Recent technological progress is supported by the generalization of numerical tools for simulating, controlling, and observing physical systems. Yet, by focusing on more and more complex phenomena, our conventional tools are falling short of meeting the growing expectations of engineers, whether in terms of accuracy or computation time. Data-driven approaches, in particular neural networks, offer promising alternatives to address these new challenges. These models can capture complex, nonlinear relationships in physical systems, and shift the burden from manual derivation of tedious mathematical formulas towards large-scale data collection. However, these methods often sacrifice stability, robustness, precision, and more generally guarantees classically offered by traditional approaches. In this thesis, we propose combining the fields of physics, deep learning, and control theory to propose new hybrid methods, taking advantage of the expressivity of neural networks, while relying on inductive biases from physics. We describe theoretical tools (discussed in Part 1) related to the simulation of dynamical systems and connect them to neural network design. In a second time (Part 2), we leverage these insights to design control algorithms and simulation techniques addressing the resolution of complex problems related to partial differential equations. Finally, in Part 3, we focus on larger-scale simulations such as fluid dynamics and counterfactual reasoning. Our work has been presented at scientific conferences in the field of artificial intelligence and control theory. By bridging the gap between physics and machine learning, we believe that this paves the way toward a new generation of methods for the simulation and control of physical systems.

About the speaker: Steeven Janny just completed his PhD at INSA Lyon within the LIRIS and LAGEPP research labs, specializing in the interdisciplinary realms of physics, control, and machine learning. He harbors a profound interest in the fusion of physical simulation with deep learning techniques, and are eager to further explore related areas such as ML-based control and robotics. With a solid foundation in electrical engineering and signal processing, complemented by a degree in artificial intelligence, Steeven brings a diverse skill set to his research pursuits. In addition to his academic endeavors, Steeven Janny is committed to teaching and is a certified "agrégé" teacher in engineering and computer science, ensuring that education remains an integral part of their career trajectory.