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Related papers: Deep Koopman Learning using Noisy Data

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We propose a data-driven method for controlling the frequency and convergence rate of black-box nonlinear dynamical systems based on the Koopman operator theory. With the proposed method, a policy network is trained such that the…

Systems and Control · Electrical Eng. & Systems 2022-08-19 Tomoharu Iwata , Yoshinobu Kawahara

We introduce a data-driven method and shows its skills for spatiotemporal prediction of high-dimensional chaotic dynamics and turbulence. The method is based on a finite-dimensional approximation of the Koopman operator where the…

Fluid Dynamics · Physics 2019-09-04 Mohammad Amin Khodkar , Pedram Hassanzadeh , Athanasios Antoulas

The Koopman operator has become an essential tool for data-driven approximation of dynamical (control) systems, e.g., via extended dynamic mode decomposition. Despite its popularity, convergence results and, in particular, error bounds are…

Optimization and Control · Mathematics 2022-02-16 Feliks Nüske , Sebastian Peitz , Friedrich Philipp , Manuel Schaller , Karl Worthmann

With the current trend of increasing complexity of industrial systems, the construction and monitoring of health indicators becomes even more challenging. Given that health indicators are commonly employed to predict the end of life, a…

Systems and Control · Electrical Eng. & Systems 2023-08-04 Sergei Garmaev , Olga Fink

For dynamical systems involving decision making, the success of the system greatly depends on its ability to make good decisions with incomplete and uncertain information. By leveraging the Koopman operator and its adjoint property, we…

Dynamical Systems · Mathematics 2020-08-21 Adam R. Gerlach , Andrew Leonard , Jonathan Rogers , Chris Rackauckas

We present a low-rank Koopman operator formulation for accelerating deformable subspace simulation. Using a Dynamic Mode Decomposition (DMD) parameterization of the Koopman operator, our method learns the temporal evolution of deformable…

Graphics · Computer Science 2026-02-10 Yue Chang , Peter Yichen Chen , Eitan Grinspun , Maurizio M. Chiaramonte

Data-driven models for nonlinear dynamical systems based on approximating the underlying Koopman operator or generator have proven to be successful tools for forecasting, feature learning, state estimation, and control. It has become well…

Dynamical Systems · Mathematics 2023-10-26 Samuel E. Otto , Sebastian Peitz , Clarence W. Rowley

The Koopman operator and its data-driven approximations, such as extended dynamic mode decomposition (EDMD), are widely used for analysing, modelling, and controlling nonlinear dynamical systems. However, when the true Koopman…

Dynamical Systems · Mathematics 2026-02-05 Roland Schurig , Pieter van Goor , Karl Worthmann , Rolf Findeisen

We present a novel data-driven approach for learning linear representations of a class of stable nonlinear systems using Koopman eigenfunctions. By learning the conjugacy map between a nonlinear system and its Jacobian linearization through…

Machine Learning · Computer Science 2022-05-31 Petar Bevanda , Johannes Kirmayr , Stefan Sosnowski , Sandra Hirche

Kalman filtering can provide an optimal estimation of the system state from noisy observation data. This algorithm's performance depends on the accuracy of system modeling and noise statistical characteristics, which are usually challenging…

Systems and Control · Electrical Eng. & Systems 2025-04-18 Xun Xiao , Junbo Tie , Jinyue Zhao , Ziqi Wang , Yuan Li , Qiang Dou , Lei Wang

Representing and predicting high-dimensional and spatiotemporally chaotic dynamical systems remains a fundamental challenge in dynamical systems and machine learning. Although data-driven models can achieve accurate short-term forecasts,…

Machine Learning · Computer Science 2026-02-17 Liangyu Su , Jun Shu , Rui Liu , Deyu Meng , Zongben Xu

Koopman Operator Theory has opened the doors to data-driven learning of globally linear representations of complex nonlinear systems. However, current methodologies for Koopman Operator discovery struggle with uncertainty quantification and…

Systems and Control · Electrical Eng. & Systems 2025-11-11 Abhigyan Majumdar , Navid Mojahed , Shima Nazari

In Koopman operator theory, a finite-dimensional nonlinear system is transformed into an infinite but linear system using a set of observable functions. However, manually selecting observable functions that span the invariant subspace of…

Numerical Analysis · Mathematics 2024-02-02 Yuhuang Meng , Jianguo Huang , Yue Qiu

Purpose of review: We review recent advances in algorithmic development and validation for modeling and control of soft robots leveraging the Koopman operator theory. Recent findings: We identify the following trends in recent research…

Robotics · Computer Science 2023-02-09 Lu Shi , Zhichao Liu , Konstantinos Karydis

Koopman operator theory has found significant success in learning models of complex, real-world dynamical systems, enabling prediction and control. The greater interpretability and lower computational costs of these models, compared to…

Dynamical Systems · Mathematics 2025-01-08 William T. Redman , Dean Huang , Maria Fonoberova , Igor Mezić

This paper presents a unified and scalable framework for predictive and safe autonomous navigation in dynamic transportation environments by integrating model predictive control (MPC) with distributed Koopman operator learning.…

Systems and Control · Electrical Eng. & Systems 2026-01-06 Ali Azarbahram , Shenyu Liu , Gian Paolo Incremona

Koopman operator theory provides a powerful framework for representing nonlinear dynamics through a linear operator acting on lifted observables, enabling the use of linear control techniques for nonlinear systems. However, Koopman models…

Robotics · Computer Science 2026-05-12 Chandan Kumar Sah , Rajpal Singh , Jishnu Keshavan

We develop a general framework for state estimation in systems modeled with noise-polluted continuous time dynamics and discrete time noisy measurements. Our approach is based on maximum likelihood estimation and employs the calculus of…

Optimization and Control · Mathematics 2026-01-16 Griffin M. Kearney , Makan Fardad

Uncertainty estimation for unlabeled data is crucial to active learning. With a deep neural network employed as the backbone model, the data selection process is highly challenging due to the potential over-confidence of the model…

Machine Learning · Computer Science 2024-02-14 Xingjian Li , Pengkun Yang , Yangcheng Gu , Xueying Zhan , Tianyang Wang , Min Xu , Chengzhong Xu

We demonstrate that numerically computed approximations of Koopman eigenfunctions and eigenvalues create a natural framework for data fusion in applications governed by nonlinear evolution laws. This is possible because the eigenvalues of…

Dynamical Systems · Mathematics 2015-06-23 Matthew O. Williams , Clarence W. Rowley , Igor Mezić , Ioannis G. Kevrekidis