Related papers: Bridging statistical mechanics and thermodynamics …
In spatially extended systems, it is common to find latent variables that are hard, or even impossible, to measure with acceptable precision, but are crucially important for the proper description of the dynamics. This substantially…
We study numerical methods for sampling probability measures in high dimension where the underlying model is only approximately identified with a gradient system. Extended stochastic dynamical methods are discussed which have application to…
We study stochastic thermodynamics of a Brownian particle which is subjected to a temperature gradient and is confined by an external potential. We first formulate an over-damped Ito-Langevin theory in terms of local temperature, friction…
Numerical methods such as finite element have been flourishing in the past decades for modeling solid mechanics problems via solving governing partial differential equations (PDEs). A salient aspect that distinguishes these numerical…
Many complex systems operating far from the equilibrium exhibit stochastic dynamics that can be described by a Langevin equation. Inferring Langevin equations from data can reveal how transient dynamics of such systems give rise to their…
How can we learn the laws underlying the dynamics of stochastic systems when their trajectories are sampled sparsely in time? Existing methods either require temporally resolved high-frequency observations, or rely on geometric arguments…
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics like work, heat and entropy production to the level of individual trajectories of well-defined…
Cross-sectional studies are widely prevalent since they are more feasible to conduct compared to longitudinal studies. However, cross-sectional data lack the temporal information required to study the evolution of the underlying processes.…
Stochastic thermodynamics is a framework for describing non-equilibrium processes at the level of fluctuating trajectories, where the state of a system evolves as a stochastic time series, allowing thermodynamic quantities such as work,…
The Information bottleneck method is an unsupervised non-parametric data organization technique. Given a joint distribution P(A,B), this method constructs a new variable T that extracts partitions, or clusters, over the values of A that are…
Data-driven and deep learning approaches have demonstrated to have the potential of replacing classical constitutive models for complex materials. Yet, the necessity of structuring constitutive models with an incremental formulation has…
We describe a stochastic, dynamical system capable of inference and learning in a probabilistic latent variable model. The most challenging problem in such models - sampling the posterior distribution over latent variables - is proposed to…
We describe a method to extract from experimental data the important dynamical modes in spatio-temporal patterns in a system driven out of thermodynamic equilibrium. Using a novel optical technique for controlling fluid flow, we create an…
Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges of equilibrium, including accurately describing the joint distribution of a large number of configurations, and also…
A central problem in machine learning involves modeling complex data-sets using highly flexible families of probability distributions in which learning, sampling, inference, and evaluation are still analytically or computationally…
This article covers thermodynamic, dynamic, and kinetic models that are suitable for the analysis of wetting, adsorption, and related interfacial phenomena in colloidal and multiphase systems. Particular emphasis is made on describing…
Deep Neural Networks (DNNs) excel at many tasks, often rivaling or surpassing human performance. Yet their internal processes remain elusive, frequently described as "black boxes." While performance can be refined experimentally, achieving…
Machine learning methods are powerful in distinguishing different phases of matter in an automated way and provide a new perspective on the study of physical phenomena. We train a Restricted Boltzmann Machine (RBM) on data constructed with…
Stochastic thermodynamics provides the framework to analyze thermodynamic laws and quantities along individual trajectories of small but fully observable systems. If the observable level fails to capture all relevant degrees of freedom,…
We propose a latent space dynamics identification method, namely tLaSDI, that embeds the first and second principles of thermodynamics. The latent variables are learned through an autoencoder as a nonlinear dimension reduction model. The…