Robust Reconstruction of High-Fidelity Fluid Field Using Physics-informed Diffusion Model*

Reconstructing high-fidelity fluid flow data from low-fidelity input is a path of great potential towards mitigating the conflict between efficiency and accuracy in Computational Fluid Dynamics (CFD) simulations. The fast advancement of deep learning in image super-resolution and inpainting has motivated increasing research interest in using neural network models for CFD data reconstruction. While many proposed models have achieved competitive results in their specific numerical experiment settings, they tend to be subject to one common limitation, that is, the model inference performance is highly dependent on the similarity between the input (low-fidelity) training data and the input (low-fidelity) test data. To alleviate this limitation, we propose a deep learning-based method for CFD data reconstruction. Our method first processes the input data samples of different low-res patterns to reduce their discrepancy on data distributions. The processed data samples are then sent to a denoising diffusion probabilistic model to generate high-fidelity CFD data. More specifically, we adds Gaussian noise to the original input data samples such that their distributions are all drawn towards Gaussian distribution. This processing allows the goal of data reconstruction to be formulated as a data denoising problem. Under this new problem formulation, the noisy input data is considered as an intermediate state of a backward diffusion process, and is sent to a pretrained diffusion model for high-fidelity data generation. To further improve the data fidelity, we design our model to enable the use of partial differential equation residual gradient as a physics-informed conditioning information. Numerical experimental results show that our model has a marginally better L² reconstruction accuracy compared with benchmark method which learns the direct-mapping from low-fidelity to high-fidelity data, while having the advantage of being much more robust to unseen low-fidelity pattern and being more accurate in the kinetic energy spectrum distribution of the reconstructed data.