Dynamical system reconstruction from partial observations using stochastic dynamics

• URL: http://arxiv.org/abs/2510.01089v1
• Date: Wed, 01 Oct 2025 16:36:18 GMT
• Title: Dynamical system reconstruction from partial observations using stochastic dynamics
• Authors: Viktor Sip, Martin Breyton, Spase Petkoski, Viktor Jirsa,
• Abstract summary: Learning models of dynamical systems underlying observed data is of interest in many scientific fields.<n>We propose a novel method for this task, based on the framework of variational autoencoders for dynamical systems.<n>We demonstrate the performance of the proposed approach on six test problems, covering simulated and experimental data.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Learning stochastic models of dynamical systems underlying observed data is of interest in many scientific fields. Here we propose a novel method for this task, based on the framework of variational autoencoders for dynamical systems. The method estimates from the data both the system state trajectories and noise time series. This approach allows to perform multi-step system evolution and supports a teacher forcing strategy, alleviating limitations of autoencoder-based approaches for stochastic systems. We demonstrate the performance of the proposed approach on six test problems, covering simulated and experimental data. We further show the effects of the teacher forcing interval on the nature of the internal dynamics, and compare it to the deterministic models with equivalent architecture.

Related papers

• Data-driven Effective Modeling of Multiscale Stochastic Dynamical Systems [4.357350642401934]
  We present a numerical method for learning the dynamics of slow components of unknown multiscale dynamical systems. By utilizing the observation data, our proposed method is capable of constructing a generative model that can accurately capture the effective dynamics of the slow variables in distribution.
  arXiv  Detail & Related papers  (2024-08-27T07:03:51Z)
• Learning System Dynamics without Forgetting [60.08612207170659]
  We investigate the problem of Continual Dynamics Learning (CDL), examining task configurations and evaluating the applicability of existing techniques.<n>We propose the Mode-switching Graph ODE (MS-GODE) model, which integrates the strengths LG-ODE and sub-network learning with a mode-switching module.<n>We construct a novel benchmark of biological dynamic systems for CDL, Bio-CDL, featuring diverse systems with disparate dynamics.
  arXiv  Detail & Related papers  (2024-06-30T14:55:18Z)
• Learning Latent Dynamics via Invariant Decomposition and (Spatio-)Temporal Transformers [0.6767885381740952]
  We propose a method for learning dynamical systems from high-dimensional empirical data. We focus on the setting in which data are available from multiple different instances of a system. We study behaviour through simple theoretical analyses and extensive experiments on synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2023-06-21T07:52:07Z)
• 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)
• 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)
• Modeling Systems with Machine Learning based Differential Equations [0.0]
  We propose the design of time-continuous models of dynamical systems as solutions of differential equations. Our results suggest that this approach can be an useful technique in the case of synthetic or experimental data.
  arXiv  Detail & Related papers  (2021-09-09T19:10:46Z)
• 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)
• 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)
• Bridging the Gap: Machine Learning to Resolve Improperly Modeled Dynamics [4.940323406667406]
  We present a data-driven modeling strategy to overcome improperly modeled dynamics for systems exhibiting complex-temporal behaviors. We propose a Deep Learning framework to resolve the differences between the true dynamics of the system and the dynamics given by a model of the system that is either inaccurately or inadequately described.
  arXiv  Detail & Related papers  (2020-08-23T04:57:02Z)

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.