Mini-Workshop: Mathematics of Entropic AI in the Natural Sciences

Abstract

The mathematical framework of approximate entropic learning introduced very recently promises to provide robust, cheap and efficient ways of machine learning in the so called "small data" regime, when the underlying learning task is highly-underdetermined, due to a large problem dimension and relatively small data statistics size. Such "small data" learning challenges are particularly common in the natural sciences (e.g., in geosciences, in climate research, in economics, and in biomedicine), imposing considerable difficulties for the numerics of common "data-hungry" Artificial Intelligence (AI) tools like Deep Learning (DL). The aim of this workshop will be to bring together experts in the emergent fields of entropic and DL mathematics/numerics, with some lead experts applying AI in the domain disciplines. The goal will be to detect and to discuss the commonalities in the challenges and in their mathematical solutions, as well as to discuss and fine-tune common mathematical problem formulations that are motivated by the AI applications in natural sciences. The establishment of a common mathematical framework for such small-data machine learning tasks would not only bolster future methodological developments but would also lay solid foundations to further in-depth rigorous analysis and theoretically founded interpretation of these methods and their results.