PiRD: Physics-informed Residual Diffusion for Flow Field Reconstruction

TL;DR

This paper introduces PiRD, a physics-informed residual diffusion model that enhances flow field reconstruction from various low-fidelity data, improving accuracy and robustness without retraining, by integrating physics principles into a diffusion-based framework.

Contribution

The paper presents a novel physics-informed residual diffusion approach that outperforms CNN-based methods in flow reconstruction, offering better generalization and physical consistency.

Findings

Effective reconstruction of turbulent flows from diverse low-fidelity inputs.

No retraining needed for different low-fidelity data conditions.

Improved data fidelity and physical accuracy in flow field reconstruction.

Abstract

The use of machine learning in fluid dynamics is becoming more common to expedite the computation when solving forward and inverse problems of partial differential equations. Yet, a notable challenge with existing convolutional neural network (CNN)-based methods for data fidelity enhancement is their reliance on specific low-fidelity data patterns and distributions during the training phase. In addition, the CNN-based method essentially treats the flow reconstruction task as a computer vision task that prioritizes the element-wise precision which lacks a physical and mathematical explanation. This dependence can dramatically affect the models' effectiveness in real-world scenarios, especially when the low-fidelity input deviates from the training data or contains noise not accounted for during training. The introduction of diffusion models in this context shows promise for improving performance and generalizability. Unlike direct mapping from a specific low-fidelity to a high-fidelity distribution, diffusion models learn to transition from any low-fidelity distribution towards a high-fidelity one. Our proposed model - Physics-informed Residual Diffusion, demonstrates the capability to elevate the quality of data from both standard low-fidelity inputs, to low-fidelity inputs with injected Gaussian noise, and randomly collected samples. By integrating physics-based insights into the objective function, it further refines the accuracy and the fidelity of the inferred high-quality data. Experimental results have shown that our approach can effectively reconstruct high-quality outcomes for two-dimensional turbulent flows from a range of low-fidelity input conditions without requiring retraining.