Filling Gaps in Scientific Data Sets Using Physics Informed Neural Networks: A Case Study in Velocity Fields

Author

Ellen Saunders, California Polytechnic State University, San Luis ObispoFollow

Available at: https://digitalcommons.calpoly.edu/theses/3015

Date of Award

6-2025

Degree Name

MS in Mathematics

Department/Program

Mathematics

College

College of Science and Mathematics

Advisor

Paul Choboter

Advisor Department

Mathematics

Advisor College

College of Science and Mathematics

Abstract

Gaps in scientific data sets are a persistent issue for researchers in a variety of fields, and while nothing makes up for missing out on real data, well-simulated synthetic data can be a useful tool. In the world of image processing, machine learning techniques have become quite sophisticated at taking an image with a missing component and filling in that space with something believable. The aim of this thesis is to take machine learning techniques similar to what gets used in image processing and repurpose them to infill gaps in scientific data sets in a realistic manner. This thesis compares and contrasts some machine learning techniques, such as basic neural networks, convolutional neural networks, and autoencoders, before focusing on neural networks. Two approaches were considered for this problem: an approach inspired by the idea of taking the weighted average of a point's neighbors to impute that point and an approach grounded in spatial coordinates. Then, a physics informed component is added to both of these networks to enforce certain physical realism standards. The physics informed component makes the neural networks marginally more accurate but noticeably more realistic and physically possible. Each of the networks, both before and after the physics informed component is added, is tested on a variety of velocity fields. Finally, a statistical analysis is done on the networks as compared to less sophisticated infill methods to demonstrate that they do perform well.