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
• Algorithm
• Quantum mechanics
• Acoustics
• Chemistry
• Thermodynamics

Selected publications

• Ecosystem-wide PFAS characterization and environmental behavior at a heavily contaminated desert oasis in the southwestern U.S.

  Environmental Research · 2025-05-22 · 8 citations

  article
  PublisherDOI

• Data assimilation and discrepancy modeling with shallow recurrent decoders

  ArXiv.org · 2025-12-01

  preprintOpen accessSenior author

  The requirements of modern sensing are rapidly evolving, driven by increasing demands for data efficiency, real-time processing, and deployment under limited sensing coverage. Complex physical systems are often characterized through the integration of a limited number of point sensors in combination with scientific computations which approximate the dominant, full-state dynamics. Simulation models, however, inevitably neglect small-scale or hidden processes, are sensitive to perturbations, or oversimplify parameter correlations, leading to reconstructions that often diverge from the reality measured by sensors. This creates a critical need for data assimilation, the process of integrating observational data with predictive simulation models to produce coherent and accurate estimates of the full state of complex physical systems. We propose a machine learning framework for Data Assimilation with a SHallow REcurrent Decoder (DA-SHRED) which bridges the simulation-to-real (SIM2REAL) gap between computational modeling and experimental sensor data. For real-world physics systems modeling high-dimensional spatiotemporal fields, where the full state cannot be directly observed and must be inferred from sparse sensor measurements, we leverage the latent space learned from a reduced simulation model via SHRED, and update these latent variables using real sensor data to accurately reconstruct the full system state. Furthermore, our algorithm incorporates a sparse identification of nonlinear dynamics based regression model in the latent space to identify functionals corresponding to missing dynamics in the simulation model. We demonstrate that DA-SHRED successfully closes the SIM2REAL gap and additionally recovers missing dynamics in highly complex systems, demonstrating that the combination of efficient temporal encoding and physics-informed correction enables robust data assimilation.

  PublisherOA PDFDOI

• Towards remote sensing of sub-surface turbulence from surface-only measurements with the SHRED machine learning framework

  2025-03-14

  preprintOpen accessSenior author

  Near-surface turbulent fluid flows beneath a free surface are reconstructed from sparse measurements of the surface only. We study data from direct numerical simulations (DNS) as well as a laboratory experiment.  Fast and economical measurements of the turbulent flow near the free surface of natural flows is of high importance, for estimation and monitoring of a range of environmental factors. Gas evasion from rivers make a large and poorly constrained contribution to the total CO2 emissions, the transfer rates of gas and heat between water and atmosphere transfer are controlled by near-surface turbulent mixing. Transport of microplastics and nutrients and the living conditions of phytoplankton depend on turbulent mixing. The ability to estimate, e.g., the rate of gas transfer from rivers based on video footage taken from drones would enable coverage of large areas, much faster and at much lower cost than state-of-the-art in situ measurements.We employ a machine learning approach to build on recent progress in quantifying sub-surface turbulent flow from surface-only observations, such as utilising surface imprints to identify strong sub-surface turbulent flow structures [1]. A previous machine learning approach showed promise, using the same DNS data that we also employ [2].We apply a recently developed method, the Shallow Recurrent Decoder (SHRED) neural network [3], to free-surface turbulent flows. It combines a recurrent network, which learns a latent representation of the temporal dynamics of the system, with a shallow decoder network, that transforms this latent space back to real-state space. The algorithm is applied to DNS cases and experimental cases of different turbulence levels, with several horizontal subsurface velocity planes measured simultaneously as the surface. The temporal dynamics of subsurface planes are successfully reconstructed from as little as three time-resolved sensors at the surface, with low-rank features matching well with ground truth data, as well as matching turbulence spectra in the low-wavenumber regime. Depth profiles of selected error metrics suggest reasonable velocity field reconstructions, although the performance generally decreases with depth. Our results amount to a proof of concept of a method with potential to facilitate remote sensing of sub-surface flow from e.g. video images.[1] J. R. Aarnes, O.M. Babiker, A. Xuan, L. Shen, and S.Å. Ellingsen (2025). “Vortex structures under dimples and scars in turbulent free-surface flows”. J. Fluid Mech., accepted, Preprint: https://doi.org/10.48550/arXiv.2409.05409[2] A.Xuan and L.Shen (2023) “Reconstruction of three-dimensional turbulent flow structures using surface measurements for free-surface flows based on a convolutional neural network” J. Fluid Mech. 959 A34.[3] J. P. Williams, O. Zahn, and J. N. Kutz (2024), “Sensing with shallow recurrent decoder networks,” Proc. R. Soc. A, 480, no. 2298.

