相关论文: Entropy Structure Informed Learning for Inverse XD…

This paper is twofold. In the first part, we present a refinement of the R\'enyi Entropy Power Inequality (EPI) recently obtained in \cite{BM16}. The proof largely follows the approach in \cite{DCT91} of employing Young's convolution…

In this paper we present some open problems pertaining to the approximation theory involved in the solution of the important class of Nonlinear Partial Differential Equations (NPDEs) of integrable type. For this class of NPDEs, any Initial…

By using entropy and entropy production, we calculate the steady flux of some phenomena. The method we use is a competition method, $S_S/\tau+\sigma={\it maximum}$, where $S_S$ is system entropy, $\sigma$ is entropy production and $\tau$ is…

The entropies of molecules in solution are routinely calculated using gas phase formulae. It is assumed that, because implicit solvation models are fitted to reproduce free energies, this is sufficient for modeling reactions in solution.…

The ability to continuously learn remains elusive for deep learning models. Unlike humans, models cannot accumulate knowledge in their weights when learning new tasks, mainly due to an excess of plasticity and the low incentive to reuse…

We consider a rather general class of non-local in time Fokker-Planck equations and show by means of the entropy method that as $t\to \infty$ the solution converges in $L^1$ to the unique steady state. Important special cases are the…

We show that a simple geometric result suffices to derive the form of the optimal solution in a large class of finite and infinite-dimensional maximum entropy problems concerning probability distributions, spectral densities and covariance…

High-entropy alloys, which exist in the high-dimensional composition space, provide enormous unique opportunities for realizing unprecedented structural and functional properties. A fundamental challenge, however, lies in how to predict the…

We revisit the sharp-interface continuum thermodynamics of two-phase multicomponent fluid systems, accounting for partial mass and partial momentum balances both in the bulk phases and on the interface. This allows to describe the transfer…

Despite the recent proliferation of machine learning methods like SINDy that promise automatic discovery of governing equations from time-series data, there remain significant challenges to discovering models from noisy datasets. One reason…

Inverse problems are ubiquitous in science and engineering. Many of these are naturally formulated as a PDE-constrained optimization problem. These non-linear, large-scale, constrained optimization problems know many challenges, of which…

This paper focuses on an inverse problem associated with the plate equation which is derived from models in fluid mechanics and elasticity. We establish the unique identifying results in simultaneously determining both the unknown density…

High-entropy materials shift the traditional materials discovery paradigm to one that leverages disorder, enabling access to unique chemistries unreachable through enthalpy alone. We present a self-consistent approach integrating…

This paper shows that, in the formal level, the convergence of solutions of Boltzmann equation to solutions of the compressible Navier-Stokes system with small Mach number over the three-dimensional periodic domain $\mathbb{T}^3$, using the…

Entropy is a very useful concept from physics that tries to explain how a system behaves from a point of view of the thermodynamics. However, there are two ways to explain entropy, and it depends on if we are studying a microsystem or a…

Obtaining meaningful quantitative descriptions of the statistical dependence within multivariate systems is a difficult open problem. Recently, the Partial Information Decomposition (PID) was proposed to decompose mutual information (MI)…

The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…

In a recent paper, Lenz and Moody (arXiv:1111.3617) presented a method for constructing families of real solutions to the inverse problem for a given pure point diffraction measure. Applying their technique and discussing some possible…

In this paper, we propose and study several inverse problems of determining unknown parameters in nonlocal nonlinear coupled PDE systems, including the potentials, nonlinear interaction functions and time-fractional orders. In these coupled…

Identifying differential equation governing dynamical system is an important problem with wide applications. Copula Entropy (CE) is a mathematical concept for measuring statistical independence in information theory. In this paper we…