Deep Dictionary-Free Method for Identifying Linear Model of Nonlinear System with Input Delay

• URL: http://arxiv.org/abs/2511.04451v1
• Date: Thu, 06 Nov 2025 15:22:53 GMT
• Title: Deep Dictionary-Free Method for Identifying Linear Model of Nonlinear System with Input Delay
• Abstract summary: This paper introduces a novel approach to approximate the Koopman operator using an LSTM-enhanced Deep Koopman model.<n>The proposed framework captures historical dependencies and efficiently encodes time-delayed system dynamics into a latent space.
• Score: 3.1498833540989413
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Nonlinear dynamical systems with input delays pose significant challenges for prediction, estimation, and control due to their inherent complexity and the impact of delays on system behavior. Traditional linear control techniques often fail in these contexts, necessitating innovative approaches. This paper introduces a novel approach to approximate the Koopman operator using an LSTM-enhanced Deep Koopman model, enabling linear representations of nonlinear systems with time delays. By incorporating Long Short-Term Memory (LSTM) layers, the proposed framework captures historical dependencies and efficiently encodes time-delayed system dynamics into a latent space. Unlike traditional extended Dynamic Mode Decomposition (eDMD) approaches that rely on predefined dictionaries, the LSTM-enhanced Deep Koopman model is dictionary-free, which mitigates the problems with the underlying dynamics being known and incorporated into the dictionary. Quantitative comparisons with extended eDMD on a simulated system demonstrate highly significant performance gains in prediction accuracy in cases where the true nonlinear dynamics are unknown and achieve comparable results to eDMD with known dynamics of a system.

Related papers

• Beyond Linear Dynamics: Neural Bilinear Dynamical Models for Time Series Forecasting [10.24195404755377]
  Time series in real-world applications are often generated by nonlinear dynamical systems.<n>We propose the Neural Bilinear Dynamical Model (NBDM), which models nonlinear system dynamics through a bilinear latent dynamical formulation.<n>Experiments on five real-world datasets demonstrate that NBDM consistently outperforms competitive baselines in both given-control and missing-control settings.
  arXiv  Detail & Related papers  (2026-08-05T05:54:17Z)
• Learning solution operator of dynamical systems with diffusion maps kernel ridge regression [2.7802667650114485]
  We show that a simple kernel ridge regression (KRR) framework provides a strong baseline for long-term prediction of complex dynamical systems.<n>Across a broad range of systems, DM-KRR consistently outperforms state-of-the-art random feature, neural-network and operator-learning methods in both accuracy and data efficiency.
  arXiv  Detail & Related papers  (2025-12-19T03:29:23Z)
• Certified Neural Approximations of Nonlinear Dynamics [51.01318247729693]
  In safety-critical contexts, the use of neural approximations requires formal bounds on their closeness to the underlying system.<n>We propose a novel, adaptive, and parallelizable verification method based on certified first-order models.
  arXiv  Detail & Related papers  (2025-05-21T13:22:20Z)
• Latent Diffeomorphic Dynamic Mode Decomposition [0.0]
  We present a new data reduction approach for the analysis of non-linear systems that combines the interpretability of Dynamic Mode Decomposition (DMD) with the predictive power of Recurrent Neural Networks (RNNs)<n> Notably, LDDMD maintains simplicity, which enhances interpretability, while effectively modeling and learning complex non-linear systems with memory, enabling accurate predictions.
  arXiv  Detail & Related papers  (2025-05-09T18:00:09Z)
• Efficient Transformed Gaussian Process State-Space Models for Non-Stationary High-Dimensional Dynamical Systems [49.819436680336786]
  We propose an efficient transformed Gaussian process state-space model (ETGPSSM) for scalable and flexible modeling of high-dimensional, non-stationary dynamical systems.<n>Specifically, our ETGPSSM integrates a single shared GP with input-dependent normalizing flows, yielding an expressive implicit process prior that captures complex, non-stationary transition dynamics.<n>Our ETGPSSM outperforms existing GPSSMs and neural network-based SSMs in terms of computational efficiency and accuracy.
  arXiv  Detail & Related papers  (2025-03-24T03:19:45Z)
• Path-minimizing Latent ODEs for improved extrapolation and inference [0.0]
  Latent ODE models provide flexible descriptions of dynamic systems, but they can struggle with extrapolation and predicting complicated non-linear dynamics. In this paper we exploit this dichotomy by encouraging time-independent latent representations. By replacing the common variational penalty in latent space with an $ell$ penalty on the path length of each system, the models learn data representations that can easily be distinguished from those of systems with different configurations. This results in faster training, smaller models, more accurate and long-time extrapolation compared to the baseline ODE models with GRU, RNN, and LSTM/decoders on tests with
  arXiv  Detail & Related papers  (2024-10-11T15:50:01Z)
• Deep Generative Modeling for Identification of Noisy, Non-Stationary Dynamical Systems [3.1484174280822845]
  We focus on finding parsimonious ordinary differential equation (ODE) models for nonlinear, noisy, and non-autonomous dynamical systems. Our method, dynamic SINDy, combines variational inference with SINDy (sparse identification of nonlinear dynamics) to model time-varying coefficients of sparse ODEs.
  arXiv  Detail & Related papers  (2024-10-02T23:00:00Z)
• Learning Noise-Robust Stable Koopman Operator for Control with Hankel DMD [0.8021197489470758]
  We propose a noise-robust learning framework for the Koopman operator of nonlinear dynamical systems.<n>We leverage observables generated by the system dynamics, when the system dynamics is known, through a Hankel matrix.<n>We approximate them with a neural network while maintaining structural similarities to discrete Polyflow.
  arXiv  Detail & Related papers  (2024-08-13T03:39:34Z)
• Capturing Actionable Dynamics with Structured Latent Ordinary Differential Equations [68.62843292346813]
  We propose a structured latent ODE model that captures system input variations within its latent representation. Building on a static variable specification, our model learns factors of variation for each input to the system, thus separating the effects of the system inputs in the latent space.
  arXiv  Detail & Related papers  (2022-02-25T20:00:56Z)
• 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)
• Stochastically forced ensemble dynamic mode decomposition for forecasting and analysis of near-periodic systems [65.44033635330604]
  We introduce a novel load forecasting method in which observed dynamics are modeled as a forced linear system. We show that its use of intrinsic linear dynamics offers a number of desirable properties in terms of interpretability and parsimony. Results are presented for a test case using load data from an electrical grid.
  arXiv  Detail & Related papers  (2020-10-08T20:25:52Z)
• Liquid Time-constant Networks [117.57116214802504]
  We introduce a new class of time-continuous recurrent neural network models. Instead of declaring a learning system's dynamics by implicit nonlinearities, we construct networks of linear first-order dynamical systems. These neural networks exhibit stable and bounded behavior, yield superior expressivity within the family of neural ordinary differential equations.
  arXiv  Detail & Related papers  (2020-06-08T09:53:35Z)

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.