Midsummer is approaching with plenty to enjoy!

The program features Xin Guo, University of Berkely with three lectures on Reinforcement Learning, Backward equations, LLM, and Rough Paths:

You can register at the following link.

Also, we are pleased to announce the upcoming talk in the SURE-AI @ STAR seminar series on Friday, June 26th, from 11:00 to 12:00 (Oslo time).

As always, the talk will take place in a hybrid format: participants in Oslo can attend the talk in Room 723 in Niels Henrik Abels hus, whereas the international audience will be able to follow the talk via Zoom.

The speaker is Gonçalo dos Reis (University of Edinburgh) with the talk

Title: Simulation of mean-field SDEs: some recent results

Abstract: We review two results in the simulation for SDE of McKean-Vlasov type (MV-SDE). The first block of results addresses simulation of MV-SDEs having super-linear growth in the spatial and the interaction component in the drift, and non-constant Lipschitz diffusion coefficient. The 2nd block is far more curious. It addresses the study the weak convergence behaviour of the Leimkuhler--Matthews method, a non-Markovian Euler-type scheme with the same computational cost as the Euler scheme, for the approximation of the stationary distribution of a one-dimensional McKean--Vlasov Stochastic Differential Equation (MV-SDE). The particular class under study is known as mean-field (overdamped) Langevin equations (MFL). We provide weak and strong error results for the scheme in both finite and infinite time. We work under a strong convexity assumption. Based on a careful analysis of the variation processes and the Kolmogorov backward equation for the particle system associated with the MV-SDE, we show that the method attains a higher-order approximation accuracy in the long-time limit (of weak order convergence rate 3/2) than the standard Euler method (of weak order 1). While we use an interacting particle system (IPS) to approximate the MV-SDE, we show the convergence rate is independent of the dimension of the IPS and this includes establishing uniform-in-time decay estimates for moments of the IPS, the Kolmogorov backward equation and their derivatives. The theoretical findings are supported by numerical tests.

This presentation is based on the joint work [1], [2].

[1] Chen, X., Dos Reis, G., Stockinger, W. and Wilde, Z., 2025. Improved weak convergence for the long-time simulation of mean-field Langevin equations. Electronic Journal of Probability, 30, pp.1-81.

[2] X. Chen, G. dos Reis. "Euler simulation of interacting particle systems and McKean-Vlasov SDEs with fully superlinear growth drifts in space and interaction" IMA Journal of Numerical Analysis, 44, no. 2 (2024), 751-796.

Giulia, Leonardo, David, Pere