no code implementations • 21 Oct 2024 • Oliver Bensch, Leonie Bensch, Tommy Nilsson, Florian Saling, Wafa M. Sadri, Carsten Hartmann, Tobias Hecking, J. Nathan Kutz

As humanity prepares for new missions to the Moon and Mars, astronauts will need to operate with greater autonomy, given the communication delays that make real-time support from Earth difficult.

1 code implementation • 2 Oct 2024 • Doris Voina, Steven Brunton, J. Nathan Kutz

Our method, dynamic SINDy, combines variational inference with SINDy (sparse identification of nonlinear dynamics) to model time-varying coefficients of sparse ODEs.

no code implementations • 21 Sep 2024 • Oliver Bensch, Leonie Bensch, Tommy Nilsson, Florian Saling, Bernd Bewer, Sophie Jentzsch, Tobias Hecking, J. Nathan Kutz

This paper describes the capabilities and potential of the intelligent personal assistant (IPA) CORE (Checklist Organizer for Research and Exploration), designed to support astronauts during procedures onboard the International Space Station (ISS), the Lunar Gateway station, and beyond.

1 code implementation • 31 May 2024 • Paolo Conti, Jonas Kneifl, Andrea Manzoni, Attilio Frangi, Jörg Fehr, Steven L. Brunton, J. Nathan Kutz

Starting from a limited amount of high-dimensional, noisy data the proposed framework constructs an efficient ROM by leveraging variational autoencoders for dimensionality reduction along with a newly introduced, variational version of sparse identification of nonlinear dynamics (SINDy), which we refer to as Variational Identification of Nonlinear Dynamics (VINDy).

1 code implementation • 20 May 2024 • J. Nathan Kutz, Maryam Reza, Farbod Faraji, Aaron Knoll

Reduced order models are becoming increasingly important for rendering complex and multiscale spatio-temporal dynamics computationally tractable.

no code implementations • 13 Apr 2024 • Meghana Velegar, Christoph Keller, J. Nathan Kutz

Moreover, the DMD algorithm allows for rapid reconstruction of the underlying linear model, which can then easily accommodate non-stationary data and changes in the dynamics.

1 code implementation • 14 Mar 2024 • Nicholas Zolman, Urban Fasel, J. Nathan Kutz, Steven L. Brunton

Deep reinforcement learning (DRL) has shown significant promise for uncovering sophisticated control policies that interact in environments with complicated dynamics, such as stabilizing the magnetohydrodynamics of a tokamak fusion reactor or minimizing the drag force exerted on an object in a fluid flow.

no code implementations • 4 Mar 2024 • Andrei A. Klishin, Joseph Bakarji, J. Nathan Kutz, Krithika Manohar

Recovering dynamical equations from observed noisy data is the central challenge of system identification.

no code implementations • 3 Mar 2024 • Farbod Faraji, Maryam Reza, Aaron Knoll, J. Nathan Kutz

Reduced-order plasma models that can efficiently predict plasma behavior across various settings and configurations are highly sought after yet elusive.

no code implementations • 3 Mar 2024 • Farbod Faraji, Maryam Reza, Aaron Knoll, J. Nathan Kutz

Real-world systems often exhibit dynamics influenced by various parameters, either inherent or externally controllable, necessitating models capable of reliably capturing these parametric behaviors.

no code implementations • 1 Mar 2024 • Olivia T. Zahn, Thomas L. Daniel, J. Nathan Kutz

We characterize the connectivity structure of feed-forward, deep neural networks (DNNs) using network motif theory.

no code implementations • 14 Feb 2024 • Jonas Kneifl, Jörg Fehr, Steven L. Brunton, J. Nathan Kutz

We thus propose a multi-hierarchical framework for structurally creating a series of surrogate models for a kart frame, which is a good proxy for industrial-relevant crash simulations, at different levels of resolution.

