Welcome

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Welcome to my website!

Currently, I am a Postdoctoral Appointee at the Mathematics and Computer Science Division , Argonne National Laboratory under the supervision of Emil Constantinescu.

You can contact me at ebilionis[at]mcs.anl.gov.

Research Interests

I investigate the fundamental problems of uncertainty quantification, Bayesian inversion and coarse-graining involving multi-scale, multi-physics systems. My focus is on developing rigorous mathematical techniques which can make non-intrusive use of existing simulators and quantify the epistemic uncertainty introduced by the - necessarily - very limited number of observations, investigating how this uncertainty propagates across scales and identifying its effect on the final objectives. My applications are interdisciplinary in nature ranging from flow through heterogeneous random porous media, climate modeling to coarse-graining molecular systems such as proteins and finding effective energetic descriptions of alloy systems based on electronic structure calculations.

For work I have done in the past or I am doing right now, you can check my Projects page.

More details about what I want to do in the future can be found in my Research Statement.

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What I do at the lab?

I am working on calibrating part of the Community Earth System Model. In particular I incorporate measurements made by field scientists to pose and solve a large scale inverse problem involving the Community Land Model. Our goal is to study how climate change affects the yield of the crops grown in the United States. For more details check out the project page: Climate Science for a Sustainable Energy Future.

Education

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  • Diplomma in Applied Mathematics, National Technical University of Athens, Athens, Greece, 2008

    • Concentrations: Mathematical Analysis and Statistics
    • GPA: 9.3/10.0
    • Advisor: Vassilis Papanicolaou.
    • Thesis: Pricing European Call Options under Proportional Transaction Costs.

Fellowships and Honors

  • Olin Fellowship Cornell University, (August 2008 - May 2009)
  • NTUA award for best student performance in Mathematics during 2003-2005
  • State Scholarship Foundation (IKY) award for best student performance 2003-2004
  • State Scholarship Foundation (IKY) award for best student performance 2004-2005
  • National Bank of Greece award for high school students, (2002)

Selected Publications

  • I. Bilionis and N. Zabaras. Solution of inverse problems with limited forward solver evaluations: A fully Bayesian perspective, Inverse Problems, 2013 (under review).
  • J. T. Kristensen*, I. Bilionis, and N. Zabaras. Relative Entropy as model selection tool in cluster expansions. Physical Review B., 87, 174112, 2013. A copy can be found here.
  • I. Bilionis and N. Zabaras, A stochastic optimization approach to coarse-graining using a relative-entropy framework. Journal of Chemical Physics, 138, 044313, 2013. A copy can be found here.
  • I. Bilionis, N. Zabaras, B. A. Konomi, and G. Lin. Multi-output separable Gaussian process: Towards an efficient, fully Bayesian paradigm for uncertainty quantification. Journal of Computational Physics, 241:212-239, 2013. A copy can be found here <http://www.sciencedirect.com/science/article/pii/S0021999113000417>.

The ‘*’ stands for PhD students I have mentored.

For the complete list see my Refereed Journal Publications or my Google Scholar profile.

Invited Talks

  • Purdue University, Mechanical Engineering, July 2013.
  • Argonne National Laboratory, Mathematics and Computer Science Division April 2013.
  • University of Pittsburgh, Industrial Engineering, April 2013.
  • USA/Brazil Symposium on Stochastic Modeling and Uncertainty Quantification, Rio de Janeiro, Brazil, August 2011.

Selected Opensource Software

This is an (incomplete) list of open source software that I have developed. It is basically a blend of Fortran, C and C++ code interfaced via Python. My motive is to reuse as much of as possible of existing codes to create easy-to-use Python tools for carrying out uncertainty quantification tasks and the solving inverse problems. Here you go:

  • PyBest (Python Bayesian Exploration Statistical Toolbox): This is an uncertainty quantification package that I am constantly developing. It has code from all my UQ papers. It features interfaces to various legacy codes for constructing good designs and quasi-random sequences, easy construction of polynomials orthogonal with respect to arbitrary probability densities, Multidimensional Relevance Vector Machines, Multidimensional Gaussian Process Regression, etc. The documentation is by no means complete (I have other things to do also ;-)), but the package is always under active development. Get the most recent version of the code from the PyBest Github page or simply do a:

    $ git clone https://github.com/ebilionis/py-best.git

    The documentation can be found here.

  • PySmc (Python Sequential Monte Carlo): This is a very convenient Python-only package that implements an adaptive, parallel version of Sequential Monte Carlo (SMC). SMC is the tool of choice when you need to sample from multi-modal probability densities. It is the tool of choice when it comes to sovlving inverse problems using a Bayesian formalism. It can also be used to train abritrary probabilistic models in parallel (e.g., Gaussian processes). Get the most recent version of the code from the PySmc Github page or simply do a:

    $ git clone https://github.com/ebilionis/pysmc.git

    The documentation can be found here.

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