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Decomposition of Nonlinear Dynamical Systems Using Koopman Gramians [article]

Zhiyuan Liu, Soumya Kundu, Lijun Chen, Enoch Yeung
2017 arXiv   pre-print
In this paper we propose a new Koopman operator approach to the decomposition of nonlinear dynamical systems using Koopman Gramians.  ...  We then extend an existing method of dynamic mode decomposition for learning Koopman operators from data known as deep dynamic mode decomposition to systems with controls or disturbances.  ...  These results underscore the power of learning representations for approximate data-driven control.  ... 
arXiv:1710.01719v1 fatcat:ghapjdmjgvbljo3yahdymphx5e

Data-driven model reduction of agent-based systems using the Koopman generator [article]

Jan-Hendrik Niemann, Stefan Klus, Christof Schütte
2021 arXiv   pre-print
In this paper, we show how Koopman operator theory can be used to derive reduced models of agent-based systems using only simulation data.  ...  The dynamical behavior of social systems can be described by agent-based models.  ...  Berlin Mathematics Research Center, EXC-2046/1, project ID: 390685689) and through Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through grant CRC 1114 (Scaling Cascades in Complex Systems  ... 
arXiv:2012.07718v2 fatcat:y4kr6kqfojdphbwg5na6n77sma

Data-driven model reduction of agent-based systems using the Koopman generator

Jan-Hendrik Niemann, Stefan Klus, Christof Schütte, Ramon Grima
2021 PLoS ONE  
In this paper, we show how Koopman operator theory can be used to derive reduced models of agent-based systems using only simulation data.  ...  The dynamical behavior of social systems can be described by agent-based models.  ...  Our approach to learn coarse-grained systems for complex ABM dynamics relies on Koopman operator theory.  ... 
doi:10.1371/journal.pone.0250970 pmid:33984008 fatcat:cy2otbaa4vfr7lldytsnyteysa

Modern Koopman Theory for Dynamical Systems [article]

Steven L. Brunton, Marko Budišić, Eurika Kaiser, J. Nathan Kutz
2021 arXiv   pre-print
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 the space of  ...  We also thank Shervin Bagheri, Bing Brunton, Bethany Lusch, Ryan Mohr, Frank Noe, Josh Proctor, Clancy Rowley, and Peter Schmid for many fruitful discussions on DMD, Koopman theory, and control.  ... 
arXiv:2102.12086v2 fatcat:2oylyx25dbctvkjfnirfcgjuqu

A purely data-driven framework for prediction, optimization, and control of networked processes: application to networked SIS epidemic model [article]

Ali Tavasoli, Teague Henry, Heman Shakeri
2021 arXiv   pre-print
This data-driven system identification is achieved by using the Koopman operator to find a low dimensional representation of the dynamical patterns that evolve linearly.  ...  Here we develop a simple data-driven framework based on operator-theoretic techniques to identify and control stochastic nonlinear dynamics taking place over large-scale networks.  ...  Another extension of this work can be made by multi-scale identification of underlying dynamics by collecting data of agent groups instead of individual agents.  ... 
arXiv:2108.02005v1 fatcat:k7xdivceybd5tdoksg2lhxc6fa

Reconstructing data-driven governing equations for cell phenotypic transitions: integration of data science and systems biology [article]

Jianhua Xing
2022 arXiv   pre-print
system from quantitative single-cell data, beyond the dominant statistical approaches.  ...  The regulation and dynamics of cell phenotypic conversion is a fundamental problem in biology, and has a long history of being studied within the formalism of dynamical systems.  ...  This work was partially supported by National Cancer Institute (R37 CA232209), National Institute of Diabetes and Digestive and Kidney Diseases (R01DK119232), and National Science Foundation (2205148)  ... 
arXiv:2203.14964v2 fatcat:v2gp3urkibfypceve6oapzejmi

Data-driven Analysis for Understanding Team Sports Behaviors [article]

Keisuke Fujii
2021 arXiv   pre-print
These approaches can contribute to a better understanding of multi-agent behaviors in the real world.  ...  Estimation of the rules from data, i.e., data-driven approaches such as machine learning, provides an effective way for the analysis of such behaviors.  ...  DMD is based on the spectral theory of the Koopman operator [56, 57] . Theoretically, to compute DMD, the data must be rich enough to approximate the eigenfunctions of the Koopman operator.  ... 
arXiv:2102.07545v2 fatcat:hadans3a5nbbzcq4uezz2utj2e

Scanning the Issue

Azim Eskandarian
2022 IEEE transactions on intelligent transportation systems (Print)  
The efficiency and perceived safety of different signal types on the eHMI are analyzed by collecting data on the subjects' movement behavior and ratings via questionnaires.  ...  This article investigates the influence of an external humanmachine interface (eHMI) for automated vehicles on pedestrian behavior in a parking lot.  ...  based on a multi-agent system.  ... 
doi:10.1109/tits.2022.3160062 fatcat:4gklzaonfzcehnvps6oge35fwe

