Use of Machine Learning for Automated Convergence of Numerical Iterative Schemes

<p>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.</p>

Name thesis:degree_name

Doctor of Philosophy in Mechanical Engineering

Level thesis:degree_level

Dissertation - Open Access

Discipline thesis:degree_discipline

Mechanical Engineering

Year

2021

Author dc:creator

• Bueno-Benitez, Leonardo A.

• machine learning
• automated convergence
• numerical iterative schemes
• Mechanical Engineering

Repository record dc:identifier

https://commons.erau.edu/edt/606

OAI identifier oai:identifier

oai:commons.erau.edu:edt-1617