Programme détaillé: 

Tiphaine Delaunay (LAGA, Université Sorbonne Paris Nord)

Titre : Studies of inverse problems using sequential methods

Résumé : Inverse problems aim at determining unknown quantities, such as initial conditions, states, or parameters of a system, from available observations. In this work, we focus on sequential data assimilation methods, in which observations are incorporated progressively as they become available, with a particular emphasis on biological applications.

In this context, two case studies are presented. The first concerns the reconstruction of a source term in a wave equation. We define a Kalman estimator in infinite dimensions that sequentially estimates the source term. We show that this estimator is equivalent to the minimization of a cost functional, which enables a convergence analysis under observability conditions.

The second project investigates the evolution of non-spherical tumor growth by combining mathematical modeling with data assimilation from biological measurements. The approach consists in extracting relevant information from spheroid images, formulating a PDE model describing tumor evolution, and then deriving a reduced ODE model. A reduced-order unscented Kalman filter (ROUKF), coupled with a Luenberger observer, is then used to estimate both the system state and the model parameters.

Jean Feydy (Inria HeKA, ParisSantéCampus, Paris)

Titre : Biology simulations with GPUs

Résumé : Massively parallel computing, once reserved for supercomputing centers, is now accessible to every research lab via Graphics Processing Units (GPUs). Yet, we must ask: can this hardware transcend its reputation in deep learning and graphical rendering to become a cornerstone of scientific modeling? This talk explores the untapped potential of GPU for accelerated biological simulation. By examining diverse applications, ranging from the synthesis of capillaries to the mechanics of incompressible biological cells, I will demonstrate how modern hardware acts as an enabler rather than a constraint. We will explore how leveraging GPUs empowers researchers to investigate complex systems, such as swarming phenomena or large-scale biological limits, with a few lines of code.

Tabea Rebafka (MIA AgroParisTech, INRAE, Université Paris-Saclay)

Titre : Conformal novelty detection for a collection of metabolic networks

Résumé :  To analyze a set of metabolic networks of hundreds of bacteria, we consider the novelty detection problem that consists in identifying those metabolic networks that are significantly different from a reference class. Our goal is to identify as many novelties as possible, while controlling  the rate of false discoveries at a user-specified risk level. We propose a conformal prediction approach, which does not make any distributional assumptions on the data and that can be seen as a wrapper around traditional machine learning models, so that it takes full advantage of existing methods. In this talk we give a short introduction to conformal prediction and illustrate the proposed procedure on a large data set of metabolic networks.

This is joint work with Ariane Marandon, Nataliya Sokolovska and Hédi Soula.

Quentin Cormier (Inria Saclay, ASCII)

Titre : Spontaneous oscillations in a network of Integrate-And-Fire neurons.

Résumé :  The emergence of spontaneous rhythmic activity in neural networks is a fundamental phenomenon in neuroscience. In this talk, we investigate the macroscopic dynamics of large, fully connected networks of stochastic Integrate-and-Fire neurons. 

We first consider a one-dimensional model where, in the mean-field limit as the number of neurons goes to infinity, the system is described by a non-linear McKean-Vlasov (or Fokker-Planck) equation. We establish that this macroscopic PDE undergoes a Hopf bifurcation, proving the existence of periodic solutions that correspond to synchronized network oscillations. 

In the second part of the talk, we extend this work to a two-dimensional system that captures both the neuronal membrane potential and the dynamics of synaptic fatigue. A key difficulty in this 2D setting is that the invariant distributions are not explicitly known. However, we shall see that spectral analysis is still tractable exactly, and so we can find all the invariant distributions, decide their local stability and track the Hopf bifurcations. The analysis reveals a new fatigue-driven mechanism for spontaneous oscillations.