Learning Dynamics on Manifolds with Neural Ordinary Differential Equations
Keywords: Manifolds, Neural ODE, Dynamics Learning, Classification
Abstract: Neural ordinary differential equations (Neural ODEs) have garnered significant attention for their ability to efficiently learn dynamics from data. However, for high-dimensional systems, capturing dynamics remains to be a challenging task. Existing methods often rely on learning ODEs on low-dimensional manifolds but usually require the knowledge of the manifold. Nevertheless, such knowledge is usually unknown in many scenarios. Therefore, we propose a novel approach to jointly learn data dynamics and the underlying manifold. Specifically, we employ an encoder to project the original data into the manifold and leverage the Jacobian matrix of its corresponding decoder for recovery. Our experimental evaluations encompass multiple datasets, where we compare the accuracy, number of function evaluations (NFE), and convergence speed of our model against existing baselines. Our results demonstrate superior performance, underscoring the effectiveness of our approach in addressing the challenges of high-dimensional dynamic learning.
Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2024/AuthorGuide.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors' identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Submission Number: 8123
Loading