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In this paper, we develop the self-learning Monte-Carlo (SLMC) algorithm fornon-abelian gauge theory with dynamical fermions in four dimensions to resolvethe autocorrelation problem in lattice QCD. We perform simulations with thedynamical staggered fermions and plaquette gauge action by both in HMC and SLMCfor zero and finite temperature to examine the validity of SLMC. We confirmthat SLMC can reduce autocorrelation time in non-abelian gauge theory andreproduces results from HMC. For finite temperature runs, we confirm that SLMCreproduces correct results with HMC, including higher-order moments of thePolyakov loop and the chiral condensate. Besides, our finite temperaturecalculations indicate that four flavor QC${}_2$D with $\hat{m} = 0.5$ is likelyin the crossover regime in the Colombia plot.

Self-learning Monte-Carlo for non-abelian gauge theory with dynamical fermions