Stochastic and Non-local Closure Modeling for Nonlinear Dynamical Systems via Latent Score-based Generative Models

• URL: http://arxiv.org/abs/2506.20771v1
• Date: Wed, 25 Jun 2025 19:04:02 GMT
• Title: Stochastic and Non-local Closure Modeling for Nonlinear Dynamical Systems via Latent Score-based Generative Models
• Authors: Xinghao Dong, Huchen Yang, Jin-Long Wu,
• Abstract summary: We propose a latent score-based generative AI framework for learning, non-local closure models and laws in nonlinear dynamical systems.<n>This work addresses a key challenge of modeling complex multiscale dynamical systems without a clear scale separation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a latent score-based generative AI framework for learning stochastic, non-local closure models and constitutive laws in nonlinear dynamical systems of computational mechanics. This work addresses a key challenge of modeling complex multiscale dynamical systems without a clear scale separation, for which numerically resolving all scales is prohibitively expensive, e.g., for engineering turbulent flows. While classical closure modeling methods leverage domain knowledge to approximate subgrid-scale phenomena, their deterministic and local assumptions can be too restrictive in regimes lacking a clear scale separation. Recent developments of diffusion-based stochastic models have shown promise in the context of closure modeling, but their prohibitive computational inference cost limits practical applications for many real-world applications. This work addresses this limitation by jointly training convolutional autoencoders with conditional diffusion models in the latent spaces, significantly reducing the dimensionality of the sampling process while preserving essential physical characteristics. Numerical results demonstrate that the joint training approach helps discover a proper latent space that not only guarantees small reconstruction errors but also ensures good performance of the diffusion model in the latent space. When integrated into numerical simulations, the proposed stochastic modeling framework via latent conditional diffusion models achieves significant computational acceleration while maintaining comparable predictive accuracy to standard diffusion models in physical spaces.

Related papers

• Nonlinear Model Order Reduction of Dynamical Systems in Process Engineering: Review and Comparison [50.0791489606211]
  We review state-of-the-art nonlinear model order reduction methods.<n>We discuss both general-purpose methods and tailored approaches for (chemical) process systems.
  arXiv  Detail & Related papers  (2025-06-15T11:39:12Z)
• Generative Latent Neural PDE Solver using Flow Matching [8.397730500554047]
  We propose a latent diffusion model for PDE simulation that embeds the PDE state in a lower-dimensional latent space.<n>Our framework uses an autoencoder to map different types of meshes onto a unified structured latent grid, capturing complex geometries.<n> Numerical experiments show that the proposed model outperforms several deterministic baselines in both accuracy and long-term stability.
  arXiv  Detail & Related papers  (2025-03-28T16:44:28Z)
• Continuous Diffusion Model for Language Modeling [57.396578974401734]
  Existing continuous diffusion models for discrete data have limited performance compared to discrete approaches.<n>We propose a continuous diffusion model for language modeling that incorporates the geometry of the underlying categorical distribution.
  arXiv  Detail & Related papers  (2025-02-17T08:54:29Z)
• Learning Controlled Stochastic Differential Equations [61.82896036131116]
  This work proposes a novel method for estimating both drift and diffusion coefficients of continuous, multidimensional, nonlinear controlled differential equations with non-uniform diffusion. We provide strong theoretical guarantees, including finite-sample bounds for (L2), (Linfty), and risk metrics, with learning rates adaptive to coefficients' regularity. Our method is available as an open-source Python library.
  arXiv  Detail & Related papers  (2024-11-04T11:09:58Z)
• Data-Driven Stochastic Closure Modeling via Conditional Diffusion Model and Neural Operator [0.0]
  Closure models are widely used in simulating complex multiscale dynamical systems such as turbulence and the earth system.<n>For systems without a clear scale, generalization deterministic and local closure models often lack enough capability.<n>We propose a datadriven modeling framework for constructing neural operator and non-local closure models.
  arXiv  Detail & Related papers  (2024-08-06T05:21:31Z)
• Score-based Diffusion Models in Function Space [137.70916238028306]
  Diffusion models have recently emerged as a powerful framework for generative modeling.<n>This work introduces a mathematically rigorous framework called Denoising Diffusion Operators (DDOs) for training diffusion models in function space.<n>We show that the corresponding discretized algorithm generates accurate samples at a fixed cost independent of the data resolution.
  arXiv  Detail & Related papers  (2023-02-14T23:50:53Z)
• Neural Abstractions [72.42530499990028]
  We present a novel method for the safety verification of nonlinear dynamical models that uses neural networks to represent abstractions of their dynamics. We demonstrate that our approach performs comparably to the mature tool Flow* on existing benchmark nonlinear models.
  arXiv  Detail & Related papers  (2023-01-27T12:38:09Z)
• Generalized Neural Closure Models with Interpretability [28.269731698116257]
  We develop a novel and versatile methodology of unified neural partial delay differential equations. We augment existing/low-fidelity dynamical models directly in their partial differential equation (PDE) forms with both Markovian and non-Markovian neural network (NN) closure parameterizations. We demonstrate the new generalized neural closure models (gnCMs) framework using four sets of experiments based on advecting nonlinear waves, shocks, and ocean acidification models.
  arXiv  Detail & Related papers  (2023-01-15T21:57:43Z)
• Nonlinear proper orthogonal decomposition for convection-dominated flows [0.0]
  We propose an end-to-end Galerkin-free model combining autoencoders with long short-term memory networks for dynamics. Our approach not only improves the accuracy, but also significantly reduces the computational cost of training and testing.
  arXiv  Detail & Related papers  (2021-10-15T18:05:34Z)
• 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)
• Neural Closure Models for Dynamical Systems [35.000303827255024]
  We develop a novel methodology to learn non-Markovian closure parameterizations for low-fidelity models. New "neural closure models" augment low-fidelity models with neural delay differential equations (nDDEs) We show that using non-Markovian over Markovian closures improves long-term accuracy and requires smaller networks.
  arXiv  Detail & Related papers  (2020-12-27T05:55:33Z)

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.