Pi-fusion: Physics-informed diffusion model for learning fluid dynamics

TL;DR

Pi-fusion is a physics-informed diffusion model that effectively predicts the temporal evolution of fluid dynamics, improving accuracy and generalization over existing methods by incorporating physics-guided sampling and reciprocal learning.

Contribution

The paper introduces Pi-fusion, a novel physics-informed diffusion model with physics-guided sampling and reciprocal learning strategies for better fluid dynamics prediction.

Findings

Outperforms state-of-the-art methods in predicting velocity and pressure fields.

Demonstrates strong generalization on synthetic and real-world datasets.

Effectively models time-variant fluid motion with probabilistic inference.

Abstract

Physics-informed deep learning has been developed as a novel paradigm for learning physical dynamics recently. While general physics-informed deep learning methods have shown early promise in learning fluid dynamics, they are difficult to generalize in arbitrary time instants in real-world scenario, where the fluid motion can be considered as a time-variant trajectory involved large-scale particles. Inspired by the advantage of diffusion model in learning the distribution of data, we first propose Pi-fusion, a physics-informed diffusion model for predicting the temporal evolution of velocity and pressure field in fluid dynamics. Physics-informed guidance sampling is proposed in the inference procedure of Pi-fusion to improve the accuracy and interpretability of learning fluid dynamics. Furthermore, we introduce a training strategy based on reciprocal learning to learn the quasiperiodical pattern of fluid motion and thus improve the generalizability of the model. The proposed approach are then evaluated on both synthetic and real-world dataset, by comparing it with state-of-the-art physics-informed deep learning methods. Experimental results show that the proposed approach significantly outperforms existing methods for predicting temporal evolution of velocity and pressure field, confirming its strong generalization by drawing probabilistic inference of forward process and physics-informed guidance sampling. The proposed Pi-fusion can also be generalized in learning other physical dynamics governed by partial differential equations.