  PublisherDOI

• Accelerating scientific discovery with the common task framework

  ArXiv.org · 2025-11-06

  preprintOpen access1st authorCorresponding

  Machine learning (ML) and artificial intelligence (AI) algorithms are transforming and empowering the characterization and control of dynamic systems in the engineering, physical, and biological sciences. These emerging modeling paradigms require comparative metrics to evaluate a diverse set of scientific objectives, including forecasting, state reconstruction, generalization, and control, while also considering limited data scenarios and noisy measurements. We introduce a common task framework (CTF) for science and engineering, which features a growing collection of challenge data sets with a diverse set of practical and common objectives. The CTF is a critically enabling technology that has contributed to the rapid advance of ML/AI algorithms in traditional applications such as speech recognition, language processing, and computer vision. There is a critical need for the objective metrics of a CTF to compare the diverse algorithms being rapidly developed and deployed in practice today across science and engineering.

  PublisherOA PDFDOI

• Shallow Recurrent Decoders for Neural and Behavioral Dynamics

  bioRxiv (Cold Spring Harbor Laboratory) · 2025-06-26

  preprintOpen accessSenior authorCorresponding

  Abstract Machine learning algorithms are affording new opportunities for building bio-inspired and data-driven models characterizing neural activity. Critical to understanding decision making and behavior is quantifying the relationship between the activity of neuronal population codes and individual neurons. We leverage a SHallow REcurrent Decoding (SHRED) architecture for mapping the dynamics of population codes to individual neurons and other proxy measures of neural activity and behavior. SHRED is a robust and flexible sensing strategy which allows for decoding the diversity of neural measurements with only a few sensor measurements. Thus estimates of whole brain activity, behavior and individual neurons can be constructed with only a few neural time-series recordings. This opens up the potential for using non-invasive, or minimally invasive, measurements for estimating difficult to achieve, or invasive, large scale brain and neural recordings. SHRED is constructed from a temporal sequence model, which encodes the temporal dynamics of limited sensor data in multiple scenarios, and a shallow decoder, which reconstructs the corresponding high-dimensional neuronal and/or behavioral states. We demonstrate the capabilities of the method on a number of model organisms including C. elegans , mouse, zebrafish, and human biolocomotion.

  PublisherOA PDFDOI

• Data-driven local operator finding for reduced-order modeling of plasma systems

  Journal of Physics D Applied Physics · 2025-03-10 · 4 citations

  articleOpen accessSenior author

  Abstract Computationally efficient reduced-order plasma models, able to predict plasma behavior reliably and self-consistently, have remained unachievable so far. The need for these models has nonetheless continuously increased over the past decade for both fundamental studies and engineering applications. With the increase in computational power in recent years and the emergence of several approaches that lower the computational burden of generating extensive high-fidelity plasma datasets, data-driven (DD) dynamics discovery methods can play a transformative role toward the realization of predictive, generalizable and interpretable reduced-order models (ROMs) for plasma systems. In this work, we introduce a novel DD algorithm—the ‘Phi Method’—for the discovery of discretized systems of differential equations describing the dynamics. The success and generalizability of Phi Method is rooted in its constrained regression on a library of candidate terms that is informed by numerical discretization schemes. The Phi Method’s performance is first demonstrated for a one-dimensional plasma problem, representative of the discharge evolution along the azimuthal direction of a typical Hall thruster. Next, we assess the Phi Method’s application toward parametric dynamics discovery, i.e. deriving models that embed parametric variations of the dynamics and in turn aim to provide faithful predictions of the systems’ behavior over unseen parameter spaces. In terms of salient results, we observe that the Phi-method-derived ROM provides remarkably accurate predictions of the evolution dynamics of the involved plasma state variables. The parametric Phi Method is further able to well recover the governing parametric partial differential equation for the adopted plasma test case and to provide accurate predictions of the system dynamics over a wide range of test parameters.

  PublisherDOI

• Abstract Sun906: Deep Learning for Defibrillator Shock Decision Analysis during Manual CPR

  Circulation · 2025-11-03

  article

  Introduction: Successful resuscitation of ventricular fibrillation (VF) out-of-hospital cardiac arrest (OHCA) relies on timely defibrillation and minimally-interrupted CPR. Defibrillator shock decision analysis has traditionally required CPR interruption because CPR causes electrical artifacts in the ECG signal. Recent emerging defibrillator algorithms have been proposed to reduce or eliminate CPR interruption for shock decision analysis. However, these methods are challenged by lower sensitivity, a high proportion of indeterminates, or requirement for CPR-free rhythm confirmation. Aim: We sought to determine whether a deep learning algorithm can accurately detect shockable rhythms during CPR. Methods: We performed a retrospective cohort study of adult VF-OHCA cases in King County WA from 2006-2021. Patients were randomized into training (60%), validation (20%), and test (20%) groups. We annotated the entirety of defibrillator paddle ECG recordings from cohort patients as non-shockable (Asystole, Organized Rhythms) or shockable (VF, Ventricular Tachycardia). ECGs were segmented into non-overlapping 2.5-s clips. The presence of CPR was confirmed by review of thoracic impedance. The algorithm comprised two steps: (1) A deep convolutional neural network predicted individual clip classes based on ECG scalogram images, and (2) a deep long short-term memory recurrent network incorporated the sequence of prior clip predictions to inform each clip’s current-time prediction. Results: Of 2682 eligible patients, N=2011 (75%) with available defibrillator files were included in the cohort; 1207, 402, and 402 patients were used for algorithm training, validation, and test, respectively. A total of 1047601 2.5-s ECG clips were collected from the cohort, with 604484 (58%) collected during CPR. During CPR, algorithm sensitivity/specificity for detecting shockable rhythms in training, validation, and test data were 99.0%/99.0%, 97.4%/98.9%, and 99.1%/98.7% respectively (Table 1). Of the CPR clips, 99628 (16.5%) were predicted as indeterminate by the algorithm and not scored. When indeterminate decisions were disallowed, algorithm sensitivity/specificity values in training, validation, and test groups were 92.7%/98.7%, 90.8%/97.6%, and 91.8%/97.9%, respectively. Conclusions: A deep learning algorithm developed using >1 million ECG segments can accurately detect shockable rhythms during CPR, suggesting potential to reduce CPR interruption and improve VF-OHCA resuscitation.

