Scientific Machine Learning in Computational Fluid Mechanics

Jian Xun Wang, University of Notre Dame
Petascale, Adaptive CFD

Abstract: High-fidelity modeling and simulation of complex fluid systems based on partial differential equations (PDEs) and numerical discretization have been developed for decades and achieved great success. Nonetheless, efficiently solving these PDEs (e.g., Navier-Stokes equations) with high accuracy in many scenarios (e.g., turbulence, complex boundary conditions, large scale, many-query needs) are still challenging. On the other hand, recent advances in data science and machine learning, combined with the ever-increasing availability of high-fidelity simulation and measurement data, open up new opportunities for developing data-enabled computational modeling of fluid systems. Although the state-of-the-art machine/deep learning techniques hold great promise, there are still many challenges - e.g., they often need a large amount of data that might not be available, lack interpretability and explainability, often cannot guarantee convergence. On the other hand, there is often a richness of prior knowledge, including physical laws and phenomenological principles, which can be leveraged in this regard. Thus, there is an urgent need for fundamentally new and transformative machine learning techniques, closely grounded with physics, to address the aforementioned challenges in computational fluid mechanics problems. This talk will briefly discuss our recent developments of scientific machine learning techniques for fluid problems, including structure-preserved machine learning, physics-informed neural networks, geometric deep learning, and physics-informed reinforcement learning for flow control.

Bio: Dr. Jian-Xun Wang is an assistant professor of Aerospace and Mechanical Engineering at the University of Notre Dame. Dr. Wang received a Ph.D. in Aerospace Engineering from Virginia Tech in 2017 and was a postdoctoral scholar at the University of California, Berkeley before joining Notre Dame in 2018. He is a recipient of 2021 NSF CAREER Award. His research focuses on data-augmented computational modeling, scientific machine learning, Bayesian data assimilation, and uncertainty quantification.

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