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.
Webmaster University of Houston
---
Last modified: April 11 2016 - 18:14:43