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A theory to predict the steady-state position of a dissipative flow-controlled system, as defined by a control volume, is developed based on the maximum entropy principle of Jaynes, involving minimization of a generalized free-energy-like potential. The analysis provides a theoretical justification of a local, conditional form of the maximum entropy(More)
A reduced-order modelling (ROM) strategy is crucial to achieve model-based control in a wide class of flow configurations. In turbulence, ROMs are mostly derived by Galerkin projection of first-principles equations onto the proper orthogonal decomposition (POD) modes. These POD ROMs are known to be relatively fragile when used for control design. To(More)
1 Abstract This study critically analyses the information-theoretic, axiomatic and combinatorial philosophical bases of the entropy and cross-entropy concepts. The combinatorial basis is shown to be the most fundamental (most primitive) of these three bases, since it gives (i) a derivation for the Kullback-Leibler cross-entropy and Shannon entropy(More)
We examine the combinatorial or probabilistic definition (" Boltzmann's principle ") of the en-tropy or cross-entropy function H ∝ ln W or D ∝ − ln P, where W is the statistical weight and P the probability of a given realization of a system. Extremisation of H or D, subject to any constraints, thus selects the " most probable " (MaxProb) realization. If(More)
The combinatorial basis of entropy, given by Boltzmann, can be written H = N −1 ln W, where H is the dimensionless entropy, N is the number of entities and W is number of ways in which a given realization of a system can occur (its statistical weight). This can be broadened to give generalized combinatorial (or probabilistic) definitions of entropy and(More)
We propose a maximum-entropy closure strategy for dissipative dynamical systems building on and generalizing earlier examples (Noack & Niven (2012) [11]). Focus is placed on Galerkin systems arising from a projection of the incompressible Navier–Stokes equation onto orthonormal expansionmodes. Themaximum-entropy closure is motivated by a simple analytical(More)
This study examines a new formulation of non-equilibrium thermodynamics, which gives a conditional derivation of the 'maximum entropy production' (MEP) principle for flow and/or chemical reaction systems at steady state. The analysis uses a dimensionless potential function (st) for non-equilibrium systems, analogous to the free energy concept of equilibrium(More)
We study the modeling and prediction of dynamical systems based on conventional models derived from measurements. Such algorithms are highly desirable in situations where the underlying dynamics are hard to model from physical principles or simplified models need to be found. We focus on symbolic regression methods as a part of machine learning. These(More)