Quantifying Uncertainties in Physical Models

By Ilias Bilionis

Mechanical Engineering, Purdue University, West Lafayette, IN

Published on

Abstract

Increasing modeling detail is not necessarily correlated with increasing predictive ability. Setting modeling and numerical discretization errors aside, the more detailed a model gets, the larger the number of parameters required to accurately specify its initial/boundary conditions, constitutive laws, external forcing, object geometries, etc. To be predictive, we need to quantify this uncertainty by combining our prior physical knowledge with noisy experimental data obtained from various heterogeneous sources. Once we have quantified this uncertainty, all we need to do is propagate it through the model and obtain predictive error bars for any quantity of interest. What kinds of uncertainty do we encounter in physical models? How is uncertainty described mathematically? What can go wrong if uncertainty is ignored?

Bio

Ilias Bilionis Dr. Ilias Bilionis is an Assistant Professor at the School of Mechanical Engineering, Purdue University. His research is motivated by energy and material science applications and it focuses on the development of generic methodologies for design and optimization under uncertainty, reliability analysis, model calibration and learning models out of data. Prior to his appointment at Purdue he was a Postdoctoral Researcher at the Mathematics and Computer Science Division (MCS), Argonne National Laboratory. He received his PhD in Applied Mathematics from Cornell University in 2013 and his Diploma in Applied Mathematics from the National Technical University of Athens in 2008.

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Researchers should cite this work as follows:

  • Ilias Bilionis (2017), "Quantifying Uncertainties in Physical Models," http://nanohub.org/resources/27200.

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129 Burton Morgan, Purdue University, West Lafayette, IN

Tags

Quantifying Uncertainties in Physical Models
  • Quantifying Uncertainties 1. Quantifying Uncertainties 0
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  • What is Uncertainty Quantification and why is it needed? 2. What is Uncertainty Quantific… 182.41574908241574
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  • Example: Structure Reliability 3. Example: Structure Reliability 232.23223223223224
    00:00/00:00
  • Example: Oil reservoir operation 4. Example: Oil reservoir operati… 358.92559225892563
    00:00/00:00
  • Example: Prediction of extreme weather 5. Example: Prediction of extreme… 540.57390724057393
    00:00/00:00
  • What kinds of uncertainties are there and how are they modeled? Aleatory: naturally occurring randomness that we cannot (or do not know how to) reduce. Epistemic: uncertainty due to lack of knowledge that we can reduce by paying a price. 6. What kinds of uncertainties ar… 811.34467801134474
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  • Unknown Microstructure of a Manufactured Artifact 7. Unknown Microstructure of a Ma… 908.30830830830837
    00:00/00:00
  • Unknown Ground Permeability/Porosity 8. Unknown Ground Permeability/Po… 1043.1765098431765
    00:00/00:00
  • Unknown Physical Law 9. Unknown Physical Law 1072.3056389723056
    00:00/00:00
  • Cosmic Microwave Background 10. Cosmic Microwave Background 1190.3903903903904
    00:00/00:00
  • Double Slit Experiment 11. Double Slit Experiment 1241.7417417417419
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  • What about turbulence? 12. What about turbulence? 1295.6956956956958
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  • We model uncertainties using probability 13. We model uncertainties using p… 1396.3296629963297
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  • We need to be able to say things like: 14. We need to be able to say thin… 1505.171838505172
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  • UQ Problems and their Challenges 15. UQ Problems and their Challeng… 1573.9406072739407
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  • Some UQ problems 16. Some UQ problems 1635.4020687354021
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  • The Uncertainty Propagation Problem 17. The Uncertainty Propagation Pr… 1639.4060727394062
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  • Example: Bevel Gear Failure time 18. Example: Bevel Gear Failure ti… 1727.2939606272939
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  • Monte Carlo 19. Monte Carlo 1730.2302302302303
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  • The Uncertainty Propagation Problem 20. The Uncertainty Propagation Pr… 1794.9616282949617
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  • Issues of Monte Carlo… 21. Issues of Monte Carlo… 1832.3656990323657
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  • But, let's ignore them and start playing with the handout… 22. But, let's ignore them and sta… 1894.1274607941275
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