Newswise — Scientists and engineers use mathematical models, often realized as large-scale computational simulations, to make predictions about the physical world and to deepen their mechanistic understanding of complex physical phenomena. But uncertainty is an integral aspect of such modeling: the mathematical models we use are inevitably incomplete or under-resolved, and dependent on unknown inputs and parameters.

My work under the DOE Early Career Award developed new methodologies to quantify this uncertainty. My students and I focused on the systematic integration of models with observational data. Data—even when they are incomplete, noisy, or indirect—allow models to be refined and improved, facilitate discrimination among competing models, and allow one to assess the inadequacy of models for particular purposes. One can also “close the loop” between data and models by identifying which future data—e.g., which experiments—will be most informative. This process, known as optimal experimental design, can help reduce the cost of experimental campaigns or strategically reduce large volumes of data.

Many of these questions can be cast in a Bayesian statistical framework, but making their solutions tractable required us to develop entirely new methods for accelerating Monte Carlo sampling, for linking optimization and optimal transportation with inference, for performing dimension reduction in inverse problems, and for seeking optimal experimental designs.

The intellectual freedom and long time scale afforded by the DOE Early Career grant gave us latitude to explore and to develop fundamentally new methods. I am impressed at how far the field has come in the past five years, and pleased that these advances were driven in part by our efforts.


Youssef M. Marzouk is an associate professor of Aeronautics and Astronautics at the Massachusetts Institute of Technology (MIT) and co-director of the MIT Center for Computational Engineering. He is also a core member of MIT's Statistics and Data Science Center and Director of MIT’s Aerospace Computational Design Laboratory.


The Early Career Award program provides financial support that is foundational to young scientists, freeing them to focus on executing their research goals. The development of outstanding scientists early in their careers is of paramount importance to the Department of Energy Office of Science. By investing in the next generation of researchers, the Office of Science champions lifelong careers in discovery science. 

For more information, please go to the Early Career Research Program.


Predictive Modeling of Complex Physical Systems: New Tools for Uncertainty Quantification, Statistical Inference, and Experimental Design

The aim of this project is to develop rigorous mathematical formulations and scalable simulation approaches for quantifying uncertainties in large‐scale simulations of complex systems. The research will focus on quantifying uncertainties that may arise due to incomplete knowledge of the phenomena, imprecise measurements, or insufficient computing power, when making predictions through modeling and simulation. Advanced mathematical and statistical techniques will be employed to develop tools for efficiently computing uncertainties in complex systems, test new techniques for using available observation data to improve models, build a comprehensive, scalable framework for automating the modeling and simulation‐uncertainty quantification process, and demonstrate the utility of these tools through the modeling and simulations of combustion processes and subsurface flows. This research in quantification of uncertainties will allow scientists to understand how to use available knowledge to improve models of complex systems, effect sound management of limited resources in designing and conducting experiments, and make simulation‐based predictions with increased confidence.


T. Moselhy and Y.M. Marzouk, “Bayesian inference with optimal maps.” Journal of Computational Physics 231, 7815 (2012). [DOI: 10.1016/j.jcp.2012.07.022]

X. Huan and Y.M. Marzouk, “Simulation-based optimal Bayesian experimental design for nonlinear systems.” Journal of Computational Physics 232, 288 (2013). [DOI: 10.1016/j.jcp.2012.08.013]

A.Spantini, A. Solonen, T. Cui, J. Martin, L. Tenorio, and Y.M. Marzouk, “Optimal low-rank approximations of linear Bayesian inverse problems.” SIAM Journal on Scientific Computing 37, A2451 (2015). [DOI: 10.1137/140977308]