Center for Advanced Intelligence Project

Title: Probabilistic Numerics for Scientific Experts

Abstract: Integrating advancements in machine learning with traditional scientific methods has g aine d significant attention. Existing approaches often demand well-defined and error-free expert inputs, such as physical knowled ge, or they relegate experts to the role of mere data providers for machines. However, at the forefront of scientific advancement, even human experts encounter uncertainties in p rocesses, necessitating a balanced collaboration with algorithms. This talk delves into the synergistic potential between machine learning and expert knowledge, focus ing on two main areas: (A) Probabilistic Numerics: Probabilistic numerics offers a solution by introducing flexibility and adaptive capabilities into classical numerical methods. It utilizes computational uncertainty through the reinterpretation of numerical tasks as Bayesian in ference problems. Among these methods, we investigate Bayesian quadrature as a primary scientific tool for developing efficient and adaptive methods that relax the assumptions experts need to provide. (B) Expert Knowledge Elicitation and Integration: We examine robust, efficient, and faithful strateg ies for capturing and integrating human expertise with numerical methods. I will close the talk with a few open questions and thoughts on the importance of balanced collaboration with humans in modern models, such as Large Language Models.

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