Plenary Lectures

 


Prof. H. Thomas Banks

Center for Research in Scientific Computation, North Carolina State University, USA

Lecture Title: The prohorov metric framework and aggregate data inverse problems for random PDEs

Abstract: We consider nonparametric estimation of probability measures for parameters in problems where only aggregate (population level) data are available. We summarize an existing computational method for the estimation problem which has been developed over the past several decades [1-6]. Theoretical results are presented which establish the existence and consistency of very general (ordinary, generalized and other) least squares estimates and estimators for the measure estimation problem with specific application to random PDEs.

[1] HT Banks, WC Thompson. Existence and consistency of a nonparametric estimator of probability measures in the Prohorov Metric Framework. International Journal of Pure and Applied Mathematics, 2015, 103: 819-843.

[2] HT Banks, S Hu, WC Thompson. Modeling and Inverse Problems in the Presence of Uncertainty, CRC Press, Chapman & Hall, 2014.

[3] HT Banks, ZR Kenz, WC Thompson. A review of selected techniques in inverse problem nonparametric probability distribution estimation. Journal of Inverse and Ill-Posed Problems, 2012, 429-460.

[4] HT Banks, D Bortz, G Pinter, L Potter. Modeling and imaging techniques with potential for application in bioterrorism. Bioterrorism: Mathematical Modeling Applications in Homeland Security. SIAM, 2003, 129-154.

[5] HT Banks and KL Bihari. Modelling and estimating uncertainty in parameter estimation. Inverse Problems, 2001, 17 (1): 95-111.

[6] HT Banks and BG Fitzpatrick. Estimation of growth rate distributions in size structured population models. Quarterly of Applied Mathematics. 1991, 49: 215-235.

 

Prof. Gengdong Cheng

State Key Laboratory of Structural Analysis for Industrial Equipment,Dalian University of Technology, China

Lecture Title:

Abstract:

 

 

 

Prof. Kalyanmoy Deb

Electrical and Computer Engineering, Michigan State University, USA

Lecture Title: Customized Optimization for Practical Problem solving

Abstract: Practitioners are often reluctant to use a formal optimization method for routine design and other practical applications, mainly due to the general perception of requiring a large computational time and ending up with a specialized and often "brittle" solution. Optimization methods have come a long way and are made flexible to handle various practicalities including reduction of solution time, handle large dimensions, search for robust and reliable solutions, and discover useful knowledge understanding intricacies of the problem. In this talk, we shall emphasize the importance of customized optimization algorithms in handling various practicalities. A few case studies from industries involving an extreme scale (billion-dimensional) problem and computationally expensive (consuming two days per evaluation) will be presented to demonstrate the usefulness of computational intelligence methods.

 

Prof. Jari Kaipio

Department of Mathematics, The University of Auckland, New Zealand

Lecture Title: Modelling of boundary uncertainties in inverse problems

Abstract: A large class of inverse problems are induced by partial differential equations and the related initial-boundary value problems. In many cases, the exact shape of the domains is only approximately known[1]. Furthermore, domain truncation is also often carried out for computational reasons. On these truncation boundaries, the boundary conditions are unknown [2,3]. In this talk, we consider the modelling of such boundary uncertainties [4].

[1] A Nissinen, V Kolehmainen, JP Kaipio. Compensation ofmodelling errors due to unknown domain boundary in electricalimpedance tomography. IEEE Transactions on Medical Imaging, 2011, 30: 231-242.

[2] D Calvetti, PJ Hadwin, JMJ Huttunen, D Isaacson, JP Kaipio, D McGivney, E Somersalo, J Volzer. Artificial boundary conditionsand domain truncation in electrical impedance tomography, Part I: Theory and preliminary results. Inverse Problem Imaging, 2015, 9: 749-766.

[3] D Calvetti, PJ Hadwin, JMJ Huttunen, JP Kaipio, E Somersalo. Artificial boundary conditions and domain truncation inelectrical impedance tomography. Part II: Computational results. Inverse Problem Imaging, 2015, 9: 767-789, .

[4] JP Kaipio, V Kolehmainen. Approximate marginalization overmodeling errors and uncertainties in inverse problems. Bayesian Theory and Applications, Oxford University Press, 2013.

 

(Relevant information will be updated soon)

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