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

TL;DR

This paper introduces a versatile, energy-constrained score-based diffusion model for multi-scenario fluid flow prediction, achieving accurate, stable, and physically consistent results with minimal training and flexible sampling.

Contribution

It presents a novel conditional diffusion approach with an energy constraint that simplifies multi-scenario fluid flow prediction without requiring problem-specific redesigns.

Findings

Achieves stable and robust predictions across various turbulent flow regimes.

Supports efficient, low-cost sampling with minimal training.

Maintains key physical and statistical properties in predictions.

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.