no code implementations • 5 Sep 2024 • Esther Lagemann, Julia Roeb, Steven L. Brunton, Christian Lagemann

To address this gap, we introduce a deep learning architecture that ingests wall-parallel velocity fields from the logarithmic layer of turbulent wall-bounded flows and outputs the corresponding 2D wall-shear stress fields with identical spatial resolution and domain size.

no code implementations • 29 Aug 2024 • Tanner D. Harms, Steven L. Brunton, Beverley J. McKeon

The goal of this work is to extend gradient-based dynamical systems analyses to real-world applications characterized by complex, feature-rich image sequences with imperfect tracers.

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).

no code implementations • 7 May 2024 • Ricardo Vinuesa, Jean Rabault, Hossein Azizpour, Stefan Bauer, Bingni W. Brunton, Arne Elofsson, Elias Jarlebring, Hedvig Kjellstrom, Stefano Markidis, David Marlevi, Paola Cinnella, Steven L. Brunton

Technological advancements have substantially increased computational power and data availability, enabling the application of powerful machine-learning (ML) techniques across various fields.

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 • Preston Rozwood, Edward Mehrez, Ludger Paehler, Wen Sun, Steven L. Brunton

In particular, the Koopman operator is able to capture the expectation of the time evolution of the value function of a given system via linear dynamics in the lifted coordinates.

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.

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 • 17 Oct 2023 • Esther Lagemann, Steven L. Brunton, Christian Lagemann

Friction drag from a turbulent fluid moving past or inside an object plays a crucial role in domains as diverse as transportation, public utility infrastructure, energy technology, and human health.

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 • 23 Jun 2023 • Niharika Karnik, Mohammad G. Abdo, Carlos E. Estrada Perez, Jun Soo Yoo, Joshua J. Cogliati, Richard S. Skifton, Pattrick Calderoni, Steven L. Brunton, Krithika Manohar

Strategically placing sensors within defined spatial constraints is essential for the reconstruction of reactor flow fields and the creation of nuclear digital twins.

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 • 28 Mar 2023 • Ricardo Vinuesa, Steven L. Brunton, Beverley J. McKeon

The field of machine learning has rapidly advanced the state of the art in many fields of science and engineering, including experimental fluid dynamics, which is one of the original big-data disciplines.

no code implementations • 4 Feb 2023 • Alan A. Kaptanoglu, Lanyue Zhang, Zachary G. Nicolaou, Urban Fasel, Steven L. Brunton

Sparse system identification is the data-driven process of obtaining parsimonious differential equations that describe the evolution of a dynamical system, balancing model complexity and accuracy.

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 • 25 Jan 2023 • Sebastian Peitz, Jan Stenner, Vikas Chidananda, Oliver Wallscheid, Steven L. Brunton, Kunihiko Taira

We present a convolutional framework which significantly reduces the complexity and thus, the computational effort for distributed reinforcement learning control of dynamical systems governed by partial differential equations (PDEs).

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 • 8 Apr 2022 • Emma Hansen, Steven L. Brunton, Zhuoyuan Song

Modelling biological or engineering swarms is challenging due to the inherently high dimension of the system, despite the often low-dimensional emergent dynamics.

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.

no code implementations • 11 Feb 2022 • Said Ouala, Steven L. Brunton, Ananda Pascual, Bertrand Chapron, Fabrice Collard, Lucile Gaultier, Ronan Fablet

The complexity of real-world geophysical systems is often compounded by the fact that the observed measurements depend on hidden variables.

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.

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 • 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 • 28 Oct 2021 • Moritz Hoffmann, Martin Scherer, Tim Hempel, Andreas Mardt, Brian de Silva, Brooke E. Husic, Stefan Klus, Hao Wu, Nathan Kutz, Steven L. Brunton, Frank Noé

Generation and analysis of time-series data is relevant to many quantitative fields ranging from economics to fluid mechanics.

no code implementations • 5 Oct 2021 • Steven L. Brunton

This paper provides a short overview of how to use machine learning to build data-driven models in fluid mechanics.

no code implementations • 5 Oct 2021 • Ricardo Vinuesa, Steven L. Brunton

Machine learning is rapidly becoming a core technology for scientific computing, with numerous opportunities to advance the field of computational fluid dynamics.

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.

5 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.

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.

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.

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.

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 • 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.

1 code implementation • 22 Apr 2020 • Alan A. Kaptanoglu, Kyle D. Morgan, Chris J. Hansen, Steven L. Brunton

Galerkin models, obtained by projection of the MHD equations onto a truncated modal basis, and data-driven models, obtained by modern machine learning and system identification, can furnish this gap in the lower levels of the model hierarchy.

Computational Physics Fluid Dynamics Plasma Physics

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.

2 code implementations • 1 Apr 2020 • Henning Lange, Steven L. Brunton, Nathan Kutz

We propose spectral methods for long-term forecasting of temporal signals stemming from linear and nonlinear quasi-periodic dynamical systems.

1 code implementation • 8 Feb 2020 • Nicola Fonzi, Steven L. Brunton, Urban Fasel

Accurate and efficient aeroelastic models are critically important for enabling the optimization and control of highly flexible aerospace structures, which are expected to become pervasive in future transportation and energy systems.

Fluid Dynamics Optimization and Control

1 code implementation • 10 Dec 2019 • Thomas L. Mohren, Thomas L. Daniel, Steven L. Brunton

In this work, we investigate biologically inspired strategies to develop precisely timed feedforward control laws for engineered systems with large time delays.

Systems and Control Systems and Control

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.

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 • 28 Nov 2018 • Chen Gong, N. Benjamin Erichson, John P. Kelly, Laura Trutoiu, Brian T. Schowengerdt, Steven L. Brunton, Eric J. Seibel

To the best of our knowledge, this is the first template matching algorithm for retina images with small template images from unconstrained retinal areas.

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 • 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.

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

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

3 code implementations • 5 Feb 2017 • Kunihiko Taira, Steven L. Brunton, Scott T. M. Dawson, Clarence W. Rowley, Tim Colonius, Beverley J. McKeon, Oliver T. Schmidt, Stanislav Gordeyev, Vassilios Theofilis, Lawrence S. Ukeiley

Simple aerodynamic configurations under even modest conditions can exhibit complex flows with a wide range of temporal and spatial features.

Fluid Dynamics

no code implementations • 12 Jan 2017 • Wei Guo, Krithika Manohar, Steven L. Brunton, Ashis G. Banerjee

Topological data analysis (TDA) has emerged as one of the most promising techniques to reconstruct the unknown shapes of high-dimensional spaces from observed data samples.

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

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

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