University of Texas at Austin

Cross-
Cutting
Research Area

Optimization, Inversion and UQ

From forward simulation to the outer loop

Optimization, inversion and UQ bring the power of computational modeling to grand challenge problems that require estimation, design and control.

Optimal design of an aircraft wing. Inferring ocean state from satellite and in situ observations. Quantifying the uncertainty in predictions of a cancer patient’s tumor growth. Optimization, inversion and UQ are the computational technologies that connect data, predictive models and decisions in high-impact applications across science, engineering and medicine.

An Overview: Optimization, Inversion & Uncertainty Quantification

Why are optimization, inversion and UQ important?

Optimization, inversion and UQ are the key mathematical and computational tasks in what is often referred to as the “outer loop” (i.e., computational applications that form outer loops around a forward model).

Optimization A significant aspect of the field of CSE is the development of theory and methods for optimizing systems governed by large-scale CSE models, typically involving systems of ODEs or PDEs. Such problems are prevalent in applications of optimal control, optimal design and optimal experimental design.

Inversion In general, any endeavor to infer cause from effect — to extract knowledge from data — can be viewed as an inverse problem. Inverse problems sit at the heart of discovery and innovation in every area of science, engineering and medicine. As just a few examples of model-based inverse problems, we may infer: coalescing binary system properties from detected gravitational waves, earth structure from reflected seismic waves, reaction rates from measurements of chemically reacting flows, ice sheet basal friction from satellite observations of surface flow, and three-dimensional bone structure from X-ray computed tomography measurements.

Uncertainty quantification (UQ) involves the quantitative characterization and management of uncertainty in a broad range of applications. It employs both computational models and observational data, together with theoretical analysis. UQ encompasses many different tasks, including uncertainty propagation, sensitivity analysis, statistical inference and model calibration, decision making under uncertainty, experimental design and model validation.

News in brief

Oden Institute Joins the Forty for 40 Party

News

Sept. 22, 2021

Oden Institute Joins the Forty for 40 Party

  • First time Oden Institute participates in 40 hours for the Forty Acres  
  • Annual UT Austin fundraising event now in its ninth year

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Introducing The 2021 Fellowship…

Feature

Aug. 31, 2021

Introducing The 2021 Fellowship…

  • 2021 Peter O'Donnell, Jr. Postdoctoral Fellows bring variety of new skillsets and diverse research interests
  • Scope of projects range from computational modeling at atomic scale to development of tsunami simulation techniques

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Thomas Hughes Honored by Japan Association for Computational Mechanics

News

Aug. 30, 2021

Thomas Hughes Honored by Japan Association for Computational Mechanics

  • Peter O'Donnell, Jr. Chair in Computational and Applied Mathematics inducted with Tayfun Tezduyar from Rice University
  • Tezduyar and Hughes first non-Japanese so honored by JACM

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Preschoolers, PhDs and The Pandemic

Profile

April 27, 2021

Preschoolers, PhDs and The Pandemic

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