Machine Learning for Physics-based Systems - Optimal Approximations - Architectures and Training
Abstract
The central conceit of this project is that the above challenges can be addressed and overcome by exploiting the structure—geometry, smoothness, low intrinsic dimensionality, sparsity—of both the surrogate architectures and of underlying physical models. To exploit such structure, we will build on state-of-the-art ideas from large scale optimization, inverse problems, model reduction, Bayesian inference, optimal control, and dynamical systems—which have historically exploited model structure to powerful effect—tailoring these approaches to DNNs and other ML surrogates. Our project research objectives are (1) to exploit PDE-based physics model structure to determine optimal surrogate approximations, architectures, and training algorithms, and (2) to use certified surrogates to make optimal design, data assimilation, and control tractable, for complex physics systems. To achieve these objectives, we propose an integrated research program arranged into three thrusts: (1) Architectures: principled methods to select and design ML surrogate architectures, including physics-informed base models and physics-informed DNN architectures that embed problem structure; (2) Training: new algorithms to achieve scalable training, through improved optimization methods and optimized training data selection strategies; and (3) Approximations: theoretical analysis of the approximation and generalization properties of ML surrogates, and rigorous uncertainty quantification to support certified predictions.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jan 21, 2022
- Source ID
- FA95502110084XX0
Entities
People
- Karen Willcox
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- University of Texas at Austin