ALOP Colloquium with Christina Schenk

On Monday, December 16, 2024 at 16:00 c.t. Dr. Christina Schenk, IMDEA Materials Insitute, Getafe (Madrid), will speak at the ALOP Colloquium about her recent work.

Mixed-dimensional Linked Models and Reinforcement Learning-Based Control of Reaction-Diffusion Problems

Abstract:

In Mathematical modeling is a powerful tool for tackling complex challenges across various fields. For instance, during the SARS-CoV-2 pandemic, modeling spatial dynamics and high-diffusion pathways, such as airways and highways, proved essential for effective decision-making in managing the crisis.

In this talk, we present two approaches to enhance modeling and decision-making. We start with linking models of different dimensionalities to represent a single physical phenomenon, specifically coupling two diffusive models—one over a continuum and another over a curve—resulting in a mixed-dimensional problem. We establish the unconditional stability and convergence of both continuous and discrete linked models using mixed finite elements. Supported by numerical examples, we demonstrate the benefits of combining these models and show how our methods can infer solutions from incomplete data.

Building on these results, we explore the application of reinforcement learning (RL) to automatic control problems in thermal and disease transport. We adapt a stochastic policy gradient algorithm and propose novel reward functions to guide the RL agent in interacting with a reaction-diffusion model. Our approach successfully implements control strategies despite necessary model simplifications, showcasing the potential of RL to solve complex control problems.

By combining theoretical and numerical insights from mixed-dimensional modeling and machine learning, this talk highlights new results for advancing diffusive modeling and data-driven control strategies, opening new avenues for research in data science and control applications.

This is joint work with Aditya Vasudevan, David Portillo (UPM), Ignacio Romero, and Maciej Haranczyk.

Please join us at 16:00 c.t. in HS 9.