[Amath-seminars] Feb. 4 - Special AMATH Seminar - Benjamin Peherstorfer (MIT)

Ulrich Hetmaniuk hetmaniu at uw.edu
Sun Jan 31 15:19:54 PST 2016

Dear All,

We hope you can join us for our special AMATH seminar on **Thursday**
February 4th.

Speaker: Benjamin Peherstorfer, MIT
Time: February 4th, 16h00
Location: SMI 102

Title: Data-driven multi-fidelity methods for uncertainty quantification

Quantifying uncertainty in systems described by partial differential
equations (PDEs) typically requires solving the PDEs many times for
different realizations of the stochastic parameters. Solving the PDEs for
thousands or even millions of parameter realizations is often intractable.
A common remedy is to replace the high-fidelity model (system of equations)
stemming from the discretization of the PDEs with a reduced model that
provides low-cost approximations of the PDE solutions; however, reduced
models induce an error into the overall result that typically leads to the
loss of accuracy guarantees for the statistics of interest (often the error
cannot even be quantified). We introduce multi-fidelity methods that
combine, instead of replace, the high-fidelity model with reduced
models---to increase the accuracy of the overall result and to ultimately
establish accuracy guarantees. We first present an online adaptive model
reduction approach that uses sparse data of the high-fidelity model to
adapt a reduced model while it is evaluated. Numerical results demonstrate
that our online adaptive reduced models achieve higher accuracies in
approximating nonlinear PDEs than static models. In the second part, we
introduce the multi-fidelity Monte Carlo method that combines the
high-fidelity model with reduced models and data-fit models to efficiently
estimate statistics of outputs of the high-fidelity model. Our
multi-fidelity method is guaranteed to provide unbiased estimates
("accuracy guarantees"). In our numerical experiments with linear and
nonlinear models from aerospace engineering, the multi-fidelity Monte Carlo
method achieves speedups by orders of magnitude compared to methods that
invoke a single high-fidelity or reduced model only.

Speaker webpage
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