Variational PDEs for Acceleration on Manifolds and Application to Diffeomorphisms
Authors: Ganesh Sundaramoorthi, Anthony Yezzi
NeurIPS 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We now show empirical evidence to illustrate the behavior of our accelerated optimization by comparing it to gradient descent. |
| Researcher Affiliation | Collaboration | Ganesh Sundaramoorthi United Technologies Research Center East Hartford, CT 06118 sundarga1@utrc.utc.com Anthony Yezzi School of Electrical & Computer Engineering Georgia Institute of Technology, Atlanta, GA 30332 ayezzi@ece.gatech.edu |
| Pseudocode | No | The paper describes the numerical discretization in text but does not include structured pseudocode or an algorithm block in the main body. |
| Open Source Code | No | The paper does not provide any explicit statements about the release of source code or links to a code repository for the described methodology. |
| Open Datasets | No | The paper mentions using "binary images" and "MR cardiac images" but does not provide specific access information (link, DOI, repository, or formal citation) for these datasets to be publicly available. |
| Dataset Splits | No | The paper describes image registration experiments which involve optimizing a cost functional, but it does not specify explicit training, validation, or test dataset splits in the conventional sense of supervised machine learning. |
| Hardware Specification | No | The paper does not provide specific details about the hardware used for running its experiments, such as GPU/CPU models or memory specifications. |
| Software Dependencies | No | The paper does not provide specific software dependency details with version numbers, such as programming languages, libraries, or solvers used for the implementation. |
| Experiment Setup | Yes | The initialization is φ(x) = ψ(x) = x, v(x) = 0, and ρ(x) = 1/|Ω| where |Ω| is the area the image. ... where α > 0 is a weight ... For gradient descent we choose t < 1/(4α); for accelerated gradient descent we have the additional evolution of the velocity (12), and our numerical scheme has CFL condition t < 1/(4α maxx Ω{|v(x)|, |Dv(x)|}). ... Here α = 5. |