Department of Math & Stat Webinar: Monday, April 19, 2021 @ 01:00 PM (13:00 hrs KSA Time)

Abstract

Data acquisition for real-world problems, such that seismic events and CO2 sequestration in geological formations, is a time-consuming and expensive process. Yet, the quality of the data is not guaranteed, in advance, for performing features learning in the presence of uncertainties. Bayesian optimal experimental design is a simulations-based approach of generating the most informative data, and appears to be a good rampart against budgetary constraints for the acquisition of data to analyze reliably the uncertainties in real-world problems. In this talk, we present the data goodness criterion and some computational methods for its approximation. We show that using the Laplace approximation to build the biasing distribution in the importance sampling reduce drastically the total computational work. And for experiments modeled by Partial Differential Equations (PDEs), multilevel methods have been proven to reduce the computational complexity. The optimization process consists then in combining those methods with gradient-based approaches for the search of the best design setup. We present numerical results for a CO2 sequestration problem with leakage risk assessment, and an electrical impedance tomography problem for laminated materials. 

Keywords:

Laplace approximation, Kullback-Leibler divergence, Importance sampling, Parameter learning, Monte Carlo methods, CO2 sequestration, stochastic optimization.