Improving accuracy of parametric surrogate model for turbidity currents using diffusion-based super-resolution

Resumo

Turbidity currents are a sort of density-driven flow carrying particles that are generated between fluids with small density differences. They also are a mechanism responsible for the deposition of sediments on a seabed. A deep understanding of this phenomenon may help geologists on strategic knowledge in oil exploration. We simulate such currents using a stabilized finite element formulation in a Eulerian-Eulerian framework.

This brings the challenge of a high computational cost for the evaluation of the high-fidelity model. We thus use a surrogate model composed of one linear (Proper Orthogonal Decomposition) and one non-linear (Autoencoder) reduction [1,2]. Once the surrogate is trained for a set of parameters with data generated by the high-fidelity model, one can use such a surrogate model for predicting the dynamics for unseen values of the parameter.

Denoising Diffusion Probabilistic Models (DDPM) [3] is the method behind SOTA generative AI algorithms with very good performance in tasks like super-resolution. Based on such usage of diffusion for generative AI, the authors in [4] developed a framework for flow field reconstruction using a super-resolution task. Such a diffusion model is trained only using high-resolution data, without a pairing between low and high-resolution data, common in other techniques in the area.

The present work aims to use the dataset of high-fidelity parametric simulations of turbidity currents for training both the surrogate and the diffusion model for the super-resolution task. The goal is: using the trained super-resolution model, improve the fields predicted by the reduced model for unseen points of the parametric space.

[1] - M. Cracco et al., Deep learning-based reduced-order methods for fast transient dynamics, Arxiv Preprint 2212.07737, 2022.

[2] - S. Fresca and A. Manzoni, POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition, Comput. Methods Appl. Mech. Engrg., 2022.

[3] - J. Ho, A. Jain and P. Abbeel, Denoising Diffusion Probabilistic Models, arXiv: 2006.11239, 2020.

[4] - D. Shu, Z. Li, A. Barati Farimani, A physics-informed diffusion model for high-fidelity flow field reconstruction, Journal of Computational Physics, Volume 478, 2023