# Collaborative Research: MATH-DT: Reduced order modeling and data assimilation for wave-dominated systems with applications to digital twins in ultrasonics

> **NSF 01002526RB NSF RESEARCH & RELATED ACTIVIT** · Southern Methodist University (TX) · $354,485

## Abstract

Millions of patients each year rely on medical procedures that use sound waves to break apart kidney stones or target diseased tissues without surgery. As these technologies advance, so does the need for greater precision, safety, and adaptability in treatment. This project contributes to the development of digital twins — real-time computer models that simulate how sound waves interact with the body and, based on imaging as the procedures unfold, help guide the process. By enabling more accurate and responsive treatments, such models could significantly improve clinical outcomes and reduce costs in noninvasive medicine. Beyond the immediate medical application, the project addresses a broader national need: the development of fast, reliable computational tools for predicting and controlling complex physical systems in real time. These methods are broadly applicable to technologies that rely on wave-based sensing and actuation, including systems in biotechnology, nondestructive materials testing, environmental monitoring, and national defense. The project will also serve as a multidisciplinary training ground for graduate students working at the intersection of applied mathematics, computation, and engineering.

The research aims to develop fast, accurate algorithms that simulate how high-frequency waves, such as shock waves or focused ultrasound, propagate through complex, heterogeneous materials. The key technical challenge is that, in many real-world systems, waves must 

## Key facts

- **NSF award ID:** 2529316
- **Awardee organization:** Southern Methodist University (TX)
- **SAM.gov UEI:** D33QGS3Q3DJ3
- **PI:** Thomas M Hagstrom
- **Primary program:** 01002526RB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** COMPUTATIONAL SCIENCE & ENGING
- **Estimated total:** $354,485
- **Funds obligated:** $354,485
- **Transaction type:** Standard Grant
- **Period:** 09/01/2025 → 08/31/2028

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2529316

## Citation

> US National Science Foundation, Award 2529316, Collaborative Research: MATH-DT: Reduced order modeling and data assimilation for wave-dominated systems with applications to digital twins in ultrasonics. Retrieved via AI Analytics 2026-06-06 from https://api.ai-analytics.org/grant/nsf/2529316. Licensed CC0.

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