Publication Date
Summer 7-13-2019
Abstract
In this thesis we consider ordinary differential equations (ODEs) with random parameters. We focus on Monte Carlo (MC) sampling for computing the statistics of some quantities of interest (QoIs) given by the solution of the ODE problems. We use the 4th order accurate Runge-Kutta (RK4) method as the deterministic ODE solver. We then develop a hybrid MC sampling method that combines RK4 with neural network models to efficiently compute the statistics of QoIs within a desired accuracy. We present several numerical examples to verify the accuracy and efficiency of the proposed hybrid method compared to classical MC sampling. The hybrid method that we develop can be applied to more complicated physical problems given by partial differential equations (PDEs).
Degree Name
Mathematics
Level of Degree
Masters
Department Name
Mathematics & Statistics
First Committee Member (Chair)
Mohammad Motamed
Second Committee Member
Stephen Lau
Third Committee Member
Jacob Bayer Schroder
Language
English
Keywords
Neural Network, Uncertainty Quantification, Monte Carlo, RK4 Method, ODE
Document Type
Thesis
Recommended Citation
Akter, Mst Afroja. "A Deep Learning Approach to Uncertainty Quantification." (2019). https://digitalrepository.unm.edu/math_etds/133
