COURSES
1. Short Course given by Enrique Zuazua
PDEs Meet Machine Learning: Integrating Numerics, Control, and Machine Learning
This course explores these questions through an interdisciplinary lens, bridging PDE theory, control, and ML. We examine the intrinsic connections between representation, optimization, and control theory—rooted in cybernetics (from Ampère to Wiener) and historically motivated by the quest to design intelligent machines. Interestingly, the goals of control theory align closely with those of modern AI, emphasizing mathematics’ unifying power in modeling and innovation.
2. Practice Course given by Juan Daniel Meshir Vargas
Physics-Informed Neural Networks (PINNs)
Session 1: Introduction to PINNs and Mathematical Background
- Motivation: Why physics-informed learning?
- Overview of traditional neural networks vs. PINNs
- Walkthrough of a simple ODE example with PINNs
Session 2: PINNs for Solving Forward PDE Problems
- Constructing loss functions with PDE residuals and boundary conditions
- Training a PINN for the 1D Poisson equation
- Hands-on: Build your first PINN in PyTorch.
CONFERENCES
Thursday, October 9th
Víctor Hernández Santamaría
Control and Uncertainty
Abstract: Stochastic partial differential equations naturally arise in modeling physical, biological, or financial systems affected by uncertainty. Understanding their dynamics and, in particular, designing control strategies for such systems poses a timely mathematical challenge. In this talk, I will present recent developments on control and stabilization problems for stochastic equations, both in the linear and nonlinear settings. While the linear case allows for more systematic results, nonlinear scenarios bring additional difficulties and open new directions for research.
Subrata Majumdar
Control problem for the Kuramoto-Sivashinsky equation in dimensions $N\geq2$.
Abstract: In this talk, we address the boundary null controllability of the Kuramoto–Sivashinsky (KS) equation on a cylindrical domain in higher dimensions. We discuss the controllability of the system via a control applied on either the top or bottom face of the cylinder, acting through the Laplacian. The null controllability of the linearized system is established using a combination of two techniques: the method of moments and the Lebeau–Robbiano strategy. Finally, for the cases $N=2$ or $3$, we prove the local null controllability of the nonlinear system by applying the source term method along with the Banach fixed point theorem.
María de la Luz Jimena de Teresa
New results on the boundary controllability of coupled parabolic equations
Abstract: In this talk we present new results on the controllability of coupled parabolic equations in cylindrical domains. First we will explain how to use a moment method technique in the one dimensional setting and then, we will explain how to extend this technique in the n-dimensional cylindrical framework. As a consequence we present a new result on the controllability of coupled parabolic equations.
Friday, October 10th
Stephen Wright
Optimization in Theory and Practice
Abstract: Complexity analysis in optimization seeks upper bounds on the amount of work required to find approximate solutions of optimization problems in a given class with a given algorithm. The relationship between theoretical complexity bounds and practical performance of algorithms on “typical” problems varies widely across problem and algorithm classes, and relative interest among researchers between the theoretical and practical aspects of algorithm design and analysis has waxed and waned over the years. This talk surveys complexity analysis and its relationship to practice in optimization, with an emphasis on linear programming and convex and nonconvex nonlinear optimization, providing historical perspectives on research in these areas.
Oscar Dalmau Cedeño
TBA
