Doctoral Defense - Doga Dikbayir

About the Event

The Department of Computer Science & Engineering

Michigan State University

Ph.D. Dissertation Defense

July 8th, 2025 at 10:00am EST

https://msu.zoom.us/j/2875715151

Passcode: Upon Request from Vincent Mattison or Advisor

ABSTRACT

Fast Data-Driven Frameworks for Solving Three Dimensional Scattering Problems

By: Doga Dikbayir

Advisor: Dr. Metin Aktulga

Scattering problems sit at the center of many practical applications involving some form of wave-based physics. These problems can broadly be categorized as forward and inverse scattering problems. Given their wide applicability, numerous numerical methods have been proposed over the last few decades for both classes of problems. A common limitation in these methods is the computational cost which renders them unpractical for time-sensitive applications. To overcome this bottleneck, several machine learning frameworks have been proposed recently. However, most of these work are focused on the two dimensional (2D) scattering problems. Efficient data-driven methods for the three dimensional (3D) version of the problem are yet to be explored.

In this thesis, we develop data-driven deep learning models to solve 3D scattering problems in acoustics and electromagnetics. First, we seek to explore the advantages and disadvantages of using a common spherical harmonic representation for shapes and scattered data to learn solutions to the forward scattering problem. To this end, we first compute the acoustic scattering data at different frequencies for a large collection of 3D particles. Then, both the shape and scattering data of these particles are embedded into a series of spherical harmonic coefficients. A residual neural network is finally trained to learn the mapping between these two representations. We discuss the results and compare the proposed framework to methods based on spatial point-cloud representations.

Next, we present a data-driven framework to perform fast 3D shape reconstruction from acoustic scattering data. The framework is implemented by (a) using a compact probabilistic shape latent space learned by a 3D variational auto-encoder, and (b) a convolutional neural network trained to extract far-field features due to multiple incident waves, and map the acoustic scattering information to this shape representation. We demonstrate the proposed framework's 3D shape reconstruction capabilities on random rock-like particles and airplane objects from the popular ShapeNet data set. We further evaluate the framework's performance, specifically testing its robustness when trained with lower-resolution scattering data, and when both the scattered data and receiver locations are affected by noise.

Lastly, we present the extension of the proposed framework to electromagnetic inverse scattering problems. We extensively evaluate the proposed method against the state-of-the-art machine learning model. Our experiments demonstrate that the proposed method successfully reconstructs 3D shapes of complex scatterer geometries from ShapeNet. It is also robust to noise and achieves similar or better reconstruction quality than the state-of-the-art 3D inverse scattering method, while being orders of magnitude faster at inference.