Geometry-Based Deep Learning in the Natural Sciences

Nature is composed of elements at various spatial scales, ranging from the atomic to astronomical level. In general, human sensory experience limited mid-range these in that scales which represent world very small or large are generally apart our experiences. Furthermore, complexities and its underlying not tractable nor easily recognized by traditional forms reasoning. Instead, natural mathematical sciences have emerged model Nature, leading knowledge physical world. This level predictiveness far exceeds any mere visual representations as naively formed Mind. particular, geometry has served an outsized role such explanation movement planets across night sky. Geometry only provides a framework for myriad processes, but also mechanism theoretical understanding those processes yet observed, visualization, abstraction, models with insight explanatory power. Without tools, would be feedback, reflects fraction properties objects exist As consequence, taught during times antiquity, essential forming differentiating opinion true belief. It astronomy, classical mechanics, relativistic physics, morphological evolution living organisms, along cognitive systems. information sciences, where it power visualizing flow, structure, organization system. further impacts explanations internals deep learning systems developed fields computer science engineering.