Animation showing a bird’s-eye view of two groups of airplanes being rotated on a landscape. On the left side of the screen, an object detection model trained using techniques from Topology, Algebra, and Geometry in Data Science is consistently correct in its detection and labeling (indicated by the green boxes), increasing the rigor, trustworthiness, and explainability of this artificial intelligence system. On the right side, the object detector model was built without algebraic constraints, resulting in the airplanes failing to be detected or correctly labeled under different rotations.

Materials scientists visually inspect the size, number, and distribution of precipitates to help understand how process parameters affect the structure of a material. By looking at the image at different threshold values using a topological framework, the team captured physically meaningful features of precipitate size and distribution.