Deep generative modelling of canonical ensemble with differentiable thermal properties
This work addresses the simulation of physical systems for researchers in statistical physics and machine learning, offering a novel approach to model thermal effects, though it is incremental in combining existing generative models with temperature dependence.
The authors tackled the problem of modeling canonical ensembles with differentiable temperature by proposing a variational method using deep generative models, which accurately captures phase transitions in Ising and XY models with efficiency comparable to MCMC simulations and provides thermodynamic quantities as differentiable functions.
We propose a variational modelling method with differentiable temperature for canonical ensembles. Using a deep generative model, the free energy is estimated and minimized simultaneously in a continuous temperature range. At optimal, this generative model is a Boltzmann distribution with temperature dependence. The training process requires no dataset, and works with arbitrary explicit density generative models. We applied our method to study the phase transitions (PT) in the Ising and XY models, and showed that the direct-sampling simulation of our model is as accurate as the Markov Chain Monte Carlo (MCMC) simulation, but more efficient. Moreover, our method can give thermodynamic quantities as differentiable functions of temperature akin to an analytical solution. The free energy aligns closely with the exact one to the second-order derivative, so this inclusion of temperature dependence enables the otherwise biased variational model to capture the subtle thermal effects at the PTs. These findings shed light on the direct simulation of physical systems using deep generative models