Entropy-Related Extremum Principles for Model Reduction of Dissipative Dynamical Systems

Abstract

Chemical kinetic systems are modeled by dissipative ordinary differential equations involving multiple time scales. These lead to a phase flow generating anisotropic volume contraction. Kinetic model reduction methods generally exploit time scale separation into fast and slow modes, which leads to the occurrence of low-dimensional slow invariant manifolds. The aim of this paper is to review and discuss a computational optimization approach for the numerical approximation of slow attracting manifolds based on entropy-related and geometric extremum principles for reaction trajectories.

System Entropy Measurement of Stochastic Partial Differential Systems

“…Here, y(x,t) is the temperature function, location x is in meters, time t is in s, κ " 10´4 m 2 {s is the thermal diffusivity [4][5][6][7]9], and the term Aypx, tq with A "´0.1 s´1 denotes the thermal dissipation when the temperature of the plate is greater than the surrounding temperature, i.e., ypx, tq ą 0˝C, or the thermal absorption when the temperature on the plate is less than the surrounding temperature, i.e., ypx, tq ă 0˝C. The output coupling C " 1.…”

“…If y 0 pxq " 0, then Vpy 0 pxqq " 0, and the HJII in Equation (48) and Equation (E4) will lead to Equation (5).…”

“…Information entropy is considered a measure of uncertainty and its maximization guarantees the best solutions for the maximal uncertainty [1][2][3][4][5]. Information entropy characterizes uncertainty caused by random parameters of a random system and measurement noise in the environment [6].…”

“…Information entropy characterizes uncertainty caused by random parameters of a random system and measurement noise in the environment [6]. Entropy has been used for information retrieval such as systemic parametric and nonparametric estimation based on real data, which is an important topic in advanced scientific disciplines such as econometrics [1,2], financial mathematics [4], mathematical statistics [3,4,6], control theory [5,7,8], signal processing [9], and mechanical engineering [10,11]. Methods developed within this framework consider model parameters as random quantities and employ the informational entropy maximization principle to estimate these model parameters [6,9].…”

New Methods of Entropy-Robust Estimation for Randomized Models under Limited Data

“…Each method stems from certain hypotheses regarding the properties of data accumulated during the normal functioning of their source. Among advanced scientific disciplines in this field, we mention mathematical statistics [1][2][3][4], econometrics [5][6][7], financial mathematics [8,9], control theory [10,11] and others.…”