J. Nathan Kutz

About

J. Nathan Kutz is a professor at the Department of Applied Mathematics at the University of Washington. His research focuses on applied mathematics, with particular interests in areas such as nonlinear dynamics and chaos, data science, scientific computing, and mathematical methods. As a faculty member, he contributes to the understanding and development of mathematical models and computational techniques to solve complex scientific problems.

Research topics

• Computer Science
• Machine Learning
• Artificial Intelligence
• Mechanics
• Mathematics
• Classical mechanics
• Data Mining
• Physics
• Theoretical computer science
• Geometry

Selected publications

• Modern Koopman Theory for Dynamical Systems

  SIAM Review · 2022 · 486 citations

  Senior authorCorresponding

  The field of dynamical systems is being transformed by the mathematical tools and algorithms emerging from modern computing and data science. First-principles derivations and asymptotic reductions are giving way to data-driven approaches that formulate models in operator-theoretic or probabilistic frameworks. Koopman spectral theory has emerged as a dominant perspective over the past decade, in which nonlinear dynamics are represented in terms of an infinite-dimensional linear operator acting on…

  DOI

• Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control

  Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 2022 · 268 citations

  Sparse model identification enables the discovery of nonlinear dynamical systems purely from data; however, this approach is sensitive to noise, especially in the low-data limit. In this work, we leverage the statistical approach of bootstrap aggregating (bagging) to robustify the sparse identification of the nonlinear dynamics (SINDy) algorithm. First, an ensemble of SINDy models is identified from subsets of limited and noisy data. The aggregate model statistics are then used to produce inclus…

  DOI

• Shallow neural networks for fluid flow reconstruction with limited sensors

  Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 2020 · 248 citations

  Senior authorCorresponding

  In many applications, it is important to reconstruct a fluid flow field, or some other high-dimensional state, from limited measurements and limited data. In this work, we propose a shallow neural network-based learning methodology for such fluid flow reconstruction. Our approach learns an end-to-end mapping between the sensor measurements and the high-dimensional fluid flow field, without any heavy preprocessing on the raw data. No prior knowledge is assumed to be available, and the estimation…

  DOI

• Numerical Differentiation of Noisy Data: A Unifying Multi-Objective Optimization Framework

  IEEE Access · 2020 · 116 citations

  Computing derivatives of noisy measurement data is ubiquitous in the physical, engineering, and biological sciences, and it is often a critical step in developing dynamic models or designing control. Unfortunately, the mathematical formulation of numerical differentiation is typically ill-posed, and researchers often resort to an ad hoc process for choosing one of many computational methods and its parameters. In this work, we take a principled approach and propose a multi-objective optimization…

  DOI

• Mode-locked rotating detonation waves: Experiments and a model equation

  Physical review. E · 2020 · 40 citations

  Senior authorCorresponding

  Direct observation of a rotating detonation engine combustion chamber has enabled the extraction of the kinematics of its detonation waves. These records exhibit a rich set of instabilities and bifurcations arising from the interaction of coherent wave fronts and global gain dynamics. We develop a model of the observed dynamics by recasting the Majda detonation analog as an autowave process. The solution fronts become attractors of the engine, i.e., mode-locked rotating detonation waves. We find…

  PublisherOA PDFDOI

Recent grants

• Stability of Nonlinear Waves in Mode-locked Lasers and Nonlinear Optics

  NSF · $297k · 2010–2013

• Stability and Dynamics of Dispersive Waves in Nonlinear Media

  NSF · $248k · 2006–2010

Frequent coauthors

• Steven L. Brunton

  Dynamic Systems (United States)

  289 shared

• Joshua L. Proctor

  Seattle University

  63 shared

• Bingni W. Brunton

  University of Washington

  42 shared

• Brandon G. Bale

  Aston University

  37 shared

• Eli Shlizerman

  31 shared

• Thomas D. Rea

  31 shared

• Heemun Kwok

  30 shared

• Diya Sashidhar

  University of Washington Applied Physics Laboratory

  30 shared

Education

• Ph.D., Mathematics

  University of California, San Diego

  1989

• M.S., Mathematics

  University of California, San Diego

  1986

• B.S., Mathematics

  University of California, San Diego

  1984

Awards & honors

• Professor Nathan Kutz elected SIAM fellow (April 1, 2022)

Similar researchers at University of Washington

• Robert Woodh-92
• Aleksandr Aravkinh-84
• Shuyi Chenh-69