Search Results - "Kutz, Nathan"

Data-driven discovery of coordinates and governing equations by Champion, Kathleen, Lusch, Bethany, Kutz, J. Nathan, Brunton, Steven L.

“…The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative…”
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Deep learning for universal linear embeddings of nonlinear dynamics by Lusch, Bethany, Kutz, J. Nathan, Brunton, Steven L.

“…Identifying coordinate transformations that make strongly nonlinear dynamics approximately linear has the potential to enable nonlinear prediction, estimation,…”
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Discovering governing equations from data by sparse identification of nonlinear dynamical systems by Brunton, Steven L., Proctor, Joshua L., Kutz, J. Nathan

“…Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain…”
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Chaos as an intermittently forced linear system by Brunton, Steven L., Brunton, Bingni W., Proctor, Joshua L., Kaiser, Eurika, Kutz, J. Nathan

“…Understanding the interplay of order and disorder in chaos is a central challenge in modern quantitative science. Approximate linear representations of…”
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Deep learning of dynamics and signal-noise decomposition with time-stepping constraints by Rudy, Samuel H., Nathan Kutz, J., Brunton, Steven L.

“…A critical challenge in the data-driven modeling of dynamical systems is producing methods robust to measurement error, particularly when data is limited. Many…”
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DeepGreen: deep learning of Green’s functions for nonlinear boundary value problems by Gin, Craig R., Shea, Daniel E., Brunton, Steven L., Kutz, J. Nathan

“…Boundary value problems (BVPs) play a central role in the mathematical analysis of constrained physical systems subjected to external forces. Consequently,…”
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Data-driven discovery of Koopman eigenfunctions for control by Kaiser, Eurika, Kutz, J Nathan, Brunton, Steven L

“…Data-driven transformations that reformulate nonlinear systems in a linear framework have the potential to enable the prediction, estimation, and control of…”
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Extracting spatial–temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition by Brunton, Bingni W., Johnson, Lise A., Ojemann, Jeffrey G., Kutz, J. Nathan

“…•Dynamic mode decomposition (DMD) extracts dynamically coherent patterns from large-scale neuronal recordings.•Multiple, distinct sleep spindle networks are…”
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Learning dominant physical processes with data-driven balance models by Callaham, Jared L., Koch, James V., Brunton, Bingni W., Kutz, J. Nathan, Brunton, Steven L.

“…Throughout the history of science, physics-based modeling has relied on judiciously approximating observed dynamics as a balance between a few dominant…”
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Greedy Sensor Placement With Cost Constraints by Clark, Emily, Askham, Travis, Brunton, Steven L., Nathan Kutz, J.

“…The problem of optimally placing sensors under a cost constraint arises naturally in the design of industrial and commercial products, as well as in scientific…”
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Forecasting dengue fever in Brazil: An assessment of climate conditions by Stolerman, Lucas M, Maia, Pedro D, Kutz, J Nathan

“…Local climate conditions play a major role in the biology of the Aedes aegypti mosquito, the main vector responsible for transmitting dengue, zika, chikungunya…”
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Optimal Sensor and Actuator Selection Using Balanced Model Reduction by Manohar, Krithika, Kutz, J. Nathan, Brunton, Steven L.

“…Optimal sensor and actuator selection is a central challenge in high-dimensional estimation and control. Nearly all subsequent control decisions are affected…”
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Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control by Brunton, Steven L, Brunton, Bingni W, Proctor, Joshua L, Kutz, J Nathan

“…In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant…”
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Automatic differentiation to simultaneously identify nonlinear dynamics and extract noise probability distributions from data by Kaheman, Kadierdan, Brunton, Steven L, Nathan Kutz, J

“…The sparse identification of nonlinear dynamics (SINDy) is a regression framework for the discovery of parsimonious dynamic models and governing equations from…”
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A Unified Framework for Sparse Relaxed Regularized Regression: SR3 by Zheng, Peng, Askham, Travis, Brunton, Steven L., Kutz, J. Nathan, Aravkin, Aleksandr Y.

“…Regularized regression problems are ubiquitous in statistical modeling, signal processing, and machine learning. Sparse regression, in particular, has been…”
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Applied Koopman Theory for Partial Differential Equations and Data-Driven Modeling of Spatio-Temporal Systems by Nathan Kutz, J., Brunton, S. L., Proctor, J. L.

“…We consider the application of Koopman theory to nonlinear partial differential equations and data-driven spatio-temporal systems. We demonstrate that the…”
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Pruning deep neural networks generates a sparse, bio-inspired nonlinear controller for insect flight by Zahn, Olivia, Bustamante, Jr, Jorge, Switzer, Callin, Daniel, Thomas L, Kutz, J Nathan

“…Insect flight is a strongly nonlinear and actuated dynamical system. As such, strategies for understanding its control have typically relied on either…”
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Computing spectra of linear operators using the Floquet–Fourier–Hill method by Deconinck, Bernard, Nathan Kutz, J.

“…In order to establish the stability of an equilibrium solution U of an infinite-dimensional dynamical system u˙=X(u), one is interested in the spectrum of the…”
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Methods for data-driven multiscale model discovery for materials by Brunton, Steven L, Kutz, J Nathan

“…Despite recent achievements in the design and manufacture of advanced materials, the contributions from first-principles modeling and simulation have remained…”
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Dissipative soliton resonance in a passively mode-locked fiber laser by Ding, Edwin, Grelu, Philippe, Kutz, J Nathan

“…The phenomenon of dissipative soliton resonance (DSR) predicts that an increase of pulse energy by orders of magnitude can be obtained in laser oscillators…”
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