Samuel D. Leventhal

About

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.

Erdős number 4 (via J. Pach, H. Edelsbrunner, and V. Pascucci) ;p

Collaborators

I have had the fortune of working with exceptional researchers across topology, geometry, and machine learning. A few of my closest collaborators:

To see an interactive graph of my network constructed with a network buidler tool which scapes the web and uses coauthroship to build an association graph. The tool can be found on my github.

The tool creates an interactive map of my coauthorship network. Click a node to inspect a person and see their institutions and closest collaborators.

Research

My research sits at the intersection of machine learning, geometry, and topology, with an emphasis on structure that can be built into a model and reasoned about directly. A selection of publications and preprints follows, beginning with the most recent.

Publications & Preprints

Topological Neural OperatorsNew

Topological Neural Operators (TNOs) lift operator learning from points and edges onto cell complexes, separating where information flows—governed by fixed topological operators—from how it is transformed, which is learned. The result respects the geometric support of physical quantities, exposes conservation and compatibility structure, and, with hierarchical variants for long-range coupling, improves accuracy across PDE benchmarks, including flows on irregular geometries.

I've put together a fully executable tutorial (linked below) that walks through the core ablation study — building the TNO layer from scratch, switching each Hodge channel on and off across domains of increasing topological complexity, and watching the harmonic gates open only when the domain actually has holes.

L. Bastian, S. Leventhal, M. Hajij, T. Birdal. Topological Neural Operators. arXiv:2606.09806, 2026.

arXiv Project Page Tutorial: GradCAM viz of Channels

PAVE: An In Situ Framework for Scientific Visualization and Machine Learning

PAVE addresses the gap between machine learning pipelines and in situ scientific visualization. It couples running simulations to ML over memory-to-memory transport, meeting the data-management needs of integrated workflows while avoiding the I/O bottlenecks that typically separate a model from the system it is learning from.

S. Leventhal, et al. The International Workshop for Data-Driven Reduction of Big Scientific Data (DRBSD), 2019.

PDF Venue

Exploring Classification of Topological Priors with Machine Learning for Feature Extraction

We describe an approach to learning topological priors with machine learning, using the resulting representations to improve feature extraction in complex scientific data.

S. Leventhal, A. Gyulassy, M. Heimann, V. Pascucci. Exploring Classification of Topological Priors with Machine Learning for Feature Extraction.

PDF

Modeling Hierarchical Topological Structure in Scientific Images with Graph Neural Networks

Topological analysis reveals meaningful structure across scientific domains. We integrate topological priors with graph neural networks for hierarchical feature extraction in scientific images, treating multi-scale structure as a first-class, learnable representation.

S. Leventhal, A. Gyulassy, V. Pascucci. Modeling Hierarchical Topological Structure in Scientific Images with Graph Neural Networks.

PDF

Topological Distortion from Dimension Reduction

With Bei Wang, we study how to reduce high-dimensional data while minimizing topological distortion. By preserving similarity between persistence diagrams, we identify projections that maintain first-degree homological features.

S. Leventhal, B. Wang.

Code

Application of a Convolutional Neural Network to Distinguish Burkitt Lymphoma from Diffuse Large B-Cell Lymphoma

Burkitt lymphoma and diffuse large B-cell lymphoma require accurate differentiation for treatment decisions. This work applies convolutional neural networks to assist pathological classification.

S. Leventhal, et al. American Journal of Clinical Pathology.

PDF Journal

High-throughput Feature Extraction for Measuring Attributes of Deforming Open-Cell Foams

Metallic open-cell foams are promising structural materials for multifunctional systems. This work presents high-throughput methods for extracting and measuring foam-cell attributes during deformation.

S. Petruzza, et al. (incl. S. Leventhal). IEEE, 2019.

IEEE

A Deterministic Sketch for Geometric Extents

Given a point set in d-dimensional space, we develop deterministic sketching techniques for efficiently computing geometric extent measures.

S. Leventhal, J. M. Phillips.

Recent Projects

Classification of Songs via Homology of Chroma Features

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.

View on GitHub

Stochastic Nondeterministic Automaton and Applications

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.

View Project

Protein Family Classification

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.

View on GitHub

Other Interests

Beyond research, I explore creative outlets that complement my technical work.

Contact

Email sl@samleventhal.com

Phone +1.801.808.6428

LinkedIn sam-leventhal

ORCID 0000-0003-2454-0311