Leveraging Neural Koopman Operators to Learn Continuous Representations of Dynamical Systems from Scarce Data

• URL: http://arxiv.org/abs/2303.06972v1
• Date: Mon, 13 Mar 2023 10:16:19 GMT
• Title: Leveraging Neural Koopman Operators to Learn Continuous Representations of Dynamical Systems from Scarce Data
• Authors: Anthony Frion (Lab-STICC_OSE, IMT Atlantique - MEE, ODYSSEY), Lucas Drumetz (Lab-STICC_OSE, IMT Atlantique - MEE, ODYSSEY), Mauro Dalla Mura (IUF, GIPSA-SIGMAPHY), Guillaume Tochon (LRDE), Abdeldjalil Aissa El Bey (Lab-STICC\_COSYDE, IMT Atlantique - MEE)
• Abstract summary: We propose a new deep Koopman framework that represents dynamics in an intrinsically continuous way. This framework leads to better performance on limited training data.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Over the last few years, several works have proposed deep learning architectures to learn dynamical systems from observation data with no or little knowledge of the underlying physics. A line of work relies on learning representations where the dynamics of the underlying phenomenon can be described by a linear operator, based on the Koopman operator theory. However, despite being able to provide reliable long-term predictions for some dynamical systems in ideal situations, the methods proposed so far have limitations, such as requiring to discretize intrinsically continuous dynamical systems, leading to data loss, especially when handling incomplete or sparsely sampled data. Here, we propose a new deep Koopman framework that represents dynamics in an intrinsically continuous way, leading to better performance on limited training data, as exemplified on several datasets arising from dynamical systems.

Related papers

• Learning System Dynamics without Forgetting [60.08612207170659]
  Predicting trajectories of systems with unknown dynamics is crucial in various research fields, including physics and biology. We present a novel framework of Mode-switching Graph ODE (MS-GODE), which can continually learn varying dynamics. We construct a novel benchmark of biological dynamic systems, featuring diverse systems with disparate dynamics.
  arXiv  Detail & Related papers  (2024-06-30T14:55:18Z)
• Semi-Supervised Learning of Dynamical Systems with Neural Ordinary Differential Equations: A Teacher-Student Model Approach [10.20098335268973]
  TS-NODE is the first semi-supervised approach to modeling dynamical systems with NODE. We show significant performance improvements over a baseline Neural ODE model on multiple dynamical system modeling tasks.
  arXiv  Detail & Related papers  (2023-10-19T19:17:12Z)
• CoDBench: A Critical Evaluation of Data-driven Models for Continuous Dynamical Systems [8.410938527671341]
  We introduce CodBench, an exhaustive benchmarking suite comprising 11 state-of-the-art data-driven models for solving differential equations. Specifically, we evaluate 4 distinct categories of models, viz., feed forward neural networks, deep operator regression models, frequency-based neural operators, and transformer architectures. We conduct extensive experiments, assessing the operators' capabilities in learning, zero-shot super-resolution, data efficiency, robustness to noise, and computational efficiency.
  arXiv  Detail & Related papers  (2023-10-02T21:27:54Z)
• Neural Koopman prior for data assimilation [7.875955593012905]
  We use a neural network architecture to embed dynamical systems in latent spaces. We introduce methods that enable to train such a model for long-term continuous reconstruction. The potential for self-supervised learning is also demonstrated, as we show the promising use of trained dynamical models as priors for variational data assimilation techniques.
  arXiv  Detail & Related papers  (2023-09-11T09:04:36Z)
• Physics-Inspired Temporal Learning of Quadrotor Dynamics for Accurate Model Predictive Trajectory Tracking [76.27433308688592]
  Accurately modeling quadrotor's system dynamics is critical for guaranteeing agile, safe, and stable navigation. We present a novel Physics-Inspired Temporal Convolutional Network (PI-TCN) approach to learning quadrotor's system dynamics purely from robot experience. Our approach combines the expressive power of sparse temporal convolutions and dense feed-forward connections to make accurate system predictions.
  arXiv  Detail & Related papers  (2022-06-07T13:51:35Z)
• Decomposed Linear Dynamical Systems (dLDS) for learning the latent components of neural dynamics [6.829711787905569]
  We propose a new decomposed dynamical system model that represents complex non-stationary and nonlinear dynamics of time series data. Our model is trained through a dictionary learning procedure, where we leverage recent results in tracking sparse vectors over time. In both continuous-time and discrete-time instructional examples we demonstrate that our model can well approximate the original system.
  arXiv  Detail & Related papers  (2022-06-07T02:25:38Z)
• Learning Fine Scale Dynamics from Coarse Observations via Inner Recurrence [0.0]
  Recent work has focused on data-driven learning of the evolution of unknown systems via deep neural networks (DNNs) This paper presents a computational technique to learn the fine-scale dynamics from such coarsely observed data.
  arXiv  Detail & Related papers  (2022-06-03T20:28:52Z)
• Leveraging the structure of dynamical systems for data-driven modeling [111.45324708884813]
  We consider the impact of the training set and its structure on the quality of the long-term prediction. We show how an informed design of the training set, based on invariants of the system and the structure of the underlying attractor, significantly improves the resulting models.
  arXiv  Detail & Related papers  (2021-12-15T20:09:20Z)
• Constructing Neural Network-Based Models for Simulating Dynamical Systems [59.0861954179401]
  Data-driven modeling is an alternative paradigm that seeks to learn an approximation of the dynamics of a system using observations of the true system. This paper provides a survey of the different ways to construct models of dynamical systems using neural networks. In addition to the basic overview, we review the related literature and outline the most significant challenges from numerical simulations that this modeling paradigm must overcome.
  arXiv  Detail & Related papers  (2021-11-02T10:51:42Z)
• 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)
• Forecasting Sequential Data using Consistent Koopman Autoencoders [52.209416711500005]
  A new class of physics-based methods related to Koopman theory has been introduced, offering an alternative for processing nonlinear dynamical systems. We propose a novel Consistent Koopman Autoencoder model which, unlike the majority of existing work, leverages the forward and backward dynamics. Key to our approach is a new analysis which explores the interplay between consistent dynamics and their associated Koopman operators.
  arXiv  Detail & Related papers  (2020-03-04T18:24:30Z)

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.