Leveraging Scale Separation and Stochastic Closure for Data-Driven Prediction of Chaotic Dynamics
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908984359780352 |
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| author | Zighed, Ismaël Thome, Nicolas Gallinari, Patrick Sayadi, Taraneh |
| author_facet | Zighed, Ismaël Thome, Nicolas Gallinari, Patrick Sayadi, Taraneh |
| contents | Simulating turbulent fluid flows is a computationally prohibitive task, as it requires the resolution of fine-scale structures and the capture of complex nonlinear interactions across multiple scales. This is particularly the case in direct numerical simulation (DNS) applied to real-world turbulent applications. Consequently, extensive research has focused on analysing turbulent flows from a data-driven perspective. However, due to the complex and chaotic nature of these systems, traditional models often become unstable as they accumulate errors through autoregression, severely degrading even short-term predictions. To overcome these limitations, we propose a purely stochastic approach that separately addresses the evolution of large-scale coherent structures and the closure of high-fidelity statistical data. To this end, the dynamics of the filtered data (i.e. coherent motion) are learnt using an autoregressive model. This combines a VAE and Transformer architecture. The VAE projection is probabilistic, ensuring consistency between the model's stochasticity and the flow's statistical properties. To recover high-fidelity velocity fields from the filtered latent space, Gaussian Process (GP) regression is employed. This strategy has been tested in the context of a Kolmogorov flow exhibiting chaotic behaviour analogous to real-world turbulence. We compare the performance of our model with state-of-the-art probabilistic baselines, including a VAE and a diffusion model. We demonstrate that our Gaussian process-based closure outperforms these baselines in capturing first and second moment statistics in this particular test bed, providing robust and adaptive confidence intervals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_24583 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Leveraging Scale Separation and Stochastic Closure for Data-Driven Prediction of Chaotic Dynamics Zighed, Ismaël Thome, Nicolas Gallinari, Patrick Sayadi, Taraneh Fluid Dynamics Simulating turbulent fluid flows is a computationally prohibitive task, as it requires the resolution of fine-scale structures and the capture of complex nonlinear interactions across multiple scales. This is particularly the case in direct numerical simulation (DNS) applied to real-world turbulent applications. Consequently, extensive research has focused on analysing turbulent flows from a data-driven perspective. However, due to the complex and chaotic nature of these systems, traditional models often become unstable as they accumulate errors through autoregression, severely degrading even short-term predictions. To overcome these limitations, we propose a purely stochastic approach that separately addresses the evolution of large-scale coherent structures and the closure of high-fidelity statistical data. To this end, the dynamics of the filtered data (i.e. coherent motion) are learnt using an autoregressive model. This combines a VAE and Transformer architecture. The VAE projection is probabilistic, ensuring consistency between the model's stochasticity and the flow's statistical properties. To recover high-fidelity velocity fields from the filtered latent space, Gaussian Process (GP) regression is employed. This strategy has been tested in the context of a Kolmogorov flow exhibiting chaotic behaviour analogous to real-world turbulence. We compare the performance of our model with state-of-the-art probabilistic baselines, including a VAE and a diffusion model. We demonstrate that our Gaussian process-based closure outperforms these baselines in capturing first and second moment statistics in this particular test bed, providing robust and adaptive confidence intervals. |
| title | Leveraging Scale Separation and Stochastic Closure for Data-Driven Prediction of Chaotic Dynamics |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2510.24583 |