
• Quantum Entanglement in Neural Network States (2017, background): “…conventional symmetry-broken [33, 35, 37, 38] or topological phases [32]), modeling thermodynamic observables [36], constructing decoders for topological codes [39], accelerating Monte Carlo simulations [41, 42], and establishing connections to renormalization group techniques [45, 46], etc.”
• Neural-network quantum state tomography (2017, background): “Applications to quantum many-body systems have been put forward last year, to classify phases of matter 3–6 , and to improve the simulation of classical 7,8 and quantum 9 systems.”
• Neural Network Renormalization Group (2018, result): “Building the neural network using Normalizing Flows provides a generative model with explicit and tractable likelihoods compared to previous studies [21, 23, 24, 50–52].”
• Neural-Network Quantum States, String-Bond States, and Chiral Topological States (2017, background): “In the last few years we are experiencing interesting developments also for some central problems in condensed matter, such as quantum phase classification/recognition[7–10], improvement of dynamical mean field theory[11], enhancement of Quantum Monte Carlo methods [12, 13] or approximations of ther”
• Monge-Ampère Flow for Generative Modeling (2018, methodology): “Therefore, it can be used to accelerate Monte Carlo simulations, by either recommending the updates as a generative model Huang & Wang (2017); Liu et al. (2017) or performing hybrid Monte Carlo in the latent space Li & Wang (2018).”