4 papers
Topology-Preserving Scaling in Data Augmentation
Vu-Anh Le, Mehmet Dik
We propose an algorithmic framework for dataset normalization in data augmentation pipelines that preserves topological stability under non-uniform scaling transformations. Given a…
The Stability of Persistence Diagrams Under Non-Uniform Scaling
Vu-Anh Le, Mehmet Dik
We investigate the stability of persistence diagrams \( D \) under non-uniform scaling transformations \( S \) in \( \mathbb{R}^n \). Given a finite metric space \( X \subset \math…
How Analysis Can Teach Us the Optimal Way to Design Neural Operators
Vu-Anh Le, Mehmet Dik
This paper presents a mathematics-informed approach to neural operator design, building upon the theoretical framework established in our prior work. By integrating rigorous mathem…
A Mathematical Analysis of Neural Operator Behaviors
Vu-Anh Le, Mehmet Dik
Neural operators have emerged as transformative tools for learning mappings between infinite-dimensional function spaces, offering useful applications in solving complex partial di…