Autoregressive regularized score-based diffusion models for multi-scenarios fluid flow prediction

2025-05-30

AI Summary

To address the challenge of multi-regime fluid flow prediction, this paper proposes a conditional fractional diffusion model with energy constraints. Methodologically, it introduces a novel turbulence-driven energy regularization mechanism, embedding physical energy conservation priors into the fractional score matching and conditional diffusion frameworks. By formulating the problem via stochastic differential equations and adopting an autoregressive generation strategy, the approach avoids custom network architectures and enables plug-and-play physics enhancement alongside cross-scenario, retraining-free conditional injection. Experiments on a multi-flow-regime complex flow dataset demonstrate that the model significantly improves physical consistency and turbulence statistical fidelity of predictions, while achieving high sampling efficiency and strong generalization capability—delivering high-physical-fidelity generative solutions at low training cost.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Natural Language Processing: Generation

Application Category

• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

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.

Problem

• Multi-scenarios fluid flow prediction using diffusion models
• Energy constraint improves turbulent flow prediction quality
• Efficient conditioning for training across diverse flow scenarios

Innovation

• Conditional score-based diffusion model
• Energy constraint for turbulent flows
• Efficient multi-scenario conditioning mechanism