Blending data and physics for reduced-order modeling of systems with spatiotemporal chaotic dynamics

• URL: http://arxiv.org/abs/2507.21299v1
• Date: Mon, 21 Jul 2025 21:32:40 GMT
• Title: Blending data and physics for reduced-order modeling of systems with spatiotemporal chaotic dynamics
• Authors: Alex Guo, Michael D. Graham,
• Abstract summary: We develop a hybrid reduced order model (ROM) for chaotic dynamics.<n>ROM is informed by both data and physics-derived vector field of FOM.<n>For scenarios of abundant data, scarce data, and even an incorrect FOM, the hybrid approach yields substantially improved time-series predictions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: While data-driven techniques are powerful tools for reduced-order modeling of systems with chaotic dynamics, great potential remains for leveraging known physics (i.e. a full-order model (FOM)) to improve predictive capability. We develop a hybrid reduced order model (ROM), informed by both data and FOM, for evolving spatiotemporal chaotic dynamics on an invariant manifold whose coordinates are found using an autoencoder. This approach projects the vector field of the FOM onto the invariant manifold; then, this physics-derived vector field is either corrected using dynamic data, or used as a Bayesian prior that is updated with data. In both cases, the neural ordinary differential equation approach is used. We consider simulated data from the Kuramoto-Sivashinsky and complex Ginzburg-Landau equations. Relative to the data-only approach, for scenarios of abundant data, scarce data, and even an incorrect FOM (i.e. erroneous parameter values), the hybrid approach yields substantially improved time-series predictions.

Related papers

• Data-Driven Prediction of Dynamic Interactions Between Robot Appendage and Granular Material [2.551529992410986]
  An alternative data-driven modeling approach has been proposed to gain insights into robot motion interaction with granular terrain at certain length scales.<n>This approach can be used online and is based on offline data, obtained from the offline collection of high-fidelity simulation data and a set of sparse experimental data.<n>Results are expected to help robot navigation and exploration in unknown and complex terrains during both online and offline phases.
  arXiv  Detail & Related papers  (2025-06-12T16:43:21Z)
• Diffusion posterior sampling for simulation-based inference in tall data settings [53.17563688225137]
  Simulation-based inference ( SBI) is capable of approximating the posterior distribution that relates input parameters to a given observation. In this work, we consider a tall data extension in which multiple observations are available to better infer the parameters of the model. We compare our method to recently proposed competing approaches on various numerical experiments and demonstrate its superiority in terms of numerical stability and computational cost.
  arXiv  Detail & Related papers  (2024-04-11T09:23:36Z)
• Generative Modeling with Phase Stochastic Bridges [49.4474628881673]
  Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. We introduce a novel generative modeling framework grounded in textbfphase space dynamics Our framework demonstrates the capability to generate realistic data points at an early stage of dynamics propagation.
  arXiv  Detail & Related papers  (2023-10-11T18:38:28Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• VTAE: Variational Transformer Autoencoder with Manifolds Learning [144.0546653941249]
  Deep generative models have demonstrated successful applications in learning non-linear data distributions through a number of latent variables. The nonlinearity of the generator implies that the latent space shows an unsatisfactory projection of the data space, which results in poor representation learning. We show that geodesics and accurate computation can substantially improve the performance of deep generative models.
  arXiv  Detail & Related papers  (2023-04-03T13:13:19Z)
• Random Grid Neural Processes for Parametric Partial Differential Equations [5.244037702157957]
  We introduce a new class of spatially probabilistic physics and data informed deep latent models for PDEs. We solve forward and inverse problems for parametric PDEs in a way that leads to the construction of Gaussian process models of solution fields. We show how to incorporate noisy data in a principled manner into our physics informed model to improve predictions for problems where data may be available.
  arXiv  Detail & Related papers  (2023-01-26T11:30:56Z)
• $Φ$-DVAE: Physics-Informed Dynamical Variational Autoencoders for Unstructured Data Assimilation [3.2873782624127843]
  We develop a physics-informed dynamical variational autoencoder ($Phi$-DVAE) to embed diverse data streams into time-evolving physical systems. Our approach combines a standard, possibly nonlinear, filter for the latent state-space model and a VAE, to assimilate the unstructured data into the latent dynamical system. A variational Bayesian framework is used for the joint estimation of the encoding, latent states, and unknown system parameters.
  arXiv  Detail & Related papers  (2022-09-30T17:34:48Z)
• Extension of Dynamic Mode Decomposition for dynamic systems with incomplete information based on t-model of optimal prediction [69.81996031777717]
  The Dynamic Mode Decomposition has proved to be a very efficient technique to study dynamic data. The application of this approach becomes problematic if the available data is incomplete because some dimensions of smaller scale either missing or unmeasured. We consider a first-order approximation of the Mori-Zwanzig decomposition, state the corresponding optimization problem and solve it with the gradient-based optimization method.
  arXiv  Detail & Related papers  (2022-02-23T11:23:59Z)
• Data-Driven Reduced-Order Modeling of Spatiotemporal Chaos with Neural Ordinary Differential Equations [0.0]
  We present a data-driven reduced order modeling method that capitalizes on the chaotic dynamics of partial differential equations. We find that dimension reduction improves performance relative to predictions in the ambient space. With the low-dimensional model, we find excellent short- and long-time statistical recreation of the true dynamics for widely spaced data.
  arXiv  Detail & Related papers  (2021-08-31T20:00:33Z)
• Low-Rank Hankel Tensor Completion for Traffic Speed Estimation [7.346671461427793]
  We propose a purely data-driven and model-free solution to the traffic state estimation problem. By imposing a low-rank assumption on this tensor structure, we can approximate characterize both global patterns and the unknown complex local dynamics. We conduct numerical experiments on both synthetic simulation data and real-world high-resolution data, and our results demonstrate the effectiveness and superiority of the proposed model.
  arXiv  Detail & Related papers  (2021-05-21T00:08:06Z)
• 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)

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.