CTUATOR AND SENSOR PLACEMENT FOR NEURAL FIELDS

L2S - Laboratoire des signaux et systèmes; Gif-sur-Yvette; Sur place; EUR 7 800 - 15 000; Temps partiel

Résumé du poste

L2S - Laboratoire des signaux et systèmes, CNRS, CentraleSupélec, Université Paris-Saclay, Gif-sur-Yvette, France, invites applications for an internship on actuator and sensor placement for neural fields.

You will project nonlinear integro-differential models to finite dimensions and apply optimal control techniques to improve observability and controllability, with a view toward applications such as deep brain stimulation. The project may lead to PhD opportunities.

Qualifications

• Required strong mathematical background in control theory or applied mathematics.
• Familiarity with neural field models and integro-differential equations preferred.
• Experience with model reduction and optimization is a plus.

Responsabilités

• Conduct actuator and sensor placement analyses for neural field models.
• Develop finite-dimensional approximations and apply control techniques to improve observability and controllability.
• Collaborate with advisors and iterate on methods for practical constraints near deep brain stimulation applications.

Connaissances

Observability analysis

Controllability analysis

Finite‑dimensional modeling

Optimal control

Neural field theory

Formation

Master’s or PhD in Control Theory/Applied Mathematics/Neuroscience

Outils

Python

MATLAB

Description du poste

Actuator and Sensor Placement for Neural Fields (Internship)

Laboratory: Laboratoire des signaux et syst`emes, CNRS, CentraleSupélec, Université Paris – Saclay, 91190, Gif-sur-Yvette, France

Internship Advisors: Jean AURIOL, Lucas BRIVADIS, Antoine CHAILLET (Emails: [e-mail], [e-mail], [e-mail])

Overview

Neural fields are nonlinear integro‑differential equations that model the activity of neuronal populations. They provide a continuum approximation of brain structures, enabling analysis of spatial heterogeneity and complex synaptic connections. This internship focuses on the impact of actuator and sensor placement on the control and estimation of neural fields comprising multiple neural populations.

Research Goal

The objective is to analyze and develop actuator and sensor placement methods that ensure observability and controllability of neural fields. Particular emphasis is placed on practical constraints where only a limited number of local actuators and sensors are available, as in deep brain stimulation applications for Parkinson’s disease.

Scientific Approach

We will project the kernel of the integro‑differential equations onto a functional basis to obtain a finite‑dimensional system. Finite‑dimensional control techniques—such as optimal control—will then be employed to assess and improve observability and controllability of the reduced model while managing the spill‑over effect inherent in the projection. The internship will start with a simplified linearized neural population and progress toward more complex multi‑population dynamics.

Application

To apply, send an email with your CV and transcript to Jean Auriol, Lucas Brivadis, and Antoine Chaillet at [e-mail]. This internship may lead to a Ph.D. position.