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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