1 code implementation • 12 Nov 2023 • Ziyu Lu, Anika Tabassum, Shruti Kulkarni, Lu Mi, J. Nathan Kutz, Eric Shea-Brown, Seung-Hwan Lim

This paper explores the potential of the transformer models for learning Granger causality in networks with complex nonlinear dynamics at every node, as in neurobiological and biophysical networks.

no code implementations • 1 Nov 2023 • Samuel E. Otto, Nicholas Zolman, J. Nathan Kutz, Steven L. Brunton

For example, translation invariance in image classification allows models with fewer parameters, such as convolutional neural networks, to be trained on smaller data sets and achieve state-of-the-art performance.

no code implementations • 7 Oct 2023 • Mozes Jacobs, Bingni W. Brunton, Steven L. Brunton, J. Nathan Kutz, Ryan V. Raut

Taken together, HyperSINDy offers a promising framework for model discovery and uncertainty quantification in real-world systems, integrating sparse equation discovery methods with advances in statistical machine learning and deep generative modeling.

1 code implementation • 1 Sep 2023 • Paolo Conti, Mengwu Guo, Andrea Manzoni, Attilio Frangi, Steven L. Brunton, J. Nathan Kutz

High-fidelity numerical simulations of partial differential equations (PDEs) given a restricted computational budget can significantly limit the number of parameter configurations considered and/or time window evaluated for modeling a given system.

no code implementations • 26 Aug 2023 • Farbod Faraji, Maryam Reza, Aaron Knoll, J. Nathan Kutz

As the OPT-DMD can be constrained to produce stable reduced-order models (ROMs) by construction, in this paper, we extend the application of the OPT-DMD and investigate the capabilities of the linear ROM from this algorithm toward forecasting in time of the plasma dynamics in configurations representative of the radial-azimuthal and axial-azimuthal cross-sections of a Hall thruster and over a range of simulation parameters in each test case.

no code implementations • 26 Aug 2023 • Farbod Faraji, Maryam Reza, Aaron Knoll, J. Nathan Kutz

In this two-part article, we evaluate the utility and the generalizability of the Dynamic Mode Decomposition (DMD) algorithm for data-driven analysis and reduced-order modelling of plasma dynamics in cross-field ExB configurations.

no code implementations • 21 Jul 2023 • Andrei A. Klishin, J. Nathan Kutz, Krithika Manohar

Because of this structure, we can use just a few spatially localized sensor measurements to reconstruct the full state of a complex system.

no code implementations • 20 Jul 2023 • Megan R. Ebers, Jan P. Williams, Katherine M. Steele, J. Nathan Kutz

Sensing is one of the most fundamental tasks for the monitoring, forecasting and control of complex, spatio-temporal systems.

1 code implementation • 22 Jun 2023 • Shaowu Pan, Eurika Kaiser, Brian M. de Silva, J. Nathan Kutz, Steven L. Brunton

PyKoopman is a Python package for the data-driven approximation of the Koopman operator associated with a dynamical system.

no code implementations • 30 Mar 2023 • Steven L. Brunton, J. Nathan Kutz

Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multi-scale physics in a compact and symbolic representation.

no code implementations • 30 Jan 2023 • L. Mars Gao, Urban Fasel, Steven L. Brunton, J. Nathan Kutz

In the sparse model discovery experiment, we show that the bootstrapping-based sequential thresholding least-squares method can provide valid uncertainty quantification, converging to a delta measure centered around the true value with increased sample sizes.

1 code implementation • 27 Jan 2023 • Erdi Kara, George Zhang, Joseph J. Williams, Gonzalo Ferrandez-Quinto, Leviticus J. Rhoden, Maximilian Kim, J. Nathan Kutz, Aminur Rahman

We present a deep-learning based tracking objects of interest in walking droplet and granular intruder experiments.

no code implementations • 19 Nov 2022 • L. Mars Gao, J. Nathan Kutz

Recent progress in autoencoder-based sparse identification of nonlinear dynamics (SINDy) under $\ell_1$ constraints allows joint discoveries of governing equations and latent coordinate systems from spatio-temporal data, including simulated video frames.

no code implementations • 20 Sep 2022 • Andrea Tagliabue, Yi-Hsuan Hsiao, Urban Fasel, J. Nathan Kutz, Steven L. Brunton, Yufeng Chen, Jonathan P. How

Accurate and agile trajectory tracking in sub-gram Micro Aerial Vehicles (MAVs) is challenging, as the small scale of the robot induces large model uncertainties, demanding robust feedback controllers, while the fast dynamics and computational constraints prevent the deployment of computationally expensive strategies.

