相关论文: Entropy Structure Informed Learning for Inverse XD…
Entropy is a measure of self-information which is used to quantify losses. Entropy was developed in thermodynamics, but is also used to compare probabilities based on their deviating information content. Corresponding model uncertainty is…
Although the governing equations of many systems, when derived from first principles, may be viewed as known, it is often too expensive to numerically simulate all the interactions they describe. Therefore researchers often seek simpler…
In this paper we apply the entropy principle to the relativistic version of the differential equations describing a standard fluid flow, that is, the equations for mass, momentum, and a system for the energy matrix. These are the second…
Entropic lattice Boltzmann methods have been developed to alleviate intrinsic stability issues of lattice Boltzmann models for under-resolved simulations. Its reliability in combination with moving objects was established for various…
This paper is concerned with reconstruction issue of inverse obstacle problems governed by partial differential equations and consists of two parts. (i) The first part considers the foundation of the probe and enclosure methods for an…
This paper is concerned with an inverse moving point source problem in electromagnetics. The aim is to reconstruct the moving orbit from the tangential components of magnetic fields taken at a finite number of observation points. The…
On the basis of the balance equations for energy-momentum, spin, particle and entropy density, an approach is considered which represents a comparatively general framework for special- and general-relativistic continuum thermodynamics. In…
In this paper, we establish a new uniqueness result of a (continuous) viscosity solution for some integro-partial differential equation (IPDE in short). The novelty is that we relax the so-called monotonicity assumption on the driver,…
Through the consideration of spherically symmetric gravitating systems consisting of perfect fluids with linear equation of state constrained to be in a finite volume, an account is given of the properties of entropy at conditions in which…
In this paper, we derive entropy estimates for a class of schemes for the Euler equations which present the following features: they are based on the internal energy equation (eventually with a positive corrective term at the righ-hand-side…
We present a brief history of how the famous Maximum Entropy Principle was used as closure of moments of the Boltzmann equation. In particular, we want to remark on the important role of two fundamental papers by Wolfgang Dreyer, one in the…
Entropy, its production, and its change in a dynamical system can be understood from either a fully stochastic dynamic description or from a deterministic dynamics exhibiting chaotic behavior. By taking the former approach based on the…
In this paper, explicit method of constructing approximations (the Triangle Entropy Method) is developed for nonequilibrium problems. This method enables one to treat any complicated nonlinear functionals that fit best the physics of a…
The entropic lattice Boltzmann framework proposed the construction of the discrete equilibrium by taking into consideration minimization of a discrete entropy functional. The effect of this form of the discrete equilibrium on properties of…
In this paper we show that the existence of a primarily discrete space-time may be a fruitful assumption from which we may develop a new approach of statistical thermodynamics in pre-relativistic conditions. The discreetness of space-time…
An experiment to study the entropy method for an anomaly detection system has been performed. The study has been conducted using real data generated from the distributed sensor networks at the Intel Berkeley Research Laboratory. The…
The explicit governing equation is one of the simplest and most intuitive forms for characterizing physical laws. However, directly discovering partial differential equations (PDEs) from data poses significant challenges, primarily in…
Integral equations frequently arise in surface science, and in some cases, they must be treated as inverse problems. In our previous work on optical tweezers, atomic force microscopy, and surface force measurement apparatus, we performed…
The method is proposed for the study of many-point boundary value problems for systems of nonlinear ODE, by reducing them to special equivalent integral equations, and allows us [in contrast with the known method [1]] to consider boundary…
Entropy estimation is of practical importance in information theory and statistical science. Many existing entropy estimators suffer from fast growing estimation bias with respect to dimensionality, rendering them unsuitable for…