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This paper presents a novel method for analyzing the latent space geometry of generative models, including statistical physics models and diffusion models, by reconstructing the Fisher information metric. The method approximates the…
A model in statistical mechanics, characterised by the corresponding Gibbs measure, is a subset of the totality of probability distributions on the phase space. The shape of this subset, i.e., the geometry, then plays an important role in…
Accurate phase diagram calculation from molecular dynamics requires systematic treatment and convergence of statistical averages. In this work we propose a Gaussian process regression based framework for reconstructing the free energy…
We introduce a computational framework to statistically infer thermophysical properties of any given wall from in-situ measurements of air temperature and surface heat fluxes. The proposed framework uses these measurements, within a…
This work explores the possibilities of the Gibbs-Bogoliubov-Feynman variational method, aiming at finding room for designing various drawing schemes. For example, mean-field approximation can be viewed as a result of using site-independent…
A new formulation of statistical mechanics is put forward according to which a random variable characterizing a macroscopic body is postulated to be infinitely divisible. It leads to a parametric representation of partition function of an…
We propose a new approach concerning the introduction of time-irreversibility in statistical mechanics. It is based on a transition function defined in terms of path integral and verifying a time-irreversible equation. We show first how…
The significance of statistical physics concepts such as entropy extends far beyond classical thermodynamics. We interpret the similarity between partitions in statistical mechanics and partitions in Bayesian inference as an articulation of…
We present a computational strategy for the evaluation of multidimensional integrals on hyper-rectangles based on Markovian stochastic exploration of the integration domain while the integrand is being morphed by starting from an initial…
Phase diagrams serve as a highly informative tool for materials design, encapsulating information about the phases that a material can manifest under specific conditions. In this work, we develop a method in which Bayesian inference is…
The three and five-dimensional convex sets of two-level complex and quaternionic quantum systems are studied in the Bayesian thermostatistical framework introduced by Lavenda. Associated with a given parameterization of each such set is a…
A fully Bayesian treatment of complicated predictive models (such as deep neural networks) would enable rigorous uncertainty quantification and the automation of higher-level tasks including model selection. However, the intractability of…
An unified thermodynamical framework based in the use of a generalized Massieu-Planck thermodynamic potential is proposed and a new formulation of Boltzmann-Gibbs Statistical Mechanics is established. Under this philosophy a generalization…
In statistical physics, phase transitions are arguably among the most extensively studied phenomena. In the computational approach to this field, the development of algorithms capable of estimating entropy across the entire energy spectrum…
State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system…
Phylodynamics focuses on the problem of reconstructing past population size dynamics from current genetic samples taken from the population of interest. This technique has been extensively used in many areas of biology, but is particularly…
We present a new approach to a classical problem in statistical physics: estimating the partition function and other thermodynamic quantities of the ferromagnetic Ising model. Markov chain Monte Carlo methods for this problem have been…
Thermodynamic integration (TI) for computing marginal likelihoods is based on an inverse annealing path from the prior to the posterior distribution. In many cases, the resulting estimator suffers from high variability, which particularly…
In this work it is shown how the immersed boundary method of (Peskin2002) for modeling flexible structures immersed in a fluid can be extended to include thermal fluctuations. A stochastic numerical method is proposed which deals with…
We analyze the dynamics of an algorithm for approximate inference with large Gaussian latent variable models in a student-teacher scenario. To model nontrivial dependencies between the latent variables, we assume random covariance matrices…