相关论文: Entropy dissipation of moving mesh adaptation
We compare the performance of energy-based and entropy-conserving schemes for modeling nonthermal energy components, such as unresolved turbulence and cosmic rays, using idealized fluid dynamics tests and isolated galaxy simulations. While…
We study the problem of entropy calibration, which asks whether a language model's entropy over generations matches its log loss on human text. Past work found that models are miscalibrated, with entropy per step increasing as generations…
This work expands on our recently introduced low Mach enthalpy method [1] for simulating the melting and solidification of a phase change material (PCM) alongside (or without) an ambient gas phase. The method captures PCM's volume change…
Current mesh reduction techniques, while numerous, all primarily reduce mesh size by successive element deletion (e.g. edge collapses) with the goal of geometric and topological feature preservation. The choice of geometric error used to…
We are interested in the approximation of a steady hyperbolic problem. In some cases, the solution can satisfy an additional conservation relation, at least when it is smooth. This is the case of an entropy. In this paper, we show, starting…
The entropy conservative/stable algorithm of Friedrich~\etal (2018) for hyperbolic conservation laws on nonconforming p-refined/coarsened Cartesian grids, is extended to curvilinear grids for the compressible Euler equations. The primary…
We explore the relationship between a machine-learned structural quantity (softness) and excess entropy in simulations of supercooled liquids. Excess entropy is known to scale well the dynamical properties of liquids, but this…
Atmospheric systems incorporating thermal dynamics must be stable with respect to both energy and entropy. While energy conservation can be enforced via the preservation of the skew-symmetric structure of the Hamiltonian form of the…
We present several algorithms to generate tables for asymmetric numeral systems and prove that they are optimal in terms of discrepancy. In turn, this gives rise to the strongest proven bound on entropy loss. We further give improved…
The following work concerns the construction of an entropy dissipative finite volume solver based on the convex combination of an entropy conservative and an entropy dissipative flux. We aim to construct a semidiscrete scheme that is…
The metriplectic formalism is useful for describing complete dynamical systems which conserve energy and produce entropy. This creates challenges for model reduction, as the elimination of high-frequency information will generally not…
To quantify the complexity of a system, entropy-based methods have received considerable critical attentions in real-world data analysis. Among numerous entropy algorithms, amplitude-based formulas, represented by Sample Entropy, suffer…
We describe a framework in which is possible to develop and implement algorithms for the approximation of invariant measures of dynamical systems with a given bound on the error of the approximation. Our approach is based on a general…
The maximal entropy moment method (MEM) is systematic solution of the challenging problem: generating extended hydrodynamic equations valid for both dense and rarefied gases. However, simulating MEM suffers from a computational expensive…
Behavior of the entropy numbers of classes of multivariate functions with mixed smoothness is studied here. This problem has a long history and some fundamental problems in the area are still open. The main goal of this paper is to develop…
This article performs a unified convergence analysis of a variety of numerical methods for a model of the miscible displacement of one incompressible fluid by another through a porous medium. The unified analysis is enabled through the…
We describe a systematic development of kinetic entropy as a diagnostic in fully kinetic particle-in-cell (PIC) simulations and use it to interpret plasma physics processes in heliospheric, planetary, and astrophysical systems. First, we…
The ability to monitor nutrient and other environmental conditions with high sensitivity is crucial for cell growth and survival. Sensory adaptation allows a cell to recover its sensitivity after a transient response to a shift in the…
Estimating the entropy of a discrete random variable is a fundamental problem in information theory and related fields. This problem has many applications in various domains, including machine learning, statistics and data compression. Over…
We study the numerical anisotropy existent in compact difference schemes as applied to hyperbolic partial differential equations, and propose an approach to reduce this error and to improve the stability restrictions based on a previous…