560. Exploring Energy Landscapes: Stochastic Methods for Index‑1 Saddle Points on Riemannian Submanifolds
Invited abstract in session TB-11: Advances in Manifold Optimization, stream Riemannian Manifold and Conic Optimization.
Tuesday, 10:30-12:30Room: B100/5017
Authors (first author is the speaker)
| 1. | Panos Parpas
|
| Computing, Imperial College London |
Abstract
We introduce a new stochastic algorithm to locate index 1 saddle points of a function defined on Riemannian submanifolds, which is particularly useful in high-dimensional settings. Our approach relies on two key ingredients: (i) the concentration properties of the first eigenmodes of the Witten Laplacian on 1 forms, specifically in the vicinity of index 1 saddle points, and (ii) a probabilistic representation of a partial differential equation involving this differential operator. Numerical examples on simple molecular systems underscore the potential of our algorithm for exploring complex potential energy landscapes in quantum chemistry applications.
Keywords
- Computational mathematical optimization
Status: accepted
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