Open Applied Topology (OAT) is a software library for beginners through advanced users in applied topology. We provide efficient, flexible tools for applied topology, built on a foundation of high-performance linear algebra solvers designed specifically for topological applications. Whether you’re computing persistent homology, visualizing data, or developing new topological methods, OAT offers both complete analysis pipelines and the fundamental building blocks to create your own.
In an era of exponentially growing scientific data, applied topology has emerged as a powerful framework for studying complex scientific problems. This innovative mathematical approach works by converting intricate, nonlinear data sets into linear representations that can be analyzed using matrix algebra—essentially transforming complicated scientific questions into precise mathematical calculations. The beauty of this approach lies in its ability to reveal hidden patterns and structures that might otherwise remain invisible to traditional analysis methods.
However, one of the greatest challenges in applied topology lies in performing these mathematical transformations efficiently enough to address the widest possible range of scientific questions. This challenge is multifaceted. Most existing linear algebra solvers weren’t designed with applied topology in mind, making programming unnecessarily laborious. Moreover, applied topology problems are exceptionally demanding computationally and often require specialized methods that aren’t implemented in mainstream mathematical software.
Open Applied Topology (OAT) was created to address these fundamental challenges. While it’s not the first effort to do so—computational topologists have worked diligently over several decades with many important successes—what distinguishes OAT from previous efforts is its generality. Most, if not all, early software packages in applied topology were designed to solve specific problems, such as computing a barcode or persistence diagram. These packages don’t expose the underlying linear algebra to the user, nor do they provide linear algebra tools for users to work with directly.
OAT seeks to change that paradigm. While it provides implementations of several important analysis pipelines, it also opens those pipelines for inspection and provides the linear algebra tools needed to modify, extend, or create entirely new pipelines of your own. This open approach empowers researchers and data scientists to not just use applied topology, but to innovate with it, pushing the boundaries of what’s possible in computational science.
Open Applied Topology is a collaborative development effort undertaken by over 20 institutions in academics, government, and industry. The library comprises 50,000 lines of code and grows annually. Pacific Northwest National Laboratory has supported the effort as the lead contributor since 2022.
Funding for this has been generously provided by the National Science Foundation through awards DMS-1854748, DMS-1854683. and DMS-1854703, and by Pacific Northwest National Laboratory.