Personal Webpage of Adrien Laurent

Publications:

1. Adrien Laurent, Robert I. McLachlan, Hans Z. Munthe-Kaas, Olivier Verdier, The aromatic bicomplex for the description of divergence-free aromatic forms and volume-preserving integrators, arXiv:2301.10998, Submitted, 41 pages.
2. Adrien Laurent, A uniformly accurate scheme for the numerical integration of penalized Langevin dynamics, arXiv:2110.03222, SIAM J. Sci. Comput. 44 (2022), no. 5, A3217-A3243.
3. Adrien Laurent, Gilles Vilmart, Order conditions for sampling the invariant measure of ergodic stochastic differential equations on manifolds, arXiv:2006.09743, Found. Comput. Math. 22, 649–695 (2022).
4. Adrien Laurent, Gilles Vilmart, Multirevolution integrators for differential equations with fast stochastic oscillations, arXiv:1902.01716, SIAM J. Sci. Comput. 42 (2020), no. 1, A115–A139.
5. Adrien Laurent, Gilles Vilmart, Exotic aromatic B-series for the study of long time integrators for a class of ergodic SDEs, arXiv:1707.02877, Math. Comp. 89 (2020), 169-202.

Software:

• The Python package HomotoPy for manipulating the aromatic forms and the aromatic bicomplex. HomotoPy represents aromatic forests as dictionaries. It contains the functions from the paper (Euler operators, horizontal, vertical, variational derivatives, homotopy operators,...), as well as understandable examples to manipulate the bicomplex.
  Here is the associated article.
• Uniformly accurate integrator for the weak approximation of overdamped Langevin dynamics in the neighbourhood of a manifold (in Julia).
  Here is the associated Yareta archive and article.
• High order integrators for sampling the invariant measure of constrained overdamped Langevin dynamic (in Julia).
  Here is the associated Yareta archive and article.
• Multirevolution integrators for SDEs with fast stochastic oscillations and the nonlinear Schrödinger equation with fast white noise dispersion (in Julia).
  Here is the associated Yareta archive and article.

Thesis:

• Algebraic Tools and Multiscale Methods for the Numerical Integration of Stochastic Evolutionary Problems, Ph.D. Thesis, University of Geneva (2021), No. 5570.

Posters:

• Order conditions for sampling the invariant measure of ergodic SDEs in R^d or on manifolds, Workshop on Multiscale Methods for Deterministic and Stochastic Dynamics, 2020.
• Exotic aromatic B-series for the study of long time integrators for a class of ergodic SDEs, SciCADE, 2017.