Seminar: Inverse Problems Using Dimensionality Reduction and Deep Learning
19/05/2019
 
Time: 9:00, 13-06-2019
 
Speaker: Dr. Bùi Thanh Tân, University of Texas at Austin 
title: Mitigating the Cost of data-driven PDE-constrained Inverse Problems Using Dimensionality Reduction and Deep Learning 
 
Abstract: 

Given a hierarchy of reduced-order models to solve the inverse problems for quantities of interest, each model with varying levels of fidelity and computational cost, a deep learning framework is proposed to improve the models by learning the errors between each successive levels. 

By statistically modeling errors of reduced order models and using training data involving forward solves of the reduced order models and the higher fidelity model, we train deep neural networks to learn the error between successive levels of the hierarchy of reduced order models thereby improving their error bounds. The training of the deep neural networks occurs during the offline phase and the error bounds can be improved online as new training data is observed. 

To mitigate the big-data aspect in inverse problems, we have developed a randomized misfit approach that blends random projection theory in high dimensions and inverse problem theory to effectively reduce high-dimensional data while preserving the accuracy of inverse solution.

 
 
 
Khoa Toán - Tin học, Trường Đại học Khoa học Tự nhiên, Đại học Quốc gia TP Hồ Chí Minh.
Phòng F.009, cơ sở 227 Nguyễn Văn Cừ, Quận 5, TP HCM.