Data-Driven Closure Models and Constitutive Relations: The Development of Principled Methodologies for Complex Multi-Physics Applications (White Paper Tracking #22-000002556)
Abstract
PROJECT ABSTRACTComputational science and engineering (CS&E) has been a central pillar of science and engineering for almost a century. Despite its successes, challenges remain, and important problems will remain beyond reach for the foreseeable future with current approaches. The rapidly increasing availability of data, and methods to use them, offer a way forward. So, the defining challenge for CS&E in the 21st century is to use data-driven methodology within the context of domain specific modeling principles. The ambitious goal of the proposed MURI project is to address this challenge, and lay the foundations for a revolution in CS&E.Our approach is to combine centuries of intellectual capital, encapsulated in the basic laws of physics (conservation laws for quantities such as mass, momentum, and energy), with data-driven learning to discover constitutive laws and closure models (collectively referred to as closure models). These closure models will enable accurate, predictive calculations at scale, with quantified uncertainties, in complex multiscale, multiphysics situations where this is not currently possible with available computational resources. The objectives of the proposed research are to develop methods for such data-driven closure models: flexible enough to employ heterogeneous and indirectly informative data; rich enough to allow for stochastic models and to account for uncertainties; able to incorporate physical constraints such as frame indifference; able to incorporate mathematical constraints such as well-posedness of the combined conservation-closure model; constructed in a manner which makes them amenable to state-of-the-art training and optimization methodology developed in machine learning; constructed to facilitate innovation in ensemble Kalman methods at the interface of physical modeling and machine learning; able to exploit multi-precision and multi-resolution computation throughout the entire model-constructionpipeline. We will achieve this by identifying four concrete methodological challenges, developing a number of innovations that address them, and doing so through continuous dialogue between the methodological innovations and four guiding applications. These four applications are: (i) Turbulence, Convection, and Clouds in Climate Models;(ii) Bias-aware Stochastic Turbulence Closure (iii) Stochastic Particle Dynamics in Complex Fluids; (iv) Free Boundary and Free Discontinuity Problems. They are individually important in their own right in terms of impact, individually pose the broad methodological challenges that are the focus of our work, and collectively represent a broad range of science and engineering applications. Thus, the work will have impact far beyond any specific application. The scope and breadth of the MURI will enable a significant, game-changing research program, led by six investigators with a proven track record of research at the interfaces between computational mathematics, CS&E, machine learning, and applications in the physical sciences. The timeline will allow for meaningful feedback between the methodological innovations and the guiding applications. And the framing of the research in terms of the defining challenge for CS&E this century means that the successful completion of the MURI will have long-term downstream impact in numerous application fields, and in particular on multiple fronts of importance to DoD and the US Navy.(Approved for public release)
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 11, 2023
- Source ID
- N000142312654
Entities
People
- Kaushik Bhattacharya
Organizations
- California Institute of Technology
- Office of Naval Research
- United States Navy