Date of Award
Summer 7-12-2021
Access Type
Dissertation - Open Access
Degree Name
Doctor of Philosophy in Mechanical Engineering
Department
Mechanical Engineering
Committee Chair
Eduardo Divo
First Committee Member
Sandra K.S. Boetcher
Second Committee Member
Victor Huayamave
Third Committee Member
Fardin Khalili
Fourth Committee Member
Alain Kassab
Abstract
Convergence of a numerical solution scheme occurs when a sequence of increasingly refined iterative solutions approaches a value consistent with the modeled phenomenon. Approximations using iterative schemes need to satisfy convergence criteria, such as reaching a specific error tolerance or number of iterations. The schemes often bypass the criteria or prematurely converge because of oscillations that may be inherent to the solution. Using a Support Vector Machines (SVM) machine learning approach, an algorithm is designed to use the source data to train a model to predict convergence in the solution process and stop unnecessary iterations. The discretization of the Navier Stokes (NS) equations for a transient local hemodynamics case requires determining a pressure correction term from a Poisson-like equation at every time-step. The pressure correction solution must fully converge to avoid introducing a mass imbalance. Considering time, frequency, and time-frequency domain features of its residual’s behavior, the algorithm trains an SVM model to predict the convergence of the Poisson equation iterative solver so that the time-marching process can move forward efficiently and effectively. The fluid flow model integrates peripheral circulation using a lumped-parameter model (LPM) to capture the field pressures and flows across various circulatory compartments. Machine learning opens the doors to an intelligent approach for iterative solutions by replacing prescribed criteria with an algorithm that uses the data set itself to predict convergence.
Scholarly Commons Citation
Bueno-Benitez, Leonardo A., "Use of Machine Learning for Automated Convergence of Numerical Iterative Schemes" (2021). Doctoral Dissertations and Master's Theses. 606.
https://commons.erau.edu/edt/606