Reduced-Order Modeling: Using Machine Learning to Enable Large-Scale Simulations for Many-Query Problems
Speaker: Kevin Carlberg, Sandia National Laboratories
Presentation
Abstract
As physics-based simulation has played an increasingly important role in science and engineering, greater demands are being placed on model fidelity. This high fidelity necessitates fine spatiotemporal resolution, which can lead to large-scale models whose simulations consume months on thousands of computing cores. Further, most practical decision-making scenarios (e.g., uncertainty quantification, design optimization) are ‘many query’ in nature, as they require the (parameterized) model to be simulated thousands of times. This leads to a computational barrier: the high cost of large-scale simulations renders them impractical for many-query problems. In this talk, I will present several approaches that exploit simulation data and machine-learning techniques to overcome this barrier.
First, I will introduce nonlinear model reduction methods that employ simulation data and subspace projection to reduce the dimensionality of nonlinear computational models while preserving critical physical properties such as discrete-time optimality, global conservation, stability, and Lagrangian structure. Second, I will describe an adaptive-refinement method that—in analogue to mesh-adaptive h-refinement—incrementally increases the fidelity of the reduced-order model until it satisfies any prescribed error tolerance, thereby allowing reduced-order model to be employed in a fail-safe manner. Finally, I will describe methods for data-driven error modeling, which apply high-dimensional regression methods from machine learning (e.g., random forests, artificial neural networks) to construct an accurate, low-variance statistical model of the error incurred by model reduction. This quantifies the (epistemic) uncertainty introduced by reduced-order models and enables them to be rigorously integrated in uncertainty-quantification applications.
Biography
Kevin Carlberg is a Principal Member of Technical Staff at Sandia National Laboratories in Livermore, CA. He was a President Harry S. Truman Postdoctoral Fellow in National Science and Engineering from 2011 to 2014, and received his Ph.D. in Aeronautics and Astronautics from Stanford University in 2011 with a Ph.D. minor in Computational and Mathematical Engineering. He also holds an M.S. in Aeronautics and Astronautics from Stanford University, and a B.S. in Mechanical Engineering from Washington University in St. Louis. His research interests include model reduction, machine learning, uncertainty quantification, computational mechanics, and numerical optimization.