Author

T. Lelièvre

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Preprint Aug 2026

A spectral approach to the narrow escape problem in two-dimensional domains

We study the law of the exit time and exit point of a Brownian motion in a two-dimensional domain with reflecting boundary conditions, except on small disjoint exit windows through which the stochastic process can escape the domain. In the limit of infinitely small exit windows, it is natural to assume that the process...

L. Carillo, T. Lelièvre, Thomas Normand et al. · 2 citations

Review Jul 2026

Approximating committor functions: Objective functions and training data sampling

A new loss function based on the application of It\={o}'s formula is proposed to learn the committor function with a minimization procedure on the parameters of a neural network to better approximate the committor function using a better sampling of the reactive trajectories.

Thomas Pigeon, Gabriel Stoltz, T. Lelièvre · 1 citation