XI Partial Differential Equations, Optimization, Numerics, and Machine Learning
XI Partial Differential Equations, Optimization, Numerics, and Machine Learning

Organizers:

J. Giesselmann (TU Darmstadt), O. Glass (U. Paris-Dauphine), A. Hayat (Ecole des Ponts Paristech), N. de Nitti (PoliBA), E. Zuazua (FAU Erlangen-Nürnberg, University of Deusto - UAM)


Monday, August 24

08:30-09:30 Registration
09:30-09:40 Opening Address
Enrique Zuazua
09:40-10:20 Machine learning from an applied mathematician's perspective
Enrique Zuazua
10:20-11:00 On simultaneous exact--null controllability
Marius Tucsnak
11:00-11:40 Coffee Break
11:40-12:20 From heat equation to diffusion models
Kang Liu
12:20-13:00 Blow-up for weakly superlinear heat equations and blow-up controllability
Kevin Le Balch
13:00-16:30 Lunch Break
16:30-18:00 Thematic session "PDEs on Networks" (chaired by Nicola De Nitti & Jan Giesselmann)
16:31-16:50 Reduced-model observers for isothermal gas flows on networks
Jan Giesselmann
16:50-17:10 Observers for gas network flow: Synchronization
Martin Gugat
17:10-17:30 Asymptotic-preserving numerical schemes for gas transport on networks
Michael Thiele
17:30-17:50 Dynamics of solutions to the Korteweg–De Vries equation on a network
Nicola De Nitti
20:00-22:30 Welcome Reception

Tuesday, August 25

09:40-10:20 Control of flexible tensegrity networks
Günter Leugering
10:20-11:00 On the stabilizability of hyperbolic systems by boundary control: How to deal with cyclic networks
Martin Gugat
11:00-11:15 Group Photo
11:15-11:40 Coffee Break
11:40-12:20 Optimal cost of fast boundary controls for the one-dimensional heat equation
Pierre Lissy
12:20-13:00 Existence and regularity of optimal potentials
Juan Casado-Díaz
13:00-16:30 Lunch Break
16:30-18:10 Thematic Session "Neural Networks and Neural ODEs" (chaired by Umberto Biccari & Ziqian Li)
16:31-16:50 Neural Networks: Approximation, Backpropagation, and Dynamics
Kang Liu
16:50-17:10 Controllability of the continuity equation for normalizing flows
Antonio Álvarez López
17:10-17:30 Stable solutions and singular representations in neural PDE models
Daniel Fernández
17:30-17:50 Hybrid Generative Modeling for Neuroscience
Daniel López Montero
17:50-18:10 Quantifying Low-Temperature Concentration in Mean-Field Transformers
Albert Alcalde

Wednesday, August 26

09:40-18:00 Thematic session of the CIN–PDE Project: "Control, inversion and numerics for Partial Differential Equations" (chaired by Yue Wang)
09:41-10:20 Shape the sampling in observability for heat equation with memory: propagation and kernel nodal sets
Yubiao Zhang
10:20-11:00 Particle Approximation for Conditional Mean Field SDEs
Yunzhang Li
11:00-11:40 Coffee Break
11:40-12:20 A unique continuation property result for stochastic wave equation
Zhonghua Liao
12:20-13:00 Boundary Stabilization of Hyperbolic Systems
Zhiqiang WANG
13:00-16:30 Lunch Break
16:30-17:00 Low-Dimensional Wave Propogation under Degeneracy: A mathematical Exploration of Control and Damage
Yue Wang
17:00-17:30 Lyapunov functions and stabilization of linear two-dimensional hyperbolic systems
Yubo Bai
17:30-18:00 Stabilization of the wave equation with memory effects within the Riemannian geometry setting
Sheng-Jie Li

