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We develop a method to learn physical systems from data that employs feedforward neural networks and whose predictions comply with the first and second principles of thermodynamics. The method employs a minimum amount of data by enforcing…
A thermodynamically motivated neural network model is described that self-organizes to transport charge associated with internal and external potentials while in contact with a thermal reservoir. The model integrates techniques for rapid,…
Data assimilation algorithms integrate prior information from numerical model simulations with observed data. Ensemble-based filters, regarded as state-of-the-art, are widely employed for large-scale estimation tasks in disciplines such as…
The fidelity per site between two ground states of a quantum lattice system corresponding to different values of the control parameter defines a surface embedded in a Euclidean space. The Gaussian curvature naturally quantifies quantum…
A stochastic deformation of a thermodynamic symplectic structure is studied. The stochastic deformation procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an imaginary deformation…
Motivated by the search for the QCD critical point, we discuss how to obtain the singular behavior of a thermodynamic system near a critical point, namely the Lee-Yang singularities, from a limited amount of local data generated in a…
The use of machine learning to build subgrid parametrizations for climate models is receiving growing attention. State-of-the-art strategies address the problem as a supervised learning task and optimize algorithms that predict subgrid…
In this article we analyze several mathematical models with singularities where the classical cotangent model is replaced by a $b$-cotangent model. We provide physical interpretations of the singular symplectic geometry underlying in…
We report on a study of the superconducting order parameter thermodynamic fluctuations in $\mathrm{YBa}_2\mathrm{Cu}_3\mathrm{O}_{7 - \delta}$, $\mathrm{Bi}_{2}\mathrm{Sr}_{2}\mathrm{CaCu}_{2}\mathrm{O}_{8+ \delta}$ and…
Biological, artificial, and physical systems dissipate energy to accurately transmit information. While tools of information theory have been used to characterize information-processing capabilities, how reliably this information is…
In this paper, we study the thermodynamical properties of the classical one-dimensional Klein-Gordan lattice model ($n \ge 2$) by using the cluster variation method with linear response theory. The results of this method are exact in the…
It has been shown that contact geometry is the proper framework underlying classical thermodynamics and that thermodynamic fluctuations are captured by an additional metric structure related to Fisher's Information Matrix. In this work we…
We write equations of motion for density variables that are equivalent to Newtons equations. We then propose a set of trial equations parameterised by two unknown functions to describe the exact equations. These are chosen to best fit the…
Results on the peridynamics equilibrium and evolution equations over the space of periodic vector-distributions in multi-spatial dimensions are presented. The associated operator considered is the linear state-based peridynamic operator for…
Atmospheric flows exhibit long-range spatiotemporal correlations manifested as the fractal geometry to the global cloud cover pattern concomitant with inverse power law form for power spectra of temporal fluctuations on all space-time…
In statistical problems, a set of parameterized probability distributions is used to estimate the true probability distribution. If Fisher information matrix at the true distribution is singular, then it has been left unknown what we can…
Self-organizing systems consume energy to generate internal order. The concept of thermodynamic efficiency, drawing from statistical physics and information theory, has previously been proposed to characterise a change in control parameter…
Wall-bounded turbulent flows are chaotic and multiscale, rendering real-time prediction at high Reynolds numbers computationally prohibitive in applications such as wind farms. Classical data assimilation methods are based on repeated…
A bar-joint mechanism is a deformable assembly of freely rotating joints connected by stiff bars. Here we develop a formalism to study the equilibration of common bar-joint mechanisms with a thermal bath. When the constraints in a mechanism…
Kernel methods are one of the mainstays of machine learning, but the problem of kernel learning remains challenging, with only a few heuristics and very little theory. This is of particular importance in methods based on estimation of…