1 code implementation • 18 Sep 2022 • Alex Mallen, Christoph A. Keller, J. Nathan Kutz

In many scenarios, it is necessary to monitor a complex system via a time-series of observations and determine when anomalous exogenous events have occurred so that relevant actions can be taken.

2 code implementations • 7 Apr 2022 • Shaowu Pan, Steven L. Brunton, J. Nathan Kutz

High-dimensional spatio-temporal dynamics can often be encoded in a low-dimensional subspace.

1 code implementation • 10 Mar 2022 • Megan R. Ebers, Katherine M. Steele, J. Nathan Kutz

We introduce a discrepancy modeling framework to identify the missing physics and resolve the model-measurement mismatch with two distinct approaches: (i) by learning a model for the evolution of systematic state-space residual, and (ii) by discovering a model for the deterministic dynamical error.

no code implementations • 9 Feb 2022 • Joseph Bakarji, Jared Callaham, Steven L. Brunton, J. Nathan Kutz

In the absence of governing equations, dimensional analysis is a robust technique for extracting insights and finding symmetries in physical systems.

1 code implementation • 14 Jan 2022 • Andy Goldschmidt, James Kunert-Graf, Adrian C. Scott, Zhihao Tan, Aimée M. Dudley, J. Nathan Kutz

To look at how morphology develops, we collect a dataset of time-lapse photographs of the growth of different strains of S. cerevisiae.

no code implementations • 13 Jan 2022 • Joseph Bakarji, Kathleen Champion, J. Nathan Kutz, Steven L. Brunton

Here, we design a custom deep autoencoder network to learn a coordinate transformation from the delay embedded space into a new space where it is possible to represent the dynamics in a sparse, closed form.

1 code implementation • 5 Jan 2022 • Olivia Zahn, Jorge Bustamante Jr., Callin Switzer, Thomas Daniel, J. Nathan Kutz

This bio-inspired approach allows us to leverage network pruning to optimally sparsify a DNN architecture in order to perform flight tasks with as few neural connections as possible, however, there are limits to sparsification.

1 code implementation • 12 Nov 2021 • Alan A. Kaptanoglu, Brian M. de Silva, Urban Fasel, Kadierdan Kaheman, Andy J. Goldschmidt, Jared L. Callaham, Charles B. Delahunt, Zachary G. Nicolaou, Kathleen Champion, Jean-Christophe Loiseau, J. Nathan Kutz, Steven L. Brunton

Automated data-driven modeling, the process of directly discovering the governing equations of a system from data, is increasingly being used across the scientific community.

1 code implementation • 8 Nov 2021 • Charles B. Delahunt, J. Nathan Kutz

Second, we propose a technique, applicable to any model discovery method based on x' = f(x), to assess the accuracy of a discovered model in the context of non-unique solutions due to noisy data.

no code implementations • 29 Oct 2021 • Henning Lange, J. Nathan Kutz

In this paper, we revisit the Taylor series expansion from a modern Machine Learning perspective.

1 code implementation • 16 Aug 2021 • Olga Dorabiala, J. Nathan Kutz, Aleksandr Aravkin

Clustering is a fundamental tool in unsupervised learning, used to group objects by distinguishing between similar and dissimilar features of a given data set.

1 code implementation • 22 Jul 2021 • Diya Sashidhar, J. Nathan Kutz

The optimized DMD algorithm minimizes the model bias with a variable projection optimization, thus leading to stabilized forecasting capabilities.

no code implementations • 10 Jun 2021 • Alex Mallen, Henning Lange, J. Nathan Kutz

Probabilistic forecasting of complex phenomena is paramount to various scientific disciplines and applications.

1 code implementation • 9 Jun 2021 • Manu Kalia, Steven L. Brunton, Hil G. E. Meijer, Christoph Brune, J. Nathan Kutz

In this work, we introduce deep learning autoencoders to discover coordinate transformations that capture the underlying parametric dependence of a dynamical system in terms of its canonical normal form, allowing for a simple representation of the parametric dependence and bifurcation structure.

