Understanding the shape of chemistry data—Applications with persistent homology

Chemical data often have complex and nonlinear patterns in how data points relate to one another. Concurrently, there are many situations where chemical data are of high dimensionality (e.g., the 3N-dimensional potential energy landscape). Both complexity and high dimensionality pose challenges for analyses that seek to uncover fundamental structure–property relationships or to develop foundational models of chemical behavior. This Perspective offers mathematical context, illustrative applications, and conceptual motivation for using persistent homology (PH) to identify and provide new physical insight into the multiple spatiotemporal-scale patterns present in chemical data. We address the implications of different data representations and highlight the relationships of PH-derived descriptors to physicochemical properties and chemical behavior. Applications in machine learning are also discussed, emphasizing how PH can enhance predictive modeling. Finally, we review commonly used PH software, offering recommendations on usability, flexibility, and data requirements.