Data-driven reduced models, multi-fidelity uncertainty quantification, and multi-fidelity optimization under uncertainty

My research interests lie in computational simulation and optimization of engineering systems, with a specific focus on data to decisions in complex systems. I develop methods that combine physics-based models with data-driven learning for applications in optimization, real-time simulation, control, and uncertainty quantification. I develop methods for multi-fidelity uncertainty quantification and multi-fidelity optimization under uncertainty. I create new methods for managing multiple models and data sources for applications in design and uncertainty quantification.

What is parameterized model reduction (also called parametric model reduction)?

What is multi-fidelity uncertainty quantification?

What is nonlinear model reduction?

What is Predictive Data Science?

Current Projects

AFOSR Dynamic Data-Driven Application Systems (DDDAS)

Enabling a self-aware UAV with dynamic data-driven model reduction

In collaboration with Aurora Flight Sciences and Texas A&M University

Funded by AFOSR Dynamic Data-Driven Application Systems (DDDAS)

AFOSR Multidisciplinary Research Program of the University Research Initiative (MURI) BWB Aircraft

Managing multiple sources of information in the design of multidisciplinary systems

In collaboration with Arizona State University, Cornell University, University of Michigan, Santa Fe Institute and Texas A&M University

Funded by AFOSR Multidisciplinary Research Program of the University Research Initiative (MURI)

Predictive Digital Twin

In collaboration with Aurora Flight Sciences and Akselos

Funded by AFOSR Dynamic Data Driven Application Systems, AFOSR Computational Mathematics, and MIT-SUTD International Design Center

AEOLUS: Advances in Experimental Design, Optimization and Learning for Uncertain Complex Systems

In collaboration with Brookhaven National Laboratory, Massachusetts Institute of Technology, Oak Ridge National Laboratory, and Texas A&M University

Funded by U.S. Department of Energy, Office of Science, Mathematical Multifaceted Integrated Capabilities Center (MMICC)

Air Force Center of Excellence on Multi-Fidelity Modeling of Rocket Combustor Dynamics

Air Force Center of Excellence on Multi-Fidelity Modeling of Rocket Combustor Dynamics

In collaboration with University of Michigan, Purdue University and New York University (Courant)

Funded by the Air Force Center of Excellence.

Gappy proper orthogonal decomposition

Gappy proper orthogonal decomposition

Our research develops gappy POD methods for flow reconstruction, flow sensing, sensor placement and structural assessment.

Multi-fidelity uncertainty quantification methods

Multi-fidelity uncertainty quantification

Multifidelity UQ is the use of multiple approximate models and other sources of information to accelerate UQ tasks such as optimization under uncertainty and estimating mean, variance, probability of failure, and global sensitivity indices.

Past Projects

U.S. Department of Energy Mathematical Multifaceted Integrated Capabilities Center MMICC

DiaMonD: An Integrated Multifaceted Approach to Mathematics at the Interfaces of Data, Models, and Decisions

In collaboration with Colorado State University, Florida State University, Los Alamos National Laboratory, Oak Ridge National Laboratory, Stanford University and University of Texas at Austin

Funded by U.S. Department of Energy, Office of Science, Mathematical Multifaceted Integrated Capabilities Center (MMICC)

QUANTUM: Inference, Simulation, and Optimization of Complex Systems Under Uncertainty: Theory, Algorithms, and Applications to Turbulent Combustion

QUANTUM: Inference, Simulation, and Optimization of Complex Systems Under Uncertainty

In collaboration with University of Auckland, University of Texas at Austin, Rice University and Warwick University

Funded by DARPA Enabling Quantification of Uncertainty in Physical Systems (EQUiPS)