A ground-up restoration of a 1973 Oldsmobile Cutlass Supreme, approached with the same documentation-first mindset I bring to research. The companion site includes step-by-step guides, parts lists, and photos — written for novice readers who, like me at the start of this project, had no prior automotive experience.
View restoration site →I received my Ph.D. in computer science from the University of Utah School of Computing and the Scientific Computing and Imaging Institute, mentored by Valerio Pascucci. I'm currently a postdoctoral researcher at the University of San Francisco, supervised by Mustafa Hajij, working on topological deep learning and neural operators.
My research sits at the intersection of machine learning, geometry, and topology, and it keeps returning to one question: what can be learned, and how is learning structured, over the geometry—intrinsic or extrinsic—of the objects that learn and the objects they learn from. These mechanics are often less about strict metrics or scales than about functional relationship and continuity between and within shapes: motifs in mutable forms, how adjoining elements relate, where information is organized and where it is separated. I've found topology naturally suited to developing tools and perspectives that bring these mechanics into view. Much of my work is an attempt to take that vantage point seriously—to treat structure not as something we read off a model after the fact, but as something we can build into it and reason about directly.
My current work on Topological Neural Operators develops learnable transports that decompose how information flows across a model into distinct, interpretable components—gradient, curl, and harmonic—on a combinatorial complex. The aim is structure that is portable across architectures rather than grafted onto a single one, and whose behavior can be reasoned about by construction rather than recovered empirically.
During my PhD I introduced topology-native learning frameworks that operate directly on simplicial and graph representations derived from Morse–Smale complexes rather than on pixels or raw adjacency. My dissertation developed hierarchical topological priors and multi-scale training schemes that exploit connectivity—via persistence filtration and hierarchical GNNs—to improve robustness and expressivity, particularly under heterophily, treating multi-scale structure as a first-class, learnable representation. I've also built production-grade systems in HPC environments at LLNL, ORNL, and Utah, including PAVE, an in-situ framework that couples running simulations to machine learning over memory-to-memory transport, designed to avoid I/O bottlenecks and keep the model in contact with the system it's learning from.
Across all of it, the constant has been a preference for impact over sophistication: not the most elaborate option, but the simpler, more portable, more scalable one—the right representations, integrated into real pipelines, and legible to the people who use them. I want to build and understand simple, elegant, useful things, with others—bicycles, not Rube Goldberg machines.
I have had the fortune of working with exceptional researchers including Mustafa Hajij Attila Gyulassy, Bei Wang, and Valerio Pascucci.
Topological analysis reveals meaningful structure in data from a variety of scientific domains. We describe an approach integrating topological priors with graph neural networks for hierarchical feature extraction in scientific images.
S. Leventhal, A. Gyulassy, V. Pascucci. Modeling hierarchical topological structure in scientific images with graph neural networks.
In this paper, we describe an approach to creating learnable topological priors using machine learning techniques for improved feature extraction in complex datasets.
S. Leventhal, A. Gyulassy, M. Heimann, and V. Pascucci, Exploring Classification of Topological Priors with Machine Learning for Feature Extraction.
Machine learning (ML) has emerged as a tool for understanding complex scientific phenomena. To address the ML and in situ visualization gap, we introduce PAVE—an in situ framework which addresses the data management needs of ML pipelines integrated with scientific simulations.
The International Workshop for Data-Driven Reduction of Big Scientific Data (DRBSD)
Metallic open-cell foams are promising structural materials with applications in multifunctional systems. This work presents high-throughput methods for extracting and measuring foam cell attributes during deformation.
Burkitt lymphoma (BL) and diffuse large B-cell lymphoma (DLBCL) require accurate differentiation for treatment decisions. This work applies convolutional neural networks to assist in pathological classification.
Bei Wang and I tackle the problem of reducing high dimensional data while minimizing topological distortion. By preserving similarity between persistence diagrams, we identify optimal projections that maintain first degree homological features.
We consider a point set P in a d-dimensional space of size u. Our goal is to efficiently compute geometric extent measures using deterministic sketching techniques.
Authors: Sam Leventhal and Jeff M. Phillips
Majority of methods for song recommendation are based on co-similarity defined by degrees of shared preference. This project explores topological approaches to song classification using persistent homology of chroma features.
Given a file, the program records word frequencies to generate text files in a similar voice using Markov chains. A literature replicator that captures stylistic patterns.
A classifier trains to label proteins by family using two approaches: supervised learning with SVMs and decision trees on amino acid chains, and convolutional neural networks on 3D protein renderings.
Beyond research, I explore creative outlets that complement my technical work.