ArticleChaos (Woodbury, N.Y.)2023
Locating saddle points using gradient extremals on manifolds adaptively revealed as point clouds.
Article in Chaos (Woodbury, N.Y.), 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 1 paper.
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1 citing paper in PubMed.
- Theory and Examples of Catch Bonds.The journal of physical chemistry. B · 2024Article
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4 authors.
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Abstract
Steady states are invaluable in the study of dynamical systems. High-dimensional dynamical systems, due to separation of time scales, often evolve toward a lower dimensional manifold M. We introduce an approach to locate saddle points (and other fixed points) that utilizes gradient extremals on such a priori unknown (Riemannian) manifolds, defined by adaptively sampled point clouds, with local coordinates discovered on-the-fly through manifold learning. The technique, which efficiently biases the dynamical system along a curve (as opposed to exhaustively exploring the state space), requires knowledge of a single minimum and the ability to sample around an arbitrary point. We demonstrate the effectiveness of the technique on the Müller-Brown potential mapped onto an unknown surface (namely, a sphere). Previous work employed a similar algorithmic framework to find saddle points using Newton trajectories and gentlest ascent dynamics; we, therefore, also offer a brief comparison with these methods.
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