Location
Innovation Lab Atrium
Start Date
4-3-2025 2:00 PM
End Date
4-3-2025 3:30 PM
Presentation Date
3 April 2025, 2:00pm - 3:30pm
Meeting Name
2025 - Miners Solving for Tomorrow Research Conference
Department(s)
Mathematics and Statistics
Document Type
Poster
Document Version
Final Version
File Type
event
Language(s)
English
Rights
© 2025 The Authors, All rights reserved
Included in
Apr 3rd, 2:00 PM
Apr 3rd, 3:30 PM
Robust Multifidelity Operator Learning for Partial Differential Equations
Innovation Lab Atrium
Comments
Advisor: Yanzhi Zhang
Abstract:
We propose a novel operator learning architecture based on learned neural representations of bases for input and output function distributions. Our method differs from existing order reduction methods like DeepONet and POD-NN/PCA-Net in its applicability to arbitrary input and output discretizations with a single model that is trained end-to-end. We demonstrate both theoretically and empirically that our method is discretization independent, and therefore well-suited for handling multifidelity and multiresolution problems. Additionally, we use our method to show that multifidelity training can improve efficiency and accuracy with numerical examples using synthetic data to learn solution operators for the 2D fractional Poisson equation, the 1D Burgers equation, and the 2D Navier-Stokes equation.