# Randomized Sketching and Tensor-Format Solvers for High-Dimensional Models

> **NSF 01002627DB NSF RESEARCH & RELATED ACTIVIT** · Virginia Polytechnic Institute and State University (VA) · $249,581

## Abstract

Modern science and engineering increasingly rely on numerical simulations of systems with large numbers of interacting variables: new quantum materials with intricate atomic geometries, hot plasmas inside fusion reactors, time-resolved medical image, and many more applications. Storage and manipulation of such high-dimensional information are often impossible using conventional methods, because the required memory and runtime grow exponentially with the number of variables. This project develops a new set of mathematical tools that represent this information in compact, structured form and use carefully designed random projections to extract answers far more efficiently than was previously possible, while rigorously ensuring a near-zero probability of failure. These techniques directly address scalability bottlenecks in modern AI and machine learning pipelines, where high-dimensional tensor operations are increasingly central to large-scale model training and inference. The resulting methods accelerate discovery in areas central to national priorities, including quantum science, where they enable improved quantum chemistry calculations, and the design of next-generation quantum moire materials for electronics; fusion energy, where they support fast digital twins of plasma turbulence in tokamak reactors; and medical imaging, where they speed up reconstruction of dynamic scans from limited data. The project also trains undergraduate and graduate students at Virginia Tech in mod

## Key facts

- **NSF award ID:** 2608677
- **Awardee organization:** Virginia Polytechnic Institute and State University (VA)
- **SAM.gov UEI:** QDE5UHE5XD16
- **PI:** Paul Cazeaux
- **Primary program:** 01002627DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** Artificial Intelligence (AI), QUANTUM INFORMATION SCIENCE, COMPUTATIONAL SCIENCE & ENGING
- **Estimated total:** $249,581
- **Funds obligated:** $249,581
- **Transaction type:** Standard Grant
- **Period:** 07/01/2026 → 06/30/2029

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2608677

## Citation

> US National Science Foundation, Award 2608677, Randomized Sketching and Tensor-Format Solvers for High-Dimensional Models. Retrieved via AI Analytics 2026-06-08 from https://api.ai-analytics.org/grant/nsf/2608677. Licensed CC0.

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