MIT Lecture “Quantifying Uncertainty in Complex Physical Systems:” Modeling Uncertainty

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“In search of better-burning fuels, or more accurate projections of climate change, researchers inevitably work through multiple models, sometimes at great cost.Youssef Marzouk hopes to provide energy and environmental scientists constructive and efficient new approaches to modeling complex engineered systems.

In this seminar, Marzouk describes ways of managing uncertainty, which “is where a lot of idealizations of modeling meet the reality of the complex systems we’re actually trying to study.” Specifically, he aims to “quantify confidence in computational predictions, and use these predictions in design and decision-making;” learn from “noisy, indirect experimental observations,” and refine and build models based on the most informative things observed and measured.

With formulas and graphs, Marzouk shows how he applies such methodologies as polynomial chaos expansion to “construct machinery that lets us propagate uncertainties, evaluate variances, evaluate any aspect of the probability distribution in the model output,” in order “to apply robust formulations much more effectively.” With statistical (Bayesian) inference and inverse problems, Marzouk extracts information from observational data to make models better, “backing out kinetic parameters working at microscale from macroscale data.”

One real-world problem on which Marzouk has been applying his methods: ice sheet dynamics in west Antarctica, which pose “an enormous inference problem,” due to unknowns about sliding friction, geothermal heat flux, and initial temperature of ice. Researchers “need to get a handle on this from the available data,” he says. Another example involves solid oxide fuel cells, which suggest “a lot of potential as high efficiency conversion devices for vehicles or stationary power generation.” Marzouk also hopes his modeling methods can help create better techniques for refining biomass for synthetic fuels.”

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