1 code implementation • 3 Apr 2021 • Daniel E. Shea, Rajiv Giridharagopal, David S. Ginger, Steven L. Brunton, J. Nathan Kutz

Time-series analysis is critical for a diversity of applications in science and engineering.

1 code implementation • 1 Apr 2021 • Jason J. Bramburger, Steven L. Brunton, J. Nathan Kutz

The mapping that iterates the dynamics through consecutive intersections of the flow with the subspace is now referred to as a Poincar\'e map, and it is the primary method available for interpreting and classifying chaotic dynamics.

4 code implementations • 24 Feb 2021 • Steven L. Brunton, Marko Budišić, Eurika Kaiser, J. Nathan Kutz

The field of dynamical systems is being transformed by the mathematical tools and algorithms emerging from modern computing and data science.

4 code implementations • 20 Feb 2021 • Brian M. de Silva, Krithika Manohar, Emily Clark, Bingni W. Brunton, Steven L. Brunton, J. Nathan Kutz

PySensors is a Python package for selecting and placing a sparse set of sensors for classification and reconstruction tasks.

1 code implementation • 31 Dec 2020 • Craig R. Gin, Daniel E. Shea, Steven L. Brunton, J. Nathan Kutz

We find that the method succeeds on a variety of nonlinear systems including nonlinear Helmholtz and Sturm--Liouville problems, nonlinear elasticity, and a 2D nonlinear Poisson equation.

no code implementations • 8 Oct 2020 • Daniel Dylewsky, David Barajas-Solano, Tong Ma, Alexandre M. Tartakovsky, J. Nathan Kutz

Time series forecasting remains a central challenge problem in almost all scientific disciplines.

2 code implementations • 12 Sep 2020 • Kadierdan Kaheman, Steven L. Brunton, J. Nathan Kutz

The sparse identification of nonlinear dynamics (SINDy) is a regression framework for the discovery of parsimonious dynamic models and governing equations from time-series data.

1 code implementation • 3 Sep 2020 • Floris van Breugel, J. Nathan Kutz, Bingni W. Brunton

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.

Dynamical Systems Signal Processing

no code implementations • 24 Aug 2020 • Steven L. Brunton, J. Nathan Kutz, Krithika Manohar, Aleksandr Y. Aravkin, Kristi Morgansen, Jennifer Klemisch, Nicholas Goebel, James Buttrick, Jeffrey Poskin, Agnes Blom-Schieber, Thomas Hogan, Darren McDonald

Indeed, emerging methods in machine learning may be thought of as data-driven optimization techniques that are ideal for high-dimensional, non-convex, and constrained, multi-objective optimization problems, and that improve with increasing volumes of data.

1 code implementation • 22 Aug 2020 • Yu-Ying Liu, J. Nathan Kutz, Steven L. Brunton

Our multiscale hierarchical time-stepping scheme provides important advantages over current time-stepping algorithms, including (i) circumventing numerical stiffness due to disparate time-scales, (ii) improved accuracy in comparison with leading neural-network architectures, (iii) efficiency in long-time simulation/forecasting due to explicit training of slow time-scale dynamics, and (iv) a flexible framework that is parallelizable and may be integrated with standard numerical time-stepping algorithms.

1 code implementation • 5 Aug 2020 • Diya Sashidhar, Heemun Kwok, Jason Coult, Jen Blackwood, Peter Kudenchuck, Shiv Bhandari, Thomas Rea, J. Nathan Kutz

Segments were collected during the 10s period of ongoing CPR prior to a pulse check, and 5s segments without CPR during the pulse check.

no code implementations • 31 Jul 2020 • Emily Clark, Angelie Vincent, J. Nathan Kutz, Steven L. Brunton

Brackets are an essential component in aircraft manufacture and design, joining parts together, supporting weight, holding wires, and strengthening joints.

