Predictive Modeling of Fluid Flows Using Conditional Score-Based Diffusion Models

With the advent of increased computational power and advanced numerical methods, the simulation of turbulent fields has become central to many contemporary disciplines. Traditional solvers, while delivering high-quality predictions, still struggle in accurately providing fast estimations of flows due to the complexity and inherently chaotic nature of turbulence. As numerous machine learning-based solvers have emerged to address this problem (e.g. physics-informed neural networks or operator learning algorithms), capturing intricate physical phenomena remains a significant challenge. In the realm of generative modeling,diffusion models have established new benchmarks for solving similar problems. In this context, we propose a model that leverages the power of conditional score-based diffusion models for fluid flow prediction. We also integrate an energy constraint that rely on the statistical properties of the flow, further enhancing the temporal stability of the simulation.Our research, centered on a highly turbulent dataset, revealed the remarkable stability and reliability of simple generative diffusion models for turbulent field prediction.