CERAMATHS - DMATHS seminar: presentations by Élisabeth Lacazedieu and Nacira Agram

The CERAMATHS mathematics department seminar will host, on Thursday June 27, 2024,
* at 2pm Elisabeth Lacazedieu (LAMIH, UPHF)

Inverse parameter identification using reduced models

Inverse parameter identification is a recurring problem in mechanics due to the multiple sources of uncertainty about media and their interactions with the environment.
In this talk, we will illustrate some methods based on reduced models applied to the prediction of bifurcations of dynamical systems of nonlinear behavior.

* at 3:30 pm Nacira Agram (Royal Institute of Technology Stockholm, Sweden)

Deep learning for conditional McKean-Vlasov Jump diffusions

My talk focuses on using deep learning methods to optimize the control of conditional McKean-Vlasov jump diffusions. We begin by exploring the dynamics of multi-particle jump-diffusion and presenting the propagation of chaos. The optimal control problem in the context of conditional McKean-Vlasov jump-diffusion is introduced along with the verification theorem (HJB equation). A linear quadratic conditional mean-field (LQ CMF) is discussed to illustrate these theoretical concepts. Then, we introduce a deep-learning algorithm that combines neural networks for optimization with path signatures for conditional expectation estimation. The algorithm is applied to practical examples, including LQ CMF and interbank systemic risk, and we share the resulting numerical outcomes.
Based on joint work with Jan Rems.