TY - JOUR A1 - Lelievre, Tony A1 - Stoltz, Gabriel A1 - Zhang, Wei T1 - Multiple projection MCMC algorithms on submanifolds JF - IMA Journal of Numerical Analysis N2 - We propose new Markov Chain Monte Carlo algorithms to sample probability distributions on submanifolds, which generalize previous methods by allowing the use of set-valued maps in the proposal step of the MCMC algorithms. The motivation for this generalization is that the numerical solvers used to project proposed moves to the submanifold of interest may find several solutions. We show that the new algorithms indeed sample the target probability measure correctly, thanks to some carefully enforced reversibility property. We demonstrate the interest of the new MCMC algorithms on illustrative numerical examples. Y1 - 2022 U6 - https://doi.org/10.1093/imanum/drac006 ER - TY - JOUR A1 - Akhyar, Fatima-Zahrae A1 - Zhang, Wei A1 - Stoltz, Gabriel A1 - Schütte, Christof T1 - Generative modeling of conditional probability distributions on the level-sets of collective variables N2 - Given a probability distribution $\mu$ in $\mathbb{R}^d$ represented by data, we study in this paper the generative modeling of its conditional probability distributions on the level-sets of a collective variable $\xi: \mathbb{R}^d \rightarrow \mathbb{R}^k$, where $1 \le k