EAS Doctoral Proposal Defense by Haolan Zheng
EAS Doctoral Proposal Defense
by Haolan Zheng
Date: Wednesday, May 28, 2025
Time: 9:30am
Topic: Reduced Basis-Driven Physics-Informed Operator Learning
Location: TXT 105A
Abstract:
Over the past decade, deep learning has achieved enormous success across numerous domains in science and engineering. One of the most significant applications is operator learning -- using deep neural networks to approximate the solution operators of Partial Differential Equations (PDEs). Neural operators (NOs) have emerged as a leading framework in this area, demonstrating strong performance on various benchmark problems. However, existing models often require a large amount of training data and tend to exhibit limited generalizability and mesh invariance.
To mitigate these issues, we propose a novel operator learning framework with its first component being the Reduced Basis Neural Operator (ReBaNO). Inspired by the Reduced Basis Method and the recently introduced Generative Pre-Trained Physics-Informed Neural Networks, ReBaNo employs on a mathematically rigorous greedy algorithm to adaptively construct its network structure offline, from ground up. Knowledge distillation via task-specific activation function allows ReBaNO to achieve a compact physics-informed architecture requiring minimal computational cost during inference. In comparison to state-of-the-art operator learning algorithms such as PCA-Net, DeepONet, FNO, and CNO, numerical results demonstrate that ReBaNO is at least equally accurate while significantly reducing the generalization gap for both in-distribution and out-of-distribution tests. Moreover, ReBaNO demonstrates superior performance in mesh invariance tests.
Advisor: Dr. Yanlai Chen, Department of Mathematics
Committee members:
Dr. Scott Field, Department of Mathematics
Dr. Alfa Heryudono, Department of Mathematics
Dr. Sarah Caudill, Department of Physics
NOTE: All EAS Students are ENCOURAGED to attend.
TXT 105A