Thursday, August 27

09:20-13:00 Thematic Session of CA24136: "Interactions between Control Theory and Machine Learning" (chaired by Martin Lazar)
09:21-09:30 Session opening and presentation of the COST Action "Interactions between Control Theory and Machine Learning"
Martin Lazar
09:30-09:50 From Reduced Bases to U-Nets: Machine Learning for Parametric Optimal Control
Martin Lazar
09:50-10:10 Inverse Problems for Nonlocal Traffic Models
Nicola De Nitti
10:10-10:30 Machine learning tools for the analysis of partial differential equations
Epiphane LOKO
10:30-11:00 Roundtable I
11:00-11:30 Coffee Break
11:30-11:50 Interpreting Machine Learning models: a broad perspective
Umberto Biccari
11:50-12:10 Perceptrons and localization of attention mean-field landscape
Antonio Álvarez López
12:10-12:30 A Bi-Objective Hybrid-Cooperative Framework for PDE-Constrained Inverse Problems
Roberto Morales
12:30-13:00 Roundtable II
13:00-16:30 Lunch Break
16:30-18:30 Thematic session "PDEs and Machine Learning" (chaired by Aidan Chaumet & Daniel Lopez)
16:31-16:45 Deep Neural ODE Operator Networks for PDEs
Ziqian Li
16:45-17:00 Data-Driven Control in Infinite-Dimensional Spaces
Daniel López Montero
17:00-17:15 Weak PINNs for Hyperbolic Conservation Laws
Aidan Chaumet
17:15-17:30 Stackelberg–Nash controllability for a multi-objective Stefan problem.
Suerlan Silva
17:30-17:45 Twofold control for dynamic systems
Mara Vlasic
17:45-18:30 Roundtable

Friday, August 28

09:40-10:20 The place of AI in the practice of mathematics
Amaury Hayat
10:20-11:00 Rigid vortex filaments
Olivier Glass
11:00-11:40 Coffee Break
11:40-12:20 Observability properties of wave equations with rough coefficients: a new approach to deal with interfaces
Sylvain ERVEDOZA
12:20-13:00 Sidewise tracking controllability for semi-discrete wave equations
Sebastián Zamorano Aliaga
13:00-16:30 Lunch Break
16:30-18:35 Thematic session "Observability and stabilisation in PDE" (chaired by Yubo Bai & Nail Baloul)
16:31-16:55 Backstepping stabilization of a hyperbolic system with a zero characteristic speed
Wenhao Yang
16:55-17:20 Stabilization of hyperbolic system: the F-equivalence method
Grégoire ELINCK
17:20-17:45 Truncated Ingham Inequalities
Ana Mimica
17:45-18:10 Optimal geometric barriers for observability of heat semigroups on metric measure spaces
Vincent Boulard
18:10-18:35 Elliptic L^p Carleman estimates initiated at the boundary, with applications to spectral inequalities and controllability
LOTFI Thabouti

Monday, August 31

09:40-10:20 TBD
Pep Mulet
10:20-11:00 Controllability of the semi-geostrophic equations
Vincent Laheurte
11:00-11:40 Coffee Break
11:40-12:20 A geometric approach to nonlocal 2-Hessian equations
Maria del Mar Gonzalez Nogueras
12:20-13:00 The two-dimensional sloshing problema: Unique continuation and control
Marco Antonio Fontelos López
13:00-16:30 Lunch Break
16:30-18:00 Thematic session (chaired by Yue Wang & Shengjie Li)
20:00-22:30 Reception

Tuesday, September 01

09:40-10:20 Nonlocal traffic models: analysis, numerical approximation, and singular limits
Nicola De Nitti
10:20-11:00 Learning from Partial Observations: HYCO and Inverse Problems in Epidemiological Models
Roberto Morales
11:00-11:40 Coffee Break
11:40-12:20 TBD
12:20-13:00 TBD
13:00-16:30 Lunch Break
16:30-18:00 Thematic session (chaired by MC?)

Wednesday, September 02

09:40-10:20 Control of fractional diffusion: old and new
Umberto Biccari
10:20-11:00 TBD
Rafael Orive Illera
11:00-11:40 Coffee Break
11:40-12:20 TBD
12:20-13:00 TBD
13:00-16:30 Lunch Break
16:30-18:30 Thematic Session (chaired by Denilson Menezes)

Thursday, September 03

09:40-10:20 From numerical approximations to rigorous existence via a posteriori error estimates for nonlinear PDEs
Jan Giesselmann
10:20-11:00 TBD
11:00-11:40 Coffee Break
11:40-12:20 TBD
12:20-13:00 TBD
13:00-16:30 Lunch Break
16:30-18:30 Thematic Session "Analysis, Numerics, and Control of Evolution Equations" (chaired by Nicola De Nitti & Vincent Laheurte)
16:31-16:45 Uniform controllability of the Allen–Cahn equation
Vincent Laheurte
16:45-17:00 On the local null controllability of a viscous Burgers’ system in finite time
Minh Nguyen Tran
17:00-17:15 Convergence of a control-volume finite element scheme for a cross-diffusion system modelling ion transport
Arne Berrens
17:15-17:30 A posteriori existence for the Keller–Segel model via a finite volume scheme
Marc Hoffmann
17:30-17:45 Uniqueness of entropy solutions to the Burgers–Hilbert equation
Nicola De Nitti
17:45-18:30 Roundtable