1 code implementation • 23 Jun 2020 • George Stepaniants, Bingni W. Brunton, J. Nathan Kutz

Our proposed PCI method demonstrated consistently strong performance in inferring causal relations for small (2-5 node) and large (10-20 node) networks, with both linear and nonlinear dynamics.

Dynamical Systems Adaptation and Self-Organizing Systems Applications 37M10, 62D20, 62M10

no code implementations • 10 Jun 2020 • Chang Sun, Eurika Kaiser, Steven L. Brunton, J. Nathan Kutz

We demonstrate that deep reinforcement learning (deep RL) provides a highly effective strategy for the control and self-tuning of optical systems.

1 code implementation • 1 Jun 2020 • Jason J. Bramburger, Daniel Dylewsky, J. Nathan Kutz

We show that for sufficiently disparate timescales this discovered mapping can be used to discover the continuous-time slow dynamics, thus providing a novel tool for extracting dynamics on multiple timescales.

1 code implementation • 28 May 2020 • Daniel Dylewsky, Eurika Kaiser, Steven L. Brunton, J. Nathan Kutz

Delay embeddings of time series data have emerged as a promising coordinate basis for data-driven estimation of the Koopman operator, which seeks a linear representation for observed nonlinear dynamics.

Computational Physics Systems and Control Systems and Control

no code implementations • 7 May 2020 • Emily Clark, Steven L. Brunton, J. Nathan Kutz

We develop greedy algorithms to approximate the optimal solution to the multi-fidelity sensor selection problem, which is a cost constrained optimization problem prescribing the placement and number of cheap (low signal-to-noise) and expensive (high signal-to-noise) sensors in an environment or state space.

2 code implementations • 17 Apr 2020 • Brian M. de Silva, Kathleen Champion, Markus Quade, Jean-Christophe Loiseau, J. Nathan Kutz, Steven L. Brunton

PySINDy is a Python package for the discovery of governing dynamical systems models from data.

Dynamical Systems Computational Physics

1 code implementation • 10 Apr 2020 • Yu-Ying Liu, Colin Ponce, Steven L. Brunton, J. Nathan Kutz

The performance gains of this adaptive multiscale architecture are illustrated through a sequence of numerical experiments on synthetic examples and real-world spatial-temporal data.

1 code implementation • 5 Apr 2020 • Kadierdan Kaheman, J. Nathan Kutz, Steven L. Brunton

In this work, we develop SINDy-PI (parallel, implicit), a robust variant of the SINDy algorithm to identify implicit dynamics and rational nonlinearities.

no code implementations • 7 Nov 2019 • Craig Gin, Bethany Lusch, Steven L. Brunton, J. Nathan Kutz

By leveraging a residual network architecture, a near-identity transformation can be exploited to encode intrinsic coordinates in which the dynamics are linear.

no code implementations • 18 Sep 2019 • Kadierdan Kaheman, Eurika Kaiser, Benjamin Strom, J. Nathan Kutz, Steven L. Brunton

First principles modeling of physical systems has led to significant technological advances across all branches of science.

1 code implementation • NeurIPS Workshop Neuro_AI 2019 • Charles B. Delahunt, J. Nathan Kutz

In this work we deploy MothNet, a computational model of the moth olfactory network, as an automatic feature generator.

1 code implementation • 28 Aug 2019 • Jason J. Bramburger, J. Nathan Kutz

Poincar\'e maps are an integral aspect to our understanding and analysis of nonlinear dynamical systems.

Dynamical Systems Chaotic Dynamics

4 code implementations • 25 Jun 2019 • Kathleen Champion, Peng Zheng, Aleksandr Y. Aravkin, Steven L. Brunton, J. Nathan Kutz

This flexible approach can be tailored to the unique challenges associated with a wide range of applications and data sets, providing a powerful ML-based framework for learning governing models for physical systems from data.

1 code implementation • 19 Jun 2019 • Brian M. de Silva, David M. Higdon, Steven L. Brunton, J. Nathan Kutz

Machine learning (ML) and artificial intelligence (AI) algorithms are now being used to automate the discovery of physics principles and governing equations from measurement data alone.

no code implementations • 24 May 2019 • Katharina Bieker, Sebastian Peitz, Steven L. Brunton, J. Nathan Kutz, Michael Dellnitz

The control of complex systems is of critical importance in many branches of science, engineering, and industry.

