Machine Learning with Constraints and Priors: A Geometric View on Scientific AI
Machine Learning has become a powerful tool for modeling complex systems, yet many scientific and engineering applications remain challenging due to limited data, physical constraints, and the need for reliable predictions. In such settings, learning from data alone is often insufficient. Instead, machine learning models must leverage prior knowledge, including physical laws, structural constraints, symmetries, and invariances. In this presentation, we explore how geometry provides a unifying framework for incorporating constraints and priors into machine learning. Through the lens of geometric learning, seemingly different approaches—including constrained optimization, manifold learning, and physics-informed models—can be viewed as ways of restricting learning to scientifically meaningful solutions. Using examples from biomedical and scientific data analysis, we illustrate how geometry-aware representations can improve robustness, data efficiency, and interpretability. More broadly, the talk advocates for a vision of Scientific AI in which learning is guided not only by data, but also by the wealth of knowledge accumulated through scientific understanding.
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Speaker
Florian Yger
Associate Professor at LITIS, INSA Rouen Normandy
Florian Yger is an Associate Professor at INSA Rouen Normandie and a researcher at LITIS. His research interests include machine learning, geometric data analysis, representation learning, and scientific AI, with a focus on integrating constraints and prior knowledge into data-driven models. He develops methods for structured and non-Euclidean data with applications ranging from biomedical data analysis to scientific and engineering systems.... read more