Data, Dynamics, and Analytics

We develop a new generalization of Koopman operator theory that incorporates the effects of inputs and control. Koopman spectral analysis is a theoretical tool for the analysis of nonlinear dynamical systems. Moreover, Koopman is intimately connected to Dynamic Mode Decomposition (DMD), a method that discovers spatial-temporal coherent modes from data, connects local-linear analysis to nonlinear…

Hybrid systems are traditionally difficult to identify and analyze using classical dynamical systems theory. Moreover, recently developed model identification methodologies largely focus on identifying a single set of governing equations solely from measurement data. In this article, we develop a new methodology, Hybrid-Sparse Identification of Nonlinear Dynamics (Hybrid-SINDy), which identifies separate nonlinear dynamical regimes, employs…

Ambitious global goals have been established to provide universal access to affordable modern contraceptive methods. The UN’s sustainable development goal 3.7.1 proposes satisfying the demand for family planning (FP) services by increasing the proportion of women of reproductive age using modern methods. To measure progress toward such goals in populous countries like Nigeria, it’s essential…

We develop an algorithm for model selection which allows for the consideration of a combinatorially large number of candidate models governing a dynamical system. The innovation circumvents a disadvantage of standard model selection which typically limits the number candidate models considered due to the intractability of computing information criteria. Using a recently developed sparse identification…

Using a computational model of the Caenorhabditis elegans connectome dynamics, we show that proprioceptive feedback is necessary for sustained dynamic responses to external input. This is consistent with the lack of biophysical evidence for a central pattern generator, and recent experimental evidence that proprioception drives locomotion. The low-dimensional functional response of the Caenorhabditis elegans network…

Will J. R. Stone, Joseph J. Campo, André Lin Ouédraogo, Lisette Meerstein-Kessel, Isabelle Morlais, Dari Da, Anna Cohuet, Sandrine Nsango, Colin J. Sutherland, Marga van de Vegte-Bolmer, Rianne Siebelink-Stoter, Geert-Jan van Gemert, Wouter Graumans, Kjerstin Lanke, Adam D. Shandling, Jozelyn V. Pablo, Andy A. Teng, Sophie Jones, Roos M. de Jong, Amanda Fabra-Garcí­a, John Bradley,…

We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large…

Understanding the interplay of order and disorder in chaos is a central challenge in modern quantitative science. Approximate linear representations of nonlinear dynamics have long been sought, driving considerable interest in Koopman theory. We present a universal, data-driven decomposition of chaos as an intermittently forced linear system. This work combines delay embedding and Koopman theory…

Identifying governing equations from data is a critical step in the modeling and control of complex dynamical systems. Here, we investigate the data-driven identification of nonlinear dynamical systems with inputs and forcing using regression methods, including sparse regression. Specifically, we generalize the sparse identification of nonlinear dynamics (SINDY) algorithm to include external inputs and feedback…

We develop a new method which extends Dynamic Mode Decomposition (DMD) to incorporate the effect of control to extract low-order models from high-dimensional, complex systems. DMD finds spatial-temporal coherent modes, connects local-linear analysis to nonlinear operator theory, and provides an equation-free architecture which is compatible with compressive sensing. In actuated systems, DMD is incapable of…