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Accurate prediction of hydrogen sorption in fine-grained geological materials is essential for evaluating underground hydrogen storage capacity, assessing caprock integrity, and characterizing hydrogen migration in subsurface energy…
Motivated by the wide range of applicability of the fluctuation and dissipation phenomena in non-equilibrium systems, we provide a universal study scheme for the dissipation of the energy and the corresponding Brownian motion analysis of…
In this work we consider conformal gauge transformations of the geometric structure of thermodynamic fluctuation theory. In particular, we show that the Thermodynamic Phase Space is naturally endowed with a non-integrable connection,…
Eigenstate thermalization has been numerically shown to occur for few-body observables in a wide range of nonintegrable models. For intensive sums of few-body observables, a weaker version of eigenstate thermalization known as weak…
In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…
Longitudinal studies with binary or ordinal responses are widely encountered in various disciplines, where the primary focus is on the temporal evolution of the probability of each response category. Traditional approaches build from the…
In many problems, the measured variables (e.g., image pixels) are just mathematical functions of the latent causal variables (e.g., the underlying concepts or objects). For the purpose of making predictions in changing environments or…
General results from statistical learning theory suggest to understand not only brain computations, but also brain plasticity as probabilistic inference. But a model for that has been missing. We propose that inherently stochastic features…
Multivariate functional data present theoretical and practical complications which are not found in univariate functional data. One of these is a situation where the component functions of multivariate functional data are positive and are…
The identification of constitutive laws is ubiquitous in engineering: in modeling of materials where experimental data are fitted to mathematical models or learning surrogate models to beat the FE\textsuperscript{2} computational cost of…
We perform direct numerical simulations of three dimensional Rayleigh-Taylor turbulence with a nonuniform singular initial temperature background. In such conditions, the mixing layer evolves under the driving of a varying effective Atwood…
The process of protein folding from an unfolded state to a biologically active, folded conformation is governed by many parameters e.g the sequence of amino acids, intermolecular interactions, the solvent, temperature and chaperon…
Understanding the high-temperature properties of materials with (anti-)fluorite structures is crucial for their application in nuclear reactors. In this study, we employ machine learning molecular dynamics (MLMD) simulations to investigate…
We present emergent dynamics of continuous and discrete thermomechanical Cucker-Smale(TCS) models equipped with temperature as an extra observable on general digraph. In previous literature, the emergent behaviors of the TCS models were…
We introduce a new, rigorously-formulated Bayesian meta-learning algorithm that learns a probability distribution of model parameter prior for few-shot learning. The proposed algorithm employs a gradient-based variational inference to infer…
In this work, we advocate for the importance of singular learning theory (SLT) as it pertains to the theory and practice of variational inference in Bayesian neural networks (BNNs). To begin, using SLT, we lay to rest some of the confusion…
Machine-learning function representations such as neural networks have proven to be excellent constructs for constitutive modeling due to their flexibility to represent highly nonlinear data and their ability to incorporate constitutive…
A fundamental principle of chaotic quantum dynamics is that local subsystems eventually approach a thermal equilibrium state. Large subsystems thermalize slower: their approach to equilibrium is limited by the hydrodynamic build-up of…
We propose that simple neural networks (NNs) trained on crossing symmetry can reconstruct conformal correlators restricted to a line to remarkable accuracy. The input is minimal: an external scaling dimension, a spectral gap, and the value…
We investigate thermodynamics of general nonequilibrium processes stopped at stochastic times. We propose a systematic strategy for constructing fluctuation-theorem-like martingales for each thermodynamic functional, yielding a family of…