Autoregressive regularized score-based diffusion models for multi-scenarios fluid flow prediction
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| author | Genuist, Wilfried Savin, Éric Gatti, Filippo Clouteau, Didier |
| author_facet | Genuist, Wilfried Savin, Éric Gatti, Filippo Clouteau, Didier |
| contents | Building on recent advances in scientific machine learning and generative modeling for computational fluid dynamics, we propose a conditional score-based diffusion model designed for multi-scenarios fluid flow prediction. Our model integrates an energy constraint rooted in the statistical properties of turbulent flows, improving prediction quality with minimal training, while enabling efficient sampling at low cost. The method features a simple and general architecture that requires no problem-specific design, supports plug-and-play enhancements, and enables fast and flexible solution generation. It also demonstrates an efficient conditioning mechanism that simplifies training across different scenarios without demanding a redesign of existing models. We further explore various stochastic differential equation formulations to demonstrate how thoughtful design choices enhance performance. We validate the proposed methodology through extensive experiments on complex fluid dynamics datasets encompassing a variety of flow regimes and configurations. Results demonstrate that our model consistently achieves stable, robust, and physically faithful predictions, even under challenging turbulent conditions. With properly tuned parameters, it achieves accurate results across multiple scenarios while preserving key physical and statistical properties. We present a comprehensive analysis of stochastic differential equation impact and discuss our approach across diverse fluid mechanics tasks. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_24145 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Autoregressive regularized score-based diffusion models for multi-scenarios fluid flow prediction Genuist, Wilfried Savin, Éric Gatti, Filippo Clouteau, Didier Machine Learning Fluid Dynamics 65N75, 35Q30, 60H15, 76F55, 68T07 I.2.6; G.1.7; I.6.1; I.6.3 Building on recent advances in scientific machine learning and generative modeling for computational fluid dynamics, we propose a conditional score-based diffusion model designed for multi-scenarios fluid flow prediction. Our model integrates an energy constraint rooted in the statistical properties of turbulent flows, improving prediction quality with minimal training, while enabling efficient sampling at low cost. The method features a simple and general architecture that requires no problem-specific design, supports plug-and-play enhancements, and enables fast and flexible solution generation. It also demonstrates an efficient conditioning mechanism that simplifies training across different scenarios without demanding a redesign of existing models. We further explore various stochastic differential equation formulations to demonstrate how thoughtful design choices enhance performance. We validate the proposed methodology through extensive experiments on complex fluid dynamics datasets encompassing a variety of flow regimes and configurations. Results demonstrate that our model consistently achieves stable, robust, and physically faithful predictions, even under challenging turbulent conditions. With properly tuned parameters, it achieves accurate results across multiple scenarios while preserving key physical and statistical properties. We present a comprehensive analysis of stochastic differential equation impact and discuss our approach across diverse fluid mechanics tasks. |
| title | Autoregressive regularized score-based diffusion models for multi-scenarios fluid flow prediction |
| topic | Machine Learning Fluid Dynamics 65N75, 35Q30, 60H15, 76F55, 68T07 I.2.6; G.1.7; I.6.1; I.6.3 |
| url | https://arxiv.org/abs/2505.24145 |