EAS Doctoral Proposal Defense by David Gillcrest
When: Thursday,
December 14, 2023
3:00 PM
-
5:00 PM
Where: > See description for location
Description: EAS Doctoral Proposal Defense by David Gillcrest
Date: Thursday, December 14, 2023
Time: 3:00 p.m.
Topic: Inverse Analysis and Calibration of Physical Models: An Approached Based on Greedy Kaczmarz Multi-Fidelity Surrogates and Aggregated Directional Statistics
Location: CSCDR - TXT 105
Abstract:
Advances in surrogate modeling have allowed for highly accurate Polynomial Chaos (PC) expansions to be constructed for physical models ranging from mild to major complexity in their respective parameter spaces. Multi-fidelity techniques in the field of uncertainty analysis have been employed to efficiently capture the variations in the outputs of models given reasonable perturbations in these parameters. Recently, a greedy Kaczmarz algorithm (GKA) has been used to cheaply construct surrogate models in a way that greatly outperforms the previous least square approaches that demand samples about 2-3 times the number of coefficients in the PC expansion.
In this research we look at the utility of GKA-produced surrogate models in solving parameter estimation problems - inverse problems typically solved using statistical least squares methods - for partial differential equations (PDEs). We present a generalized approach to solving two-dimensional parameter estimations for PDEs and demonstrate its potential using two Advection-Diffusion-Reaction equations: one for the source localization of a river contaminant, and the other for the estimations of both the area source contamination magnitude as well as ambient pollution concentration in the context of an urban heat island under the influence of mesoscale wind.
The physical domain of each problem is discretized in such a way as to accommodate the hypothetical usage of detection apparatuses. An array of surrogate models is constructed to capture the variation in outputs at these detectors with respect to the PDEs' parameter spaces. Using directional statistical techniques we examine the optimal combination of the surrogate models, specifically by looking at the local interactions of each model's slope field. The quality of the combination of surrogates can then be quantified and aggregated in order to achieve a cost value for a grouping of surrogates.
ADVISOR(S):
Dr. Mazdak Tootkaboni, Dept of Civil and Environmental Engineering
(mtootkaboni@umassd.edu)
Dr. Yanlai Chen, Dept. of Mathematics
(ychen@umassd.edu)
COMMITTEE MEMBERS:
Dr. Sigal Gottlieb, Department of Mathematics
Dr. Zheng Chen, Department of Mathematics
NOTE: All EAS Students are ENCOURAGED to attend.
Date: Thursday, December 14, 2023
Time: 3:00 p.m.
Topic: Inverse Analysis and Calibration of Physical Models: An Approached Based on Greedy Kaczmarz Multi-Fidelity Surrogates and Aggregated Directional Statistics
Location: CSCDR - TXT 105
Abstract:
Advances in surrogate modeling have allowed for highly accurate Polynomial Chaos (PC) expansions to be constructed for physical models ranging from mild to major complexity in their respective parameter spaces. Multi-fidelity techniques in the field of uncertainty analysis have been employed to efficiently capture the variations in the outputs of models given reasonable perturbations in these parameters. Recently, a greedy Kaczmarz algorithm (GKA) has been used to cheaply construct surrogate models in a way that greatly outperforms the previous least square approaches that demand samples about 2-3 times the number of coefficients in the PC expansion.
In this research we look at the utility of GKA-produced surrogate models in solving parameter estimation problems - inverse problems typically solved using statistical least squares methods - for partial differential equations (PDEs). We present a generalized approach to solving two-dimensional parameter estimations for PDEs and demonstrate its potential using two Advection-Diffusion-Reaction equations: one for the source localization of a river contaminant, and the other for the estimations of both the area source contamination magnitude as well as ambient pollution concentration in the context of an urban heat island under the influence of mesoscale wind.
The physical domain of each problem is discretized in such a way as to accommodate the hypothetical usage of detection apparatuses. An array of surrogate models is constructed to capture the variation in outputs at these detectors with respect to the PDEs' parameter spaces. Using directional statistical techniques we examine the optimal combination of the surrogate models, specifically by looking at the local interactions of each model's slope field. The quality of the combination of surrogates can then be quantified and aggregated in order to achieve a cost value for a grouping of surrogates.
ADVISOR(S):
Dr. Mazdak Tootkaboni, Dept of Civil and Environmental Engineering
(mtootkaboni@umassd.edu)
Dr. Yanlai Chen, Dept. of Mathematics
(ychen@umassd.edu)
COMMITTEE MEMBERS:
Dr. Sigal Gottlieb, Department of Mathematics
Dr. Zheng Chen, Department of Mathematics
NOTE: All EAS Students are ENCOURAGED to attend.
Contact: Engineering and Applied Sciences
Topical Areas: Faculty, Students, Students, Graduate, Students, Undergraduate, Mathematics, Bioengineering, Civil and Environmental Engineering, College of Engineering, Computer and Information Science, Co-op Program, Electrical and Computer Engineering, Mechanical Engineering, Physics