Data Driven Closure Relation
Computational 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. This MURI project seeks 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.
We 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 at the interface of physical modeling and machine learning; able to exploit multi-precision and multi-resolution computation throughout the entire model-construction pipeline.
While the methods we develop are general, they are enabled by continuous dialog with four guiding applications
- Turbulence, Convection, and Clouds in Climate Models
- Bias-aware Stochastic Turbulence Closure
- Stochastic Particle Dynamics in Complex Fluids
- Free Boundary and Free Discontinuity Problems