1 code implementation • 20 Feb 2019 • N. Benjamin Erichson, Lionel Mathelin, Zhewei Yao, Steven L. Brunton, Michael W. Mahoney, J. Nathan Kutz

In many applications, it is important to reconstruct a fluid flow field, or some other high-dimensional state, from limited measurements and limited data.

no code implementations • 26 Jan 2019 • Charles B. Delahunt, Courosh Mehanian, J. Nathan Kutz

To explore this potential resource, we develop a hybrid classifier (Softmax-Pooling Hybrid, $SPH$) that uses Softmax on high-scoring samples, but on low-scoring samples uses a log-likelihood method that pools the information from the full array $D$.

no code implementations • 2 Nov 2018 • Eurika Kaiser, J. Nathan Kutz, Steven L. Brunton

In this work, we formulate a data-driven architecture for discovering conserved quantities based on Koopman theory.

1 code implementation • 23 Aug 2018 • Charles B. Delahunt, J. Nathan Kutz

In this work, we deployed MothNet, a computational model of the insect olfactory network, as an automatic feature generator: Attached as a front-end pre-processor, its Readout Neurons provided new features, derived from the original features, for use by standard ML classifiers.

1 code implementation • 7 Aug 2018 • Samuel H. Rudy, J. Nathan Kutz, Steven L. Brunton

A critical challenge in the data-driven modeling of dynamical systems is producing methods robust to measurement error, particularly when data is limited.

Numerical Analysis

no code implementations • 14 Jul 2018 • Peng Zheng, Travis Askham, Steven L. Brunton, J. Nathan Kutz, Aleksandr Y. Aravkin

We demonstrate the advantages of SR3 (computational efficiency, higher accuracy, faster convergence rates, greater flexibility) across a range of regularized regression problems with synthetic and real data, including applications in compressed sensing, LASSO, matrix completion, TV regularization, and group sparsity.

1 code implementation • 9 May 2018 • Emily Clark, Travis Askham, Steven L. Brunton, J. Nathan Kutz

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 experiments.

Optimization and Control

no code implementations • 1 Apr 2018 • N. Benjamin Erichson, Peng Zheng, Krithika Manohar, Steven L. Brunton, J. Nathan Kutz, Aleksandr Y. Aravkin

Sparse principal component analysis (SPCA) has emerged as a powerful technique for modern data analysis, providing improved interpretation of low-rank structures by identifying localized spatial structures in the data and disambiguating between distinct time scales.

no code implementations • 23 Feb 2018 • N. Benjamin Erichson, Lionel Mathelin, Steven L. Brunton, J. Nathan Kutz

Diffusion maps are an emerging data-driven technique for non-linear dimensionality reduction, which are especially useful for the analysis of coherent structures and nonlinear embeddings of dynamical systems.

1 code implementation • 15 Feb 2018 • Charles B. Delahunt, J. Nathan Kutz

The Moth Olfactory Network is among the simplest biological neural systems that can learn, and its architecture includes key structural elements and mechanisms widespread in biological neural nets, such as cascaded networks, competitive inhibition, high intrinsic noise, sparsity, reward mechanisms, and Hebbian plasticity.

1 code implementation • 8 Feb 2018 • Charles B. Delahunt, Jeffrey A. Riffell, J. Nathan Kutz

From a biological perspective, the model provides a valuable tool for examining the role of neuromodulators, like octopamine, in learning, and gives insight into critical interactions between sparsity, Hebbian growth, and stimulation during learning.

2 code implementations • 27 Dec 2017 • Bethany Lusch, J. Nathan Kutz, Steven L. Brunton

Identifying coordinate transformations that make strongly nonlinear dynamics approximately linear is a central challenge in modern dynamical systems.

no code implementations • 14 Dec 2017 • Krithika Manohar, Eurika Kaiser, Steven L. Brunton, J. Nathan Kutz

The multiresolution DMD is capable of characterizing nonlinear dynamical systems in an equation-free manner by recursively decomposing the state of the system into low-rank spatial modes and their temporal Fourier dynamics.

