Experimental design is an important topic in
engineering and sciences
that pertains to model calibration, validation, and predictive modeling. As physical models are becoming increasingly more complex, the
evaluation of corresponding utility values and the optimization procedure in the design of an experiment are becoming computationally intensive. Techniques such as sparse
quadrature, surrogate modeling, model reduction, and asymptotic
approximation have been applied to the design of experiments. Research
activities on the subject have recently gained momentum due to the
current trend to carry out large-scale PDE related experimental designs
within a Bayesian framework.

In our current project, we are developing and analyzing fast experimental design methodologies based
on innovative Laplace methods. We provide fast asymptotic
results and explore the intrinsic system sparsity for the
numerical integration of the expected post-experimental information gain, in
both determined and ill-conditioned systems. Based on this, we propose the most
efficient design setup.

We are also applying our methodology to a
wide range of engineering applications, such as high pressure shock tube experiments and impedance tomography. The following figures show the optimal current pattern (left), the worst current pattern (right) and two current patterns with intermediate information gains. The uncertainties of the conductivities along the diagonal (top-left to bottom-right) are assumed to be higher than those in the rest of the square domain.

Two examples of current patterns inducing the highest information gains. Two examples of current patterns inducing the low information gains.

The performance of our method compared with double-loop Monte Carlo:

Parallel to methodology development, we are currently working with an extensive team of experimentalists and engineers on the experimental design of combustion in shock tube. The inference of reactive rate function for the oxidation of hydrogen is one of the experiments we are considering. The first picture below shows the expected information gain increases as the temperature and the initial concentration of hydrogen increases. The second picture visualizes the expected information gain for two experiments carried out using two different temperatures and a single iniitial concentration of hydrogen. The maximum information gain is obtained at the point where two temperatures are well-seperated. The third picture shows three iso-surfaces of the expected information gain in a series of experiments where the temperatures are different and the initial concentration of hydrogen is fixed as the maximum.

The expected information gain with respect to the initial temperature and initial hydrogen concentration. |
The expected information gain with respect to two temperatures, while the initial hydrogen concentration is a constant (0.05). |
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The iso-surface of the expected information gain with respect to three temperatures.

A shock-tube combustion method was used to demonstrate the effectiveness of the optimization method © 2015 KAUST

http://discovery.kaust.edu.sa/en/article/119/taking-the-guesswork-out-of-experimental-design

- Fabrizio Bisetti (PSE, KAUST)
- Aamir Farooq (PSE, KAUST)
- Daesang Kim (PSE, KAUST)
- Omar Knio (CEMSE, KAUST)
- Quan Long (CEMSE, KAUST)
- Mohammad Motamed (UNM)
- Marco Scavino (CEMSE, KAUST)
- Raul Tempone (CEMSE, KAUST)
- Suojin Wang (Texas A&M, USA)

- F. Bisetti, D. Kim, O. Knio, Q. Long and R. Tempone. Optimal Bayesian experimental design for priors of compact support with application to shock-tube experiments for combustion kinetics. Accepted by International Journal for Numerical Methods in Engineering, 2015
- Q. Long, M. Motamed, R. Tempone.
**Fast Bayesian optimal experimental design for seismic source inversion**, Computer Methods in Applied Mechanics and Engineering, vol. 291, pp. 123-145, 2015 - Q. Long, M. Scavino, R. Tempone and S. Wang.
**A Laplace Method for Under-Determined Bayesian Optimal Experimental Design**. Computer Methods in Applied Mechanics and Engineering, Volume 285, Pages 849–876, March 2015. - Q. Long, M. Scavino, R. Tempone and S. Wang.
**Fast Estimation of Expected Information Gains for Bayesian Experimental Designs Based on Laplace Approximations**. Computer Methods in Applied Mechanics and Engineering. 259:24-39, 2013.

- D. Kim, F. Bisetti, Q. Long, R. Tempone and O. Knio.
**Spectral uncertainty quantification and optimal Bayesian experimental design of combustion reaction systems using sparse adaptive polynomial chaos expansion**. Uncertainty Quantification in Computational Fluid Dynamics, May 26-27, 2014, Pisa, Italy. - Q. Long, M. Scavino, R. Tempone and S. Wang.
**Fast Bayesian optimal experimental design**. European Numerical Mathematics and Advanced Applications, Aug. 26-30, 2013, EPFL, Lausanne, Switzerland. - Q. Long, M. Scavino, R. Tempone and S. Wang.
**A projection method for under determined optimal experimental designs.**12nd US National Congress of Computational Mechanics, Jul. 22-25, 2013, Raleigh, NC, USA. - Q. Long, M. Scavino, R. Tempone and S. Wang.
**A projection method for under determined optimal experimental designs.**11th International Conference On Structural Safety & Reliability, Jun. 16-20, 2013, Columbia University, New York, USA. - J. Han, Q. Long, F. Bisetti and R. Tempone.
**Bayesian experimental design for ionization mechanism in a shock tube.**SAS-CI 2013-3rd Annual Meeting, Fuel and Combustion Research for Energy and Environment, Apr. 29, 2013, Dhahran, KSA. - Q. Long, M. Scavino, R. Tempone and S. Wang.
**A projection method for under determined optimal experimental designs.**11th International Conference On Structural Safety & Reliability, Jun. 16-20, 2013, Columbia University, New York, USA. - Q. Long, M. Scavino, R. Tempone and S. Wang.
**Fast evaluation of expected information gain for Bayesian experimental design based on Laplace approximation.**6th European Congress on Computational Methods in Applied Sciences and Engineering, Sep. 10-14, 2012, Vienna, Austria. - Q. Long, S. Prudhomme, M. Scavino, R. Tempone and S. Wang.
**Optimal design of model validation procedure with respect to quantity of interest.**Stochasitc Modeling Techniques and Data Analysis International Conference, Jun. 5-8, 2012, Chania, Crete, Greece.