PiRD: Physics-informed Residual Diffusion for Flow Field Reconstruction
arxiv(2024)
摘要
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.
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