A team of researchers from the Hong Kong University of Science and Technology (HKUST) has introduced a groundbreaking method for sampling the Boltzmann distribution, a key element in statistical mechanics. Led by Prof. PAN Ding and Dr. LI Shuo-Hui, the innovative approach utilizes deep generative models to facilitate efficient sampling across a continuous temperature range. The findings were published in the esteemed journal Physical Review Letters.
The Boltzmann distribution is vital for understanding systems in thermal equilibrium, playing a crucial role in the study of complex phenomena such as phase transitions, chemical reactions, and biomolecular structures. Traditionally, calculating thermodynamic quantities from this distribution has posed significant challenges, especially when high energy barriers exist. Conventional methods like molecular dynamics (MD) and Markov chain Monte Carlo (MCMC) sampling often require extensive computational resources to achieve ensemble averages.
In response to these challenges, Dr. Li and their team developed a framework known as the variational temperature-differentiable (VaTD) method. This technique is applicable to various generative models, including autoregressive models and normalizing flows. VaTD enables the learning of the Boltzmann distribution across a continuous temperature spectrum and allows for the automatic differentiation of thermodynamic quantities with respect to temperature. This capability effectively approximates an analytical partition function, which is crucial for accurate thermodynamic calculations.
Under optimal conditions, the VaTD method guarantees an unbiased representation of the Boltzmann distribution. A significant advantage of this approach is its ability to integrate over a continuous temperature range, which helps to overcome energy barriers and reduces bias in simulation results. Unlike existing generative models in statistical mechanics, VaTD relies solely on the potential energy of the system, eliminating the need for pre-generated datasets from MD or Monte Carlo simulations.
To validate their method, the HKUST team conducted numerical experiments on classical statistical physics models, including the Ising model and the XY model. These experiments demonstrated the accuracy and efficiency of the VaTD method, further establishing its potential as a transformative tool in the field.
Prof. PAN remarked on the significance of their findings, stating, “This breakthrough paves the way for studying novel phenomena in complex statistical systems, with potential applications in physics, chemistry, materials science, and life sciences.” The research received support from the Hong Kong Research Grants Council, the Croucher Foundation, and the National Excellent Young Scientists Fund under the National Natural Science Foundation of China (NSFC). Computational resources were provided by the “Tianhe-2” supercomputer at the National Supercomputer Center in Guangzhou.
This advancement not only addresses longstanding challenges in statistical mechanics but also opens new avenues for exploration in various scientific disciplines, potentially influencing future research and applications across multiple fields.
