Séminaire MACS
Monday 28 September 2026 à 13:45 - salle 430 (4ème étage, bâtiment 9)
Andrés Lopez-Lopera (Université de Montpellier, IMAG)
Probabilistic modeling of differential equations with latent forces via Gaussian processes
Séminaire commun EPS-MACS
In many applications, the mechanisms driving dynamical systems are partially unknown or costly to measure, making it challenging to obtain analytical or numerical solutions. In inverse problems, these latent forces must instead be inferred from measurements of the output process. In this talk, we discuss a probabilistic framework for modeling differential equations with latent forces, enabling both closed-form solutions and inference. The key idea is to place probabilistic priors, more precisely Gaussian processes (GP) prios, on the latent forces. Under this formulation, the solution of the dynamical system can be represented as a GP, with the parameters governing the differential equation explicitly encoded in the its kernel function. This construction provides a direct connection between the probabilistic representation and the underlying dynamics, while allowing uncertainty in the latent forces to be propagated to the output process. Two biological applications are considered for illustration, each governed by an ODE and a PDE.
Séminaire en salle 430, également retransmis sur zoom : https://umontpellier-fr.zoom.us/j/99660917688