# Ergodic SDEs on submanifolds and related numerical sampling schemes

@article{Zhang2020ErgodicSO, title={Ergodic SDEs on submanifolds and related numerical sampling schemes}, author={Wei Zhang}, journal={ESAIM: Mathematical Modelling and Numerical Analysis}, year={2020} }

In many applications, it is often necessary to sample the mean value of certain quantity with respect to a probability measure μ on the level set of a smooth function ξ : ℝd → ℝk, 1 ≤ k < d. A specially interesting case is the so-called conditional probability measure, which is useful in the study of free energy calculation and model reduction of diffusion processes. By Birkhoff’s ergodic theorem, one approach to estimate the mean value is to compute the time average along an infinitely long…

## 12 Citations

Constrained overdamped Langevin dynamics for symmetric multimarginal optimal transportation

- Computer ScienceMathematical Models and Methods in Applied Sciences
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This work designs a numerical method, built upon constrained overdamped Langevin processes to solve Moment Constrained Optimal Transport (MCOT) relaxations, and proves that there is no strict local minimizer to the resulting problem.

Order conditions for sampling the invariant measure of ergodic stochastic differential equations on manifolds

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A new methodology for the construction of high order integrators for sampling the invariant measure of ergodic stochastic differential equations with dynamics constrained on a manifold is derived using an extension of the exotic aromatic Butcher-series formalism.

Multiple projection Markov Chain Monte Carlo algorithms on submanifolds

- Computer Science, Mathematics
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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…

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- 2021

This work shows that the special case of quadratic confinement and linear constraint is exactly solvable due to a remarkable factorization, and that the conditioning has then the simple effect of shifting the cloud of particles without deformation.

A uniformly accurate scheme for the numerical integration of penalized Langevin dynamics

- Computer Science, MathematicsArXiv
- 2021

This paper proposes a new consistent method with an accuracy independent of ε for solving penalized dynamics on a manifold of any dimension and converges to the constrained Euler scheme when ε goes to zero.

Jarzynski’s Equality, Fluctuation Theorems, and Variance Reduction: Mathematical Analysis and Numerical Algorithms

- MathematicsJournal of Statistical Physics
- 2019

In this paper, we study Jarzynski’s equality and fluctuation theorems for diffusion processes. While some of the results considered in the current work are known in the (mainly physics) literature,…

Stochastic Deep-Ritz for Parametric Uncertainty Quantification

- Computer Science
- 2022

This work proposes a deep learning based numerical method for solving elliptic partial diﬀerential equations (PDE) with random coeﬁccients by elucidate the stochastic variational formulation for the problem by recourse to the direct method of calculus of variations.

Solving eigenvalue PDEs of metastable diffusion processes using artificial neural networks

- Computer ScienceJ. Comput. Phys.
- 2022

Théorie des grandes déviations en physique statistique : quelques aspects théoriques et numériques

- Physics
- 2019

Cette these s’interesse a differents problemes de grandes deviations en rapport avec la physique statistique, qu’elle aborde sous l’angle theorique aussi bien que numerique. La premiere partie…

Multiple projection MCMC algorithms on submanifolds

- Computer Science, MathematicsArXiv
- 2020

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…

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