Learning Koopman operators for coupled systems via information on governing equations of subsystems

• URL: http://arxiv.org/abs/2605.01835v1
• Date: Sun, 03 May 2026 12:03:33 GMT
• Title: Learning Koopman operators for coupled systems via information on governing equations of subsystems
• Abstract summary: Operator-theoretic methods based on the Koopman operator have attracted attention as a powerful tool for analyzing and modeling nonlinear dynamical systems.<n>We propose a method to learn the Koopman operator for coupled systems using the differential equations governing each subsystem.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Nonlinear coupled systems are ubiquitous in science and engineering. The analysis and modeling of such systems is challenging due to their high dimensionality and complex interactions among subsystems. In recent years, operator-theoretic methods based on the Koopman operator have attracted attention as a powerful tool for analyzing and modeling nonlinear dynamical systems. Extended dynamic mode decomposition (EDMD) is one of the most popular methods to approximate the Koopman operator. However, EDMD is a purely data-driven method, and it could be unstable and inaccurate for coupled systems under limited data availability. In this paper, we propose a method to learn the Koopman operator for coupled systems using the differential equations governing each subsystem. We also demonstrate its effectiveness through numerical experiments on coupled oscillator systems.

Related papers

• Koopman operator theory: fundamentals, control, and applications [1.9573380763700712]
  We provide a concise introduction into Koopman operator theory and its use in systems and control.<n>A particular focus is put on data-driven surrogate models, their extension to systems with inputs, and controller design using Koopman operator theory.<n>We provide simulation studies including source code on GitHub to enable the interested reader to experience the Koopman operator in systems and control step by step.
  arXiv  Detail & Related papers  (2026-07-02T07:31:47Z)
• Sparse and nonparametric estimation of equations governing dynamical systems with applications to biology [0.0]
  We introduce a novel framework that integrates sparse parametric estimation with nonparametric techniques.<n>It captures nonlinearities that Sindy cannot describe without requiring a priori information about their functional form.
  arXiv  Detail & Related papers  (2025-11-01T14:43:50Z)
• Efficient Parametric SVD of Koopman Operator for Stochastic Dynamical Systems [51.54065545849027]
  The Koopman operator provides a principled framework for analyzing nonlinear dynamical systems.<n>VAMPnet and DPNet have been proposed to learn the leading singular subspaces of the Koopman operator.<n>We propose a scalable and conceptually simple method for learning the top-$k$ singular functions of the Koopman operator.
  arXiv  Detail & Related papers  (2025-07-09T18:55:48Z)
• Learning Neural Differential Algebraic Equations via Operator Splitting [6.100037457394823]
  We present an Operator Splitting scheme for learning unknown components of DAEs from time-series data.<n>We show that the proposed OS-based time-stepping scheme is suitable for relevant system-theoretic data-driven modeling tasks.
  arXiv  Detail & Related papers  (2024-03-19T17:43:57Z)
• Equivariance and partial observations in Koopman operator theory for partial differential equations [1.099532646524593]
  We show that symmetries in the system dynamics can be carried over to the Koopman operator. We address the highly-relevant case where we cannot measure the full state.
  arXiv  Detail & Related papers  (2023-07-28T06:03:19Z)
• Closed-Loop Koopman Operator Approximation [5.317624228510749]
  This paper proposes a method to identify a Koopman model of a feedback-controlled system given a known controller. The advantages of the proposed closed-loop Koopman operator approximation method are demonstrated in simulation and experimentally.
  arXiv  Detail & Related papers  (2023-03-27T15:20:10Z)
• Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation [59.45669299295436]
  We propose a Monte Carlo PDE solver for training unsupervised neural solvers.<n>We use the PDEs' probabilistic representation, which regards macroscopic phenomena as ensembles of random particles.<n>Our experiments on convection-diffusion, Allen-Cahn, and Navier-Stokes equations demonstrate significant improvements in accuracy and efficiency.
  arXiv  Detail & Related papers  (2023-02-10T08:05:19Z)
• Experimental study of Neural ODE training with adaptive solver for dynamical systems modeling [72.84259710412293]
  Some ODE solvers called adaptive can adapt their evaluation strategy depending on the complexity of the problem at hand. This paper describes a simple set of experiments to show why adaptive solvers cannot be seamlessly leveraged as a black-box for dynamical systems modelling.
  arXiv  Detail & Related papers  (2022-11-13T17:48:04Z)
• Supervised DKRC with Images for Offline System Identification [77.34726150561087]
  Modern dynamical systems are becoming increasingly non-linear and complex. There is a need for a framework to model these systems in a compact and comprehensive representation for prediction and control. Our approach learns these basis functions using a supervised learning approach.
  arXiv  Detail & Related papers  (2021-09-06T04:39:06Z)
• Estimating Koopman operators for nonlinear dynamical systems: a nonparametric approach [77.77696851397539]
  The Koopman operator is a mathematical tool that allows for a linear description of non-linear systems. In this paper we capture their core essence as a dual version of the same framework, incorporating them into the Kernel framework. We establish a strong link between kernel methods and Koopman operators, leading to the estimation of the latter through Kernel functions.
  arXiv  Detail & Related papers  (2021-03-25T11:08:26Z)
• Using Data Assimilation to Train a Hybrid Forecast System that Combines Machine-Learning and Knowledge-Based Components [52.77024349608834]
  We consider the problem of data-assisted forecasting of chaotic dynamical systems when the available data is noisy partial measurements. We show that by using partial measurements of the state of the dynamical system, we can train a machine learning model to improve predictions made by an imperfect knowledge-based model.
  arXiv  Detail & Related papers  (2021-02-15T19:56:48Z)
• Model-Based Deep Learning [155.063817656602]
  Signal processing, communications, and control have traditionally relied on classical statistical modeling techniques. Deep neural networks (DNNs) use generic architectures which learn to operate from data, and demonstrate excellent performance. We are interested in hybrid techniques that combine principled mathematical models with data-driven systems to benefit from the advantages of both approaches.
  arXiv  Detail & Related papers  (2020-12-15T16:29:49Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.