Personal Webpage of Adrien Laurent

Publications:

1. Eugen Bronasco, Adrien Laurent, Hopf algebra structures for the backward error analysis of ergodic stochastic differential equations, arXiv:2407.07451.
2. Karine Beauchard, Adrien Laurent, Frédéric Marbach, Control theory and splitting methods, arXiv:2407.02127.
3. Adrien Laurent, The Lie derivative and Noether's theorem on the aromatic bicomplex for the study of volume-preserving numerical integrators, arXiv:2307.07984, Journal of Computational Dynamics, Special issue on mechanics, computation and their math foundations, 2024, 11(1): 10-22.
4. Adrien Laurent, Hans Z. Munthe-Kaas, The universal equivariance properties of exotic aromatic B-series, arXiv:2305.10993, Found. Comput. Math. (2024).
5. 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, Forum of Mathematics Sigma 11 (2023), E69.
6. 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.
7. 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 (2022), 649–695.
8. 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.
9. 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.

Conference reports and proceedings:

1. Adrien Laurent, High order integration of stochastic dynamics in Rd, on manifolds, and in the neighbourhood of manifolds, Oberwolfach Report No. 26/2024.

Thesis:

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

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 papers (Euler operators, horizontal, vertical, variational derivatives, homotopy operators, Lie derivative...), as well as understandable examples to manipulate the bicomplex.
  Here is the article describing the aromatic bicomplex (see also the article on the Lie derivative).
• 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.

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.