Deep learning method enables efficient Boltzmann distribution sampling across a continuous temperature range

A research team has developed a new direct sampling method based on deep generative models. Their method allows effective sampling of the distribution of Boltzmann on a continuous temperature range. The results were published in Physical examination letters. The team was led by Professor Pan Ding, associate professor of the departments of physics and chemistry, and Dr. Li Shuo-Hui, deputy research professor of the Physics Department of the University of Sciences and Technology of Hong Kong (HKUST).

Boltzmann’s distribution is one of the most important distributions in statistical mechanics for the thermal balance systems. Sampling is crucial to understanding complex systems, such as phase transitions, chemical reactions and biomolecular conformations. However, the effective and accurate calculation of thermodynamic quantities for such systems has long been a major challenge in the field.

Traditional digital methods in statistical mechanics, including molecular dynamics (MD) and Markov Chain Monte Carlo (MCMC) sampling require significant simulation time to obtain overall averages when the system barrier of the system is high, leading to significant calculation costs.

Inspired by recent advances in deep generative models, Dr. Li and its colleagues have proposed a general framework – the variational temperature (VATD) method – applicable to any generative model of towable density, such as self -regressive models and standardization flows.

The VATD can learn the distribution of Boltzmann through a continuous temperature range, with first and second order derivatives of the thermodynamic quantities compared to the convenient temperature obtained by automatic differentiation. This is effectively close to an analytical partition function.

Under optimal conditions, the model theoretically guarantees a distribution of impartial Boltzmann. More importantly, integration on a continuous temperature range helps to overcome energy barriers, thus reducing biases in simulations.

Unlike predominant generative models in statistical mechanics, the VATD only requires the potential energy of the system and does not rely on pre-Gented data sets from MD or Monte Carlo simulations.

The team validated the accuracy and efficiency of the method through digital experiences on conventional statistical physics models, including the Ising model and the XY model.

Professor Pan pointed out: “This breakthrough opens the way to the study of new phenomena in complex statistical systems, with potential applications in physics, chemistry, science of materials and life sciences.”