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Nathan Doumèche: Physics-Informed Machine Learning as a Kernel Method

Speaker: Nathan Doumèche Date: 09 May 2024 Title: Physics-Informed Machine Learning as a Kernel Method Abstract: Physics-informed machine learning merges the expressiveness of data-driven models with the interpretability of physical theories. This seminar explores a general regression problem where the empirical risk is augmented by a partial differential equation to enhance the model's adherence to physical laws. Our analysis reveals that with linear differential priors, the problem translates into a kernel regression framework. Leveraging kernel theory, we detail convergence rates for the solution and establish its compliance with the Sobolev minimax rates, noting that faster convergence is possible with reduced physical discrepancies. This approach is exemplified through a one-dimensional case study, highlighting the benefits of incorporating physical insights into empirical risk minimization for enhanced estimator accuracy.