About me
My name is Sébastien Macé and I am a PhD student supervised by
Adrien Busnot Laurent
and
Nicolas Crouseilles
.
I am part of the
MINGuS
team at
INRIA Rennes
.
I joined the IRMAR gender equality committee in September 2025.
Holder of the sports commissioner diploma issued by CNKDR, I contribute to the organization and supervision of national Chanbara competitions for the Dojo des Abers.
Research interests:
- Numerical analysis
- Numerical methods for stochastic differential equations
- Numerical and geometric integration
- Algebraic structures in numerical analysis
- Applied mathematics in biology and physics
My work
I study the construction of numerical methods for solving stochastic differential equations on a Riemannian manifold \(\mathcal{M}\).
In particular, I aim to approximate the invariant measure of the Riemannian Langevin equation:
\[ dX(t) = - \nabla V(X(t))\,dt + \sqrt{2}\, dB_{\mathcal{M}}(t). \]
I briefly present two second-order methods for approximating the invariant measure. Details are available on arXiv. The first one uses a post-processor:
Post-processed frozen-flow method
- \[ H_n = \exp \left( \frac{\sqrt{2h}}{2} \xi^d_n \right) E_d X_n \]
- \[ X_{n+1} = \exp \left( \frac{5h}{4} F(H_n) + \frac{\sqrt{2h}}{4} \xi^d_n E_d \right) \exp \left( -\frac{h}{4} F(H_n) + \frac{3\sqrt{2h}}{4} \xi^d_n E_d \right) X_n \]
- \[ \overline{X_N} = \exp \left( \frac{\sqrt{2h}}{2} \overline{\xi^d_N} E_d \right) X_N \]
The second corresponds to the Heun method in the Euclidean case:
Stochastic frozen-flow Heun method
- \[ H_n = \exp \left( h F(X_n) + \sqrt{2h} \xi^d_n E_d \right) X_n \]
- \[ X_{n+1} = \exp \left( \frac{h}{2} F(H_n) \right) \exp \left( \frac{h}{2} F(X_n) + \sqrt{2h} \xi^d_n E_d \right) X_n \]