Modeling Latent Non-Linear Dynamical System over Time Series

• URL: http://arxiv.org/abs/2412.08114v4
• Date: Mon, 27 Jan 2025 10:57:12 GMT
• Title: Modeling Latent Non-Linear Dynamical System over Time Series
• Authors: Ren Fujiwara, Yasuko Matsubara, Yasushi Sakurai,
• Abstract summary: We study the problem of modeling a non-linear dynamical system when given a time series by deriving equations directly from the data. We introduce a latent state to allow time-dependent modeling and formulate this problem as a dynamics estimation problem in latent states.
• Score: 7.534744211716623
• License:
• Abstract: We study the problem of modeling a non-linear dynamical system when given a time series by deriving equations directly from the data. Despite the fact that time series data are given as input, models for dynamics and estimation algorithms that incorporate long-term temporal dependencies are largely absent from existing studies. In this paper, we introduce a latent state to allow time-dependent modeling and formulate this problem as a dynamics estimation problem in latent states. We face multiple technical challenges, including (1) modeling latent non-linear dynamics and (2) solving circular dependencies caused by the presence of latent states. To tackle these challenging problems, we propose a new method, Latent Non-Linear equation modeling (LaNoLem), that can model a latent non-linear dynamical system and a novel alternating minimization algorithm for effectively estimating latent states and model parameters. In addition, we introduce criteria to control model complexity without human intervention. Compared with the state-of-the-art model, LaNoLem achieves competitive performance for estimating dynamics while outperforming other methods in prediction.

Related papers

• Hybrid Adaptive Modeling using Neural Networks Trained with Nonlinear Dynamics Based Features [5.652228574188242]
  This paper introduces a novel approach that departs from standard techniques by uncovering information from nonlinear dynamical modeling and embedding it in data-based models. By explicitly incorporating nonlinear dynamic phenomena through perturbation methods, the predictive capabilities are more realistic and insightful compared to knowledge obtained from brute-force numerical simulations.
  arXiv  Detail & Related papers  (2025-01-21T02:38:28Z)
• Trajectory Flow Matching with Applications to Clinical Time Series Modeling [77.58277281319253]
  Trajectory Flow Matching (TFM) trains a Neural SDE in a simulation-free manner, bypassing backpropagation through the dynamics. We demonstrate improved performance on three clinical time series datasets in terms of absolute performance and uncertainty prediction.
  arXiv  Detail & Related papers  (2024-10-28T15:54:50Z)
• 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)
• Towards Efficient Modelling of String Dynamics: A Comparison of State Space and Koopman based Deep Learning Methods [8.654571696634825]
  State Space Models (SSM) and Koopman-based deep learning methods for modelling the dynamics of both linear and non-linear stiff strings. Our findings indicate that our proposed Koopman-based model performs as well as or better than other existing approaches in non-linear cases for long-sequence modelling. This research contributes insights into the physical modelling of dynamical systems by offering a comparative overview of these and previous methods and introducing innovative strategies for model improvement.
  arXiv  Detail & Related papers  (2024-08-29T15:55:27Z)
• Neural Superstatistics for Bayesian Estimation of Dynamic Cognitive Models [2.7391842773173334]
  We develop a simulation-based deep learning method for Bayesian inference, which can recover both time-varying and time-invariant parameters. Our results show that the deep learning approach is very efficient in capturing the temporal dynamics of the model.
  arXiv  Detail & Related papers  (2022-11-23T17:42:53Z)
• Stability Preserving Data-driven Models With Latent Dynamics [0.0]
  We introduce a data-driven modeling approach for dynamics problems with latent variables. We present a model framework where the stability of the coupled dynamics can be easily enforced.
  arXiv  Detail & Related papers  (2022-04-20T00:41:10Z)
• Learning continuous models for continuous physics [94.42705784823997]
  We develop a test based on numerical analysis theory to validate machine learning models for science and engineering applications. Our results illustrate how principled numerical analysis methods can be coupled with existing ML training/testing methodologies to validate models for science and engineering applications.
  arXiv  Detail & Related papers  (2022-02-17T07:56:46Z)
• 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)
• Closed-form Continuous-Depth Models [99.40335716948101]
  Continuous-depth neural models rely on advanced numerical differential equation solvers. We present a new family of models, termed Closed-form Continuous-depth (CfC) networks, that are simple to describe and at least one order of magnitude faster.
  arXiv  Detail & Related papers  (2021-06-25T22:08:51Z)
• Autoregressive Dynamics Models for Offline Policy Evaluation and Optimization [60.73540999409032]
  We show that expressive autoregressive dynamics models generate different dimensions of the next state and reward sequentially conditioned on previous dimensions. We also show that autoregressive dynamics models are useful for offline policy optimization by serving as a way to enrich the replay buffer.
  arXiv  Detail & Related papers  (2021-04-28T16:48:44Z)
• Neural ODE Processes [64.10282200111983]
  We introduce Neural ODE Processes (NDPs), a new class of processes determined by a distribution over Neural ODEs. We show that our model can successfully capture the dynamics of low-dimensional systems from just a few data-points.
  arXiv  Detail & Related papers  (2021-03-23T09:32:06Z)

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.