Recent Publications

More Publications

Embedded Model Error Representation for Bayesian Model Calibration

Accepted, International Journal for Uncertainty Quantification, 2019.

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Compressive sensing adaptation for polynomial chaos expansions

Journal of Computational Physics, Vol. 380, No. 1, pp. 29–47, 2019.

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Enhancing Model Predictability for a Scramjet Using Probabilistic Learning on Manifolds

AIAA Journal, Vol. 57, No. 1, pp. 365–378, 2019.

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Uncertainty Propagation Using Conditional Random Fields in Large-Eddy Simulations of Scramjet Computations

AIAA Scitech 2019 Forum, AIAA paper 2019–0724, San Diego, CA, 2019.

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Progress in Scramjet Design Optimization Under Uncertainty Using Simulations of the HIFiRE Direct Connect Rig

AIAA Scitech 2019 Forum, AIAA paper 2019–0725, San Diego, CA, 2019.

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Design optimization of a scramjet under uncertainty using probabilistic learning on manifolds

Submitted, 2018.


Entropy-based closure for probabilistic learning on manifolds

Accepted, Journal of Computational Physics, 2018.


Selected Publications

Compressive Sensing with Cross-Validation and Stop-Sampling for Sparse Polynomial Chaos Expansions

SIAM/ASA Journal on Uncertainty Quantification, Vol. 6, No. 2, pp. 907–936, 2018.

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Global Sensitivity Analysis and Estimation of Model Error, Toward Uncertainty Quantification in Scramjet Computations

AIAA Journal, Vol. 56, No. 3, pp. 1170–1184, 2018.

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Gradient-Based Stochastic Optimization Methods in Bayesian Experimental Design

International Journal for Uncertainty Quantification, Vol. 4, No. 6, pp. 479–510, 2014.

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Simulation-based optimal Bayesian experimental design for nonlinear systems

Journal of Computational Physics, Vol. 232, No. 1, pp. 288–317, 2013.

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Optimal Experimental Design

Experiments are often expensive, time-consuming, and perhaps even dangerous. However, not all experiments are equal, and some can produce more valuable data than others. Identifying and executing these “good” experiments can lead to substantial resource savings.

We develop mathematical frameworks and computational algorithms for optimal experimental design (OED), and seek to address questions such as:

  • Under what condition should we conduct an experiment?
  • What quantities should we probe?
  • Where and when should we take measurements?

  • Have we gathered enough data and should stop, or continue with more experiments?

OED is a form of decision-making under uncertainty. For example, when our experimental goal is to learn about model parameters from noisy measurements, a possible approach involves finding the design decision maximizing the expected information gain (mutual information).

There are many challenges associated with finding the optimal design, including the need for optimization routines to accommodate noisy responses, repeated Bayesian inferences under different scenarios, and all while wrapping around an often computationally intensive and highly nonlinear physics-based forward model with high-dimensional input and output spaces.

Example: hydrogen-oxygen ignition

  • Design: initial temperature and equivalence ratio
  • Measure: ignition delay times
  • Infer: Arrhenius kinetic parameters

Below are expected utility contours approximated from using the full physical model (left), and a polynomial chaos surrogate model that greatly accelerate the computations (right); they show excellent agreement.

With full model
With polynomial chaos surrogate model
With full model With polynomial chaos surrogate model

Three experiments are simulated (at designs A, B, and C in figure above). Bayesian inference is performed and posterior densities are shown below. Designs A (which has the highest expected utility value) produces the “tightest” posterior (left), reflecting a larger reduction in uncertainty and increased confidence for estimating these parameters.

Design A
Design B
Design C
Design A Design B Design C

Sequential Experimental Design

Coming soon!

Uncertainty Quantification for Machine Learning

Coming soon!

Uncertainty Quantification in Engineering Applications

Uncertainty quantification (UQ) plays a crucial role in engineering and science. It enters research and production workflows at various points, such as the highlighted yellow fields below. UQ is particularly important for the learning process, by providing a principled framework for interactions among theory, models, and data.

Example: reactive flows inside a scramjet combustor

Scramjets are propulsive systems that can enable efficient and stable operations under hypersonic flight conditions (Mach 5+). For instance, the figure below shows the flight test payload from the Hypersonic International Flight Research Experimentation (HIFiRE) program.

Designing scramjet engines requires both accurate flow simulations as well as UQ. Enabling UQ for expensive simulations of turbulent supersonic reactive flows faces many computational challenges. Techniques such as global sensitivity analysis, surrogate modeling, compressive sensing, efficient Bayesian calibration, and multilevel multifidelity sampling are needed to make UQ analysis possible. Below is an illustration of the predictive uncertainty (blue contours) of Mach number at select vertical stations of the combustor section. Such information would be valuable for finding optimal scramjet designs that are also robust and reliable.


Current and Recent Teaching

  • MECHENG 305: Introduction to Finite Elements in Mechanical Engineering (Fall 2018)
  • MECHENG 502: Methods of Differential Equations in Mechanics (Winter 2019)


Graduate Students

Jeremiah Hauth
Wanggang Shen
Wanggang Shen


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  • 2033 AL (W. E. Lay Auto Lab), 1231 Beal Ave, Ann Arbor, MI 48109-2133