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TITLE: Scientific Machine Learning with Neural Ordinary Differential Equations

ABSTRACT: Scientific machine learning (SciML) aims to facilitate data-driven scientific discovery by incorporating prior scientific knowledge into machine learning algorithms. Within this broad and exciting field, this talk will focus on neural ordinary differential equations (neural ODEs), an approach that bridges the differential equation-based modeling paradigm of the physical sciences with the expressivity of neural networks. In the context of scientific machine learning, neural ODEs are particularly interesting because they highlight the dual aspect of the field - using machine learning models to tackle scientific questions, and drawing inspirations from the natural sciences to better understand and improve machine learning models. After a brief overview of scientific machine learning and an introduction to neural ODEs, this talk will progress in two parts. In the first part, we will discuss dynamics discovery using neural ODEs, especially in the context of atomic force microscopy. In the second part, we will switch gears and discuss the unstable training problem of these models, and how inspirations from dynamical systems and chaos theory can provide potential solutions. We will conclude with open questions and prospects in the field.