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Pré-Publication, Document De Travail Année : 2022

Using Witten Laplacians to locate index-1 saddle points

Résumé

We introduce a new stochastic algorithm to locate the index-1 saddle points of a function $V:\mathbb R^d \to \mathbb R$, with $d$ possibly large. This algorithm can be seen as an equivalent of the stochastic gradient descent which is a natural stochastic process to locate local minima. It relies on two ingredients: (i) the concentration properties on index-1 saddle points of the first eigenmodes of the Witten Laplacian (associated with $V$) on $1$-forms and (ii) a probabilistic representation of a partial differential equation involving this differential operator. Numerical examples on simple molecular systems illustrate the efficacy of the proposed approach.

Dates et versions

hal-03909090 , version 1 (21-12-2022)

Identifiants

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Tony Lelièvre, Panos Parpas. Using Witten Laplacians to locate index-1 saddle points. 2022. ⟨hal-03909090⟩
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