Vu-Anh Le

Projects

(1) A Neural Network Model to Solve PDEs

Status: In Progress

Timeline: Jan 2025 – Present

A novel neural‑operator framework designed to solve PDEs with drastic savings in time and compute. (Additional details remain under NDA.)

Diffusion Coefficients plot Diffusion RHS plot Diffusion Solution plot

(2) Mathematical Analysis of Neural Operators

Status: Published (Proc. Int’l Math. Sci., 2024)

Timeline: August 2024 – Nov 2024

Established rigorous proofs of stability, exponential convergence, and sample‑complexity bounds for neural operators that learn PDE solution maps.

Exponential Convergence surface Generalization Bound surface

(3) Optimal Design of Neural Operators

Status: Pre‑print Draft

Timeline: August 2024 – Nov 2024

Converts the above theory into practical design rules: multi‑scale Fourier + wavelet layers, spectral normalization, and parallel hardware profiling along six performance axes.

Lipschitz Constant surface Iteration Bound surface Gen‑Bound Weight‑Decay surface Multi‑Scale Error surface Capacity Growth surface Amdahl Speed‑Up surface