Energy-Conserving Neural Network Closure Model for Long-Time Accurate and Stable LES

• URL: http://arxiv.org/abs/2504.05868v1
• Date: Tue, 08 Apr 2025 09:49:18 GMT
• Title: Energy-Conserving Neural Network Closure Model for Long-Time Accurate and Stable LES
• Authors: Toby van Gastelen, Wouter Edeling, Benjamin Sanderse,
• Abstract summary: We develop a skew-symmetric neural architecture as closure model that enforces stability while preserving key physical conservation laws.<n>Our approach leverages a discretization that ensures mass, momentum, and energy conservation, along with a face-averaging filter to maintain mass conservation in coarse-grained velocity fields.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Machine learning-based closure models for LES have shown promise in capturing complex turbulence dynamics but often suffer from instabilities and physical inconsistencies. In this work, we develop a novel skew-symmetric neural architecture as closure model that enforces stability while preserving key physical conservation laws. Our approach leverages a discretization that ensures mass, momentum, and energy conservation, along with a face-averaging filter to maintain mass conservation in coarse-grained velocity fields. We compare our model against several conventional data-driven closures (including unconstrained convolutional neural networks), and the physics-based Smagorinsky model. Performance is evaluated on decaying turbulence and Kolmogorov flow for multiple coarse-graining factors. In these test cases we observe that unconstrained machine learning models suffer from numerical instabilities. In contrast, our skew-symmetric model remains stable across all tests, though at the cost of increased dissipation. Despite this trade-off, we demonstrate that our model still outperforms the Smagorinsky model in unseen scenarios. These findings highlight the potential of structure-preserving machine learning closures for reliable long-time LES.

Related papers

• From Observations to States: Latent Time Series Forecasting [65.98504021691666]
  We propose Latent Time Series Forecasting (LatentTSF), a novel paradigm that shifts TSF from observation regression to latent state prediction.<n>Specifically, LatentTSF employs an AutoEncoder to project observations at each time step into a higher-dimensional latent state space.<n>Our proposed latent objectives implicitly maximize mutual information between predicted latent states and ground-truth states and observations.
  arXiv  Detail & Related papers  (2026-01-30T20:39:44Z)
• Stochastic dynamics learning with state-space systems [5.248564173595025]
  This work advances the theoretical foundations of reservoir computing (RC) by providing a unified treatment of fading memory and the echo state property (ESP)<n>We investigate state-space systems, a central model class in time series learning, and establish that fading memory and solution stability hold generically -- even in the absence of the ESP.
  arXiv  Detail & Related papers  (2025-08-11T11:49:01Z)
• Langevin Flows for Modeling Neural Latent Dynamics [81.81271685018284]
  We introduce LangevinFlow, a sequential Variational Auto-Encoder where the time evolution of latent variables is governed by the underdamped Langevin equation.<n>Our approach incorporates physical priors -- such as inertia, damping, a learned potential function, and forces -- to represent both autonomous and non-autonomous processes in neural systems.<n>Our method outperforms state-of-the-art baselines on synthetic neural populations generated by a Lorenz attractor.
  arXiv  Detail & Related papers  (2025-07-15T17:57:48Z)
• Physics-aware generative models for turbulent fluid flows through energy-consistent stochastic interpolants [0.0]
  Generative models have demonstrated remarkable success in domains such as text, image, and video. In this work, we explore the application of generative models to fluid dynamics, specifically for turbulence simulation. We propose a novel generative model based on interpolants, which enables probabilistic forecasting while incorporating physical constraints.
  arXiv  Detail & Related papers  (2025-04-08T09:29:01Z)
• Oscillatory State-Space Models [61.923849241099184]
  We propose Lineary State-Space models (LinOSS) for efficiently learning on long sequences.<n>A stable discretization, integrated over time using fast associative parallel scans, yields the proposed state-space model.<n>We show that LinOSS is universal, i.e., it can approximate any continuous and causal operator mapping between time-varying functions.
  arXiv  Detail & Related papers  (2024-10-04T22:00:13Z)
• Towards Theoretical Understandings of Self-Consuming Generative Models [56.84592466204185]
  This paper tackles the emerging challenge of training generative models within a self-consuming loop. We construct a theoretical framework to rigorously evaluate how this training procedure impacts the data distributions learned by future models. We present results for kernel density estimation, delivering nuanced insights such as the impact of mixed data training on error propagation.
  arXiv  Detail & Related papers  (2024-02-19T02:08:09Z)
• Learning Robust Precipitation Forecaster by Temporal Frame Interpolation [65.5045412005064]
  We develop a robust precipitation forecasting model that demonstrates resilience against spatial-temporal discrepancies. Our approach has led to significant improvements in forecasting precision, culminating in our model securing textit1st place in the transfer learning leaderboard of the textitWeather4cast'23 competition.
  arXiv  Detail & Related papers  (2023-11-30T08:22:08Z)
• Koopman Invertible Autoencoder: Leveraging Forward and Backward Dynamics for Temporal Modeling [13.38194491846739]
  We propose a novel machine learning model based on Koopman operator theory, which we call Koopman Invertible Autoencoders (KIA) KIA captures the inherent characteristic of the system by modeling both forward and backward dynamics in the infinite-dimensional Hilbert space. This enables us to efficiently learn low-dimensional representations, resulting in more accurate predictions of long-term system behavior.
  arXiv  Detail & Related papers  (2023-09-19T03:42:55Z)
• Stabilizing Equilibrium Models by Jacobian Regularization [151.78151873928027]
  Deep equilibrium networks (DEQs) are a new class of models that eschews traditional depth in favor of finding the fixed point of a single nonlinear layer. We propose a regularization scheme for DEQ models that explicitly regularizes the Jacobian of the fixed-point update equations to stabilize the learning of equilibrium models. We show that this regularization adds only minimal computational cost, significantly stabilizes the fixed-point convergence in both forward and backward passes, and scales well to high-dimensional, realistic domains.
  arXiv  Detail & Related papers  (2021-06-28T00:14:11Z)
• 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)
• On the Memory Mechanism of Tensor-Power Recurrent Models [25.83531612758211]
  We investigate the memory mechanism of TP recurrent models. We show that a large degree p is an essential condition to achieve the long memory effect. New model is expected to benefit from the long memory effect in a stable manner.
  arXiv  Detail & Related papers  (2021-03-02T07:07:47Z)
• Anomaly Detection of Time Series with Smoothness-Inducing Sequential Variational Auto-Encoder [59.69303945834122]
  We present a Smoothness-Inducing Sequential Variational Auto-Encoder (SISVAE) model for robust estimation and anomaly detection of time series. Our model parameterizes mean and variance for each time-stamp with flexible neural networks. We show the effectiveness of our model on both synthetic datasets and public real-world benchmarks.
  arXiv  Detail & Related papers  (2021-02-02T06:15:15Z)
• 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.