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Karen Willcox

UT Austin



Projection-based model reduction: Physics-based approaches to learn low-dimensional models



February 6, 2019
3:00 pm    PHG 646



Abstract
 

The field of model reduction encompasses a broad range of methods that seek efficient low-dimensional representations of an underlying high-fidelity model. A large class of model reduction methods are projection-based; that is, they derive the low-dimensional approximation by projection of the original large-scale model onto a low-dimensional subspace. Model reduction has clear connections to machine learning. The difference in fields is perhaps largely one of history and perspective: model reduction methods have grown from the scientific computing community, with a focus on reducing high-dimensional models that arise from physics-based modeling, whereas machine learning has grown from the computer science community, with a focus on creating low-dimensional models from black-box data streams. Yet recent years have seen an increased blending of the two perspectives and a recognition of the associated opportunities. This talk will describe a model reduction approach that combines lifting--the introduction of auxiliary variables to transform a general nonlinear model to a model with polynomial nonlinearities--with proper orthogonal decomposition. The result is a data-driven formulation to learn the low-dimensional model from high-fidelity simulation data, but a key aspect of the approach is that the lifted state-space in which the learning is achieved is derived using the problem physics. The method is demonstrated for nonlinear systems of partial differential equations arising in rocket combustion applications.






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