Nonlinear Data-Driven Approximation of the Koopman Operator

Koopman analysis provides a general framework from which to analyze a nonlinear dynamical system in terms of a linear operator acting on an infinite-dimensional observable space. This theoretical framework provides a rigorous underpinning for widely used dynamic mode decomposition algorithms. While such methods have proven to be remarkably useful in the analysis of time-series data, the resulting linear models must generally be of high order to accurately approximate fundamentally nonlinear behaviors. This issue poses an inherent risk of overfitting to training data thereby limiting predictive capabilities. By contrast, this work explores strategies for nonlinear data-driven estimation of the action of the Koopman operator. General strategies that yield nonlinear models are presented for systems both with and without control. Subsequent projection of the resulting nonlinear equations onto a low-rank basis yields a low order representation for the underlying dynamical system. In both computational and experimental examples considered in this work, linear estimators of the Koopman operator are generally only able to provide short-term predictions for the observable dynamics while comparable nonlinear estimators provide accurate predictions on substantially longer timescales and replicate infinite-time behaviors that linear predictors cannot

Screening of energy efficient technologies for industrial buildings' retrofit

This chapter discusses screening of energy efficient technologies for industrial buildings' retrofit

Non-integrality of some Steinberg modules

We prove that the Steinberg module of the special linear group of a quadratic imaginary number ring which is not Euclidean is not generated by integral apartments. Assuming the generalized Riemann hypothesis, this shows that the Steinberg module of a number ring is generated by integral apartments if and only if the ring is Euclidean. We also construct new cohomology classes in the top dimensional cohomology group of the special linear group of some quadratic imaginary number rings.Comment: 17 pages. To appear in Journal of Topolog

Interview with Dan J. Wilson, SuDan Farms, 2007 (audio)

Interview of Dan J. Wilson by Jason Keaton at Canby, Oregon on August 10th, 2007. The interview index is available for download

The Mapping between the Mental and the Public Lexicon

We argue that the presence of a word in an utterance serves as starting point for a relevance guided inferential process that results in the construction of a contextually appropriate sense. The linguistically encoded sense of a word does not serve as its default interpretation. The cases where the contextually appropriate sense happens to be identical to this linguistic sense have no particular theoretical significance. We explore some of the consequences of this view. One of these consequences is that there may be many more mentally represented concepts than there are linguistically encoded concepts