CDS&E: Data-driven Discovery of Probabilistic Closures in Turbulent Flows

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Reliable predictive modeling of turbulent flows has remained one of the grand challenges of classical physics. This is because turbulent flows are multi-scale problems. Capturing all these scales using direct numerical simulations of turbulent flows remains cost prohibitive for the majority of the scientific and engineering applications. Therefore, in the predictive models for practical turbulent flows the small scales cannot be resolved and as a result the effect of these unresolved scales on the resolved scales must be modeled. However, except for very simple canonical flows, the functional form of these models are not known. This is the main source of uncertainty in turbulent flow predictions. With the recent development of scalable scientific machine learning algorithms as well as the growth of high performance computing resources, it is now possible to generate high-fidelity data and train machine learning models with a very large number of parameters. This opens up new opportunities to discover new turbulence models for some of the practical engineering problems and significantly improve the reliability of predictions in turbulent flows.It is widely known that one of the most accurate frameworks to discover turbulent models is a probabilistic one. However, probabilistic models are not as commonly used as the deterministic models mainly due to their computational costs. These models are expressed versus the evolution of probability density functions (PDFs), which can be very high-dimensional. Discovery of probabilistic turbulence models requires solving both the forward and inverse PDF transport equations. Classical scientific computing techniques are unable to solve this problem due to the their high dimensionality. In the project, a new physics-informed deep learning methodology will be developed and utilized to solve both forward and inverse PDF transport equations. If successful, this project will lead to the discovery of probabilistic turbulence models for diverse turbulent flows. Along with the development of technical tools, this work will also include integration with education, organization of new conferences, interaction with industry and governmental research labs, improvement of gender, ethnic and racial diversity, and expansion through K-12 outreach.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.