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Colloquium: Shane McQuarrie (Sandia National Laboratories)

Tuesday, November 14
4:00 PM
203 TMCB

Title: Learning Reduced-order Models with Uncertainty and Structure

Abstract: Many modern science problems require solving computationally expensive numerical models of complex physical systems for a variety of conditions. Model-order reduction seeks to alleviate the computational burden of such simulations by constructing computationally efficient surrogates, called reduced-order models (ROMs), which can be solved quickly to obtain approximate solutions of the emulated system. This talk develops two data-driven model reduction approaches based on Operator Inference, a paradigm in which the problem of learning the reduced operators that define a ROM is posed as a regression of state space data and corresponding time derivatives.

When time derivative data are not natively available, as is often the case in applications, they must be estimated from the state data with, e.g., finite difference approximations. The accuracy of the estimation greatly affects the quality of the learned ROM, hence learning accurate ROMs in this manner is challenging when available state data are sparse and/or noisy. To address these challenges, we incorporate Gaussian process surrogate modeling into the Operator Inference framework to probabilistically describe uncertainties in the state data and procure analytical time derivative estimates equipped with corresponding uncertainty estimates. The formulation leads to a generalized least-squares regression and, ultimately, reduced-order operators that are defined probabilistically. The resulting ROM propagates uncertainties from the observed state data to reduced-order predictions.

In addition, we describe a novel method for embedding time-periodic structure into Operator Inference ROMs. The form of the model is motivated by relating the classical projection-based ROM of a polynomial system to a linear time-periodic system whose solutions contain the harmonics of the input frequency. The data-driven nature of Operator Inference allows us to choose the ROM inputs so that solutions are composed of the same higher-frequency content as would be observed in the linear time-periodic approximation. We demonstrate this approach for a highly nonlinear plasma glow discharge process.

Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly-owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.