  PublisherDOI

• Mapping surface height dynamics to subsurface flow physics in free-surface turbulent flow using a shallow recurrent decoder

  ArXiv.org · 2025-10-07

  preprintOpen accessSenior author

  Near-surface turbulent flows beneath a free surface are reconstructed from sparse measurements of the surface height variation, by a novel neural network algorithm known as the {\em SHallow REcurrent Decoder} (SHRED). The reconstruction of turbulent flow fields from limited, partial, or indirect measurements remains a grand challenge in science and engineering. The central goal in such applications is to leverage easy-to-measure proxy variables in order to estimate quantities which have not been, and perhaps cannot in practice be, measured. Specifically, in the application considered here, the aim is to use a sparse number of surface height point measurements of a flow field, or drone video footage of surface features, in order to infer the turbulent flow field beneath the surface. SHRED is a deep learning architecture that learns a delay-coordinate embedding from a few surface height (point) sensors and maps it, via a shallow decoder trained in a compressed basis, to full subsurface fields, enabling fast, robust training from minimal data. We demonstrate the SHRED sensing architecture on two types of turbulent data from recent studies (Aarnes \emph{et al.} J.~Fluid Mech.\ \textbf{1007} A38, 2025 and Babiker \emph{et al.} arXiv:251003732, 2025, respectively): fully resolved DNS data and PIV laboratory data from a turbulent water tank. SHRED is capable of robustly mapping surface height fluctuations to full-state flow fields up to about two integral length scales deep, with as few as three surface measurements.

  PublisherOA PDFDOI

• Towards Efficient Parametric State Estimation in Circulating Fuel Reactors with Shallow Recurrent Decoder Networks

  ArXiv.org · 2025-03-11

  preprintOpen access

  The recent developments in data-driven methods have paved the way to new methodologies to provide accurate state reconstruction of engineering systems; nuclear reactors represent particularly challenging applications for this task due to the complexity of the strongly coupled physics involved and the extremely harsh and hostile environments, especially for new technologies such as Generation-IV reactors. Data-driven techniques can combine different sources of information, including computational proxy models and local noisy measurements on the system, to robustly estimate the state. This work leverages the novel Shallow Recurrent Decoder architecture to infer the entire state vector (including neutron fluxes, precursors concentrations, temperature, pressure and velocity) of a reactor from three out-of-core time-series neutron flux measurements alone. In particular, this work extends the standard architecture to treat parametric time-series data, ensuring the possibility of investigating different accidental scenarios and showing the capabilities of this approach to provide an accurate state estimation in various operating conditions. This paper considers as a test case the Molten Salt Fast Reactor (MSFR), a Generation-IV reactor concept, characterised by strong coupling between the neutronics and the thermal hydraulics due to the liquid nature of the fuel. The promising results of this work are further strengthened by the possibility of quantifying the uncertainty associated with the state estimation, due to the considerably low training cost. The accurate reconstruction of every characteristic field in real-time makes this approach suitable for monitoring and control purposes in the framework of a reactor digital twin.

  PublisherOA PDFDOI

• Information theory and discriminative sampling for model discovery

  ArXiv.org · 2025-12-17

  preprintOpen accessSenior author

  Fisher information and Shannon entropy are fundamental tools for understanding and analyzing dynamical systems from complementary perspectives. They can characterize unknown parameters by quantifying the information contained in variables, or measure how different initial trajectories or temporal segments of a trajectory contribute to learning or inferring system dynamics. In this work, we leverage the Fisher Information Matrix (FIM) within the data-driven framework of {\em sparse identification of nonlinear dynamics} (SINDy). We visualize information patterns in chaotic and non-chaotic systems for both single trajectories and multiple initial conditions, demonstrating how information-based analysis can improve sampling efficiency and enhance model performance by prioritizing more informative data. The benefits of statistical bagging are further elucidated through spectral analysis of the FIM. We also illustrate how Fisher information and entropy metrics can promote data efficiency in three scenarios: when only a single trajectory is available, when a tunable control parameter exists, and when multiple trajectories can be freely initialized. As data-driven model discovery continues to gain prominence, principled sampling strategies guided by quantifiable information metrics offer a powerful approach for improving learning efficiency and reducing data requirements.

  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)