Optimal transport based strategies in waves and dynamics
Abstract
The project, led by Cornell University and in collaboration with the New Jersey Institute of Technology, focuses on advancing the field of optimal transport. The main goal is to harness the power of optimal transport theory to capture the intrinsic characteristics of complex physical processes arising in a wide range of important scientific applications. We will tackle a fundamental problem in the theory: its inability to handle signed signals arising in models of wave propagation and dynamic processes. The theoretical components of the proposed work aim to (1) prove the ideal properties of the new metric designed explicitly for signed signals and itsrelation to the optimal transport theory; (2) investigate gradient methods driven by optimal transport-based metrics in global optimization; (3) harness the power of the optimal push-forward maps from the transport-based geometry to model nonlinear dynamics and develop a robust approximation theory that ensures provable convergence in learning approaches. The computational components of the project will involve a numerical investigation of the performance of the new optimization techniques and an in-depth exploration of these methods in several application areas, including image processing, multiscale modeling, and inversion, modeling dynamic processes, and deep learning. Approved for public release.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jan 24, 2024
- Source ID
- N000142412088
Entities
People
- Yunan Yang
Organizations
- Cornell University
- Office of Naval Research
- United States Navy