Dynamical Systems Numerical Analysis Data Analysis, Statistics and Probability

no code implementations • 24 Nov 2017 • Krithika Manohar, Thomas Hogan, Jim Buttrick, Ashis G. Banerjee, J. Nathan Kutz, Steven L. Brunton

This new approach is based on the assumption that patterns exist in shim distributions across aircraft, which may be mined and used to reduce the burden of data collection and processing in future aircraft.

2 code implementations • 15 Nov 2017 • Eurika Kaiser, J. Nathan Kutz, Steven L. Brunton

These factors limit the use of these techniques for the online identification of a model in the low-data limit, for example following an abrupt change to the system dynamics.

Optimization and Control Dynamical Systems Data Analysis, Statistics and Probability

2 code implementations • 6 Nov 2017 • N. Benjamin Erichson, Ariana Mendible, Sophie Wihlborn, J. Nathan Kutz

Nonnegative matrix factorization (NMF) is a powerful tool for data mining.

no code implementations • 2 Nov 2017 • Thomas Baumeister, Steven L. Brunton, J. Nathan Kutz

Self-tuning optical systems are of growing importance in technological applications such as mode-locked fiber lasers.

1 code implementation • 4 Jul 2017 • Eurika Kaiser, J. Nathan Kutz, Steven L. Brunton

In this work, we demonstrate a data-driven control architecture, termed Koopman Reduced Order Nonlinear Identification and Control (KRONIC), that utilizes Koopman eigenfunctions to manipulate nonlinear systems using linear systems theory.

Optimization and Control Dynamical Systems

1 code implementation • 13 Dec 2016 • Bethany Lusch, Jake Weholt, Pedro D. Maia, J. Nathan Kutz

However, we provide important insight and a quantitative framework for disorders in which FAS are implicated.

1 code implementation • 21 Sep 2016 • Samuel H. Rudy, Steven L. Brunton, Joshua L. Proctor, J. Nathan Kutz

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.

Pattern Formation and Solitons

1 code implementation • 16 Aug 2016 • Bethany Lusch, Eric C. Chi, J. Nathan Kutz

We consider $N$-way data arrays and low-rank tensor factorizations where the time mode is coded as a sparse linear combination of temporal elements from an over-complete library.

6 code implementations • 6 Aug 2016 • N. Benjamin Erichson, Sergey Voronin, Steven L. Brunton, J. Nathan Kutz

The essential idea of probabilistic algorithms is to employ some amount of randomness in order to derive a smaller matrix from a high-dimensional data matrix.

Computation Mathematical Software Methodology

no code implementations • 14 Dec 2015 • N. Benjamin Erichson, Steven L. Brunton, J. Nathan Kutz

We introduce the method of compressed dynamic mode decomposition (cDMD) for background modeling.

2 code implementations • 11 Sep 2015 • Steven L. Brunton, Joshua L. Proctor, J. Nathan Kutz

In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing physical equations from measurement data.

Dynamical Systems

2 code implementations • 22 Sep 2014 • Joshua L. Proctor, Steven L. Brunton, J. Nathan Kutz

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.

Optimization and Control

no code implementations • 30 Apr 2014 • Jacob Grosek, J. Nathan Kutz

Finding the best set of gestures to use for a given computer recognition problem is an essential part of optimizing the recognition performance while being mindful to those who may articulate the gestures.

no code implementations • 30 Apr 2014 • Jacob Grosek, J. Nathan Kutz

This paper introduces the method of dynamic mode decomposition (DMD) for robustly separating video frames into background (low-rank) and foreground (sparse) components in real-time.

no code implementations • 24 Oct 2013 • James Kunert, Eli Shlizerman, J. Nathan Kutz

We develop a biophysical model of neuro-sensory integration in the model organism Caenorhabditis elegans.

Cannot find the paper you are looking for? You can
Submit a new open access paper.

Contact us on:
hello@paperswithcode.com
.
Papers With Code is a free resource with all data licensed under CC-BY-SA.