DeepKoCo: Efficient latent planning with a task-relevant Koopman representation [article]

Bas van der Heijden, Laura Ferranti, Jens Kober, Robert Babuska
2021 arXiv   pre-print
This paper presents DeepKoCo, a novel model-based agent that learns a latent Koopman representation from images.  ...  Compared to traditional agents, DeepKoCo learns task-relevant dynamics, thanks to the use of a tailored lossy autoencoder network that allows DeepKoCo to learn latent dynamics that reconstruct and predict  ...  This motivates data-driven methodologies that learn low-dimensional latent dynamics that are robust to task-irrelevant dynamics and useful for control.  ... 
arXiv:2011.12690v3 fatcat:honlhzsz3ffube67oauzjwqrae

When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learning [article]

Chuizheng Meng, Sungyong Seo, Defu Cao, Sam Griesemer, Yan Liu
2022 arXiv   pre-print
, with data-driven machine learning models, has emerged as an effective way to mitigate the shortage of training data, to increase models' generalizability and to ensure the physical plausibility of results  ...  Physics-informed machine learning (PIML), referring to the combination of prior knowledge of physics, which is the high level abstraction of natural phenomenons and human behaviours in the long history  ...  However, the differences between the target real-world data distributions and simulation data distributions call for techniques of transfer learning to mitigate the gap. [145] present a system for training  ... 
arXiv:2203.16797v1 fatcat:zfynhlkcerfkvizlsftffr4g6a

Finding faults: A scoping study of fault diagnostics for Industrial Cyber-Physical Systems

Barry Dowdeswell, Roopak Sinha, Stephen MacDonell
2020 Journal of Systems and Software  
of current machine learning systems.  ...  Context: As Industrial Cyber-Physical Systems (ICPS) become more connected and widely-distributed, often operating in safety-critical environments, we require innovative approaches to detect and diagnose  ...  Data-Driven fault diagnostics Data-Driven diagnostic techniques employ train-655 ing and learning to forge a representation of the system's behavior [21] .  ... 
doi:10.1016/j.jss.2020.110638 fatcat:5gdzvwpzcbaxhi3cocty2pafza

Active learning in robotics: A review of control principles

Annalisa T. Taylor, Thomas A. Berrueta, Todd D. Murphey
2021 Mechatronics (Oxford)  
This is a review of active learning in robotics, focusing on methods amenable to the demands of embodied learning systems.  ...  We conclude with a discussion of control-oriented open challenges, including safety-constrained learning and distributed learning.  ...  Acknowledgments We would like to thank Muchen Sun, Ana Pervan, Kyra Rudy, Frank Park, and the anonymous reviewers of the first draft for their many helpful comments on this manuscript.  ... 
doi:10.1016/j.mechatronics.2021.102576 fatcat:qt47bncznzdtdc7ntpmis5dqw4

Driven by Data or Derived through Physics? A Review of Hybrid Physics Guided Machine Learning Techniques with Cyber-Physical System (CPS) Focus

Rahul Rai, Chandan K. Sahu
2020 IEEE Access  
A multitude of cyber-physical system (CPS) applications, including design, control, diagnosis, prognostics, and a host of other problems, are predicated on the assumption of model availability.  ...  We refer to the paradigm that combines MB approaches with ML as hybrid learning methods.  ...  The data-driven machine learning approach, however, is focused on training a model f ML : X → Y over a set of training data to produce estimates of outputsŶ given inputs X.  ... 
doi:10.1109/access.2020.2987324 fatcat:xaltpychlfcz7cec4jrdadhxem

Learning Compositional Koopman Operators for Model-Based Control [article]

Yunzhu Li, Hao He, Jiajun Wu, Dina Katabi, Antonio Torralba
2020 arXiv   pre-print
The Koopman operator theory lays the foundation for identifying the nonlinear-to-linear coordinate transformations with data-driven methods.  ...  Finding an embedding space for a linear approximation of a nonlinear dynamical system enables efficient system identification and control synthesis.  ...  A data-driven approximation of the koopman operator: Extending dynamic mode decomposition. Journal of Nonlinear Science, 25(6):1307-1346, 2015. Interaction types.  ... 
arXiv:1910.08264v2 fatcat:plcy26hrarbtnmu33jjlbvfshm

Ridesourcing systems: A framework and review

Hai Wang, Hai Yang
2019 Transportation Research Part B: Methodological  
The ridesourcing platforms consist of a typical two-sided market, which is a meeting place for two groups of agents (passengers and drivers, in this case) who interact and provide each other with network  ...  with extra seats), etc., to more than 91 million users with 15 million daily trips as of mid-2019, according to data collected by a third-party (see DMR, 2019a ).  ...  Acknowledgments This work was supported by the Lee Kong Chian (LKC) Fellowship, a Singapore Ministry of Education (MOE) Academic Research Fund (AcRF) Tier 1 grant, a grant from the Hong Kong Research Grants  ... 
doi:10.1016/j.trb.2019.07.009 fatcat:m5rxzhsxsfaunoep77nsqdhbny
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