# Leveraging Geometric Structure in Learning Dynamical Systems

> **NSF 01002526DB NSF RESEARCH & RELATED ACTIVIT** · Pennsylvania State Univ University Park (PA) · $519,851

## Abstract

Fluid-structural interactions arise in many engineering applications, such as large-scale offshore wind turbines and urban air mobility vehicles. One of the key challenges in modeling such dynamical interactions is to identify the appropriate mathematical representation that respects the physical constraints that are encoded in the observed data. The goal of this project is to model such dynamical interactions with a novel machine learning algorithm that incorporates the geometrical constraints that can be revealed from the data. The key scientific product of this research is a stable and accurate Artificial Intelligence (AI) model for long-time dynamical predictions under external disturbances. In the urban air mobility vehicles application, for example, one is interested in predicting the structural deformation with the strong coupling to the unsteady aerodynamics. Another important byproduct of this research is the reduction of the high energy consumption in training and prediction using AI models. Besides the engineering applications, this project is likely to generate new mathematical questions, fostering interactions between computational mathematics and data-enabled science. This project will contribute to the NSF's mission of advancing STEM through the training of graduate students in an interdisciplinary research training environment to be proficient in mathematical analysis, applied differential geometry, statistical learning, and scientific computing.

The goal 

## Key facts

- **NSF award ID:** 2505605
- **Awardee organization:** Pennsylvania State Univ University Park (PA)
- **SAM.gov UEI:** NPM2J7MSCF61
- **PI:** John Harlim
- **Primary program:** 01002526DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** Artificial Intelligence (AI), Machine Learning Theory, COMPUTATIONAL SCIENCE & ENGING
- **Estimated total:** $519,851
- **Funds obligated:** $519,851
- **Transaction type:** Standard Grant
- **Period:** 09/01/2025 → 08/31/2028

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2505605

## Citation

> US National Science Foundation, Award 2505605, Leveraging Geometric Structure in Learning Dynamical Systems. Retrieved via AI Analytics 2026-06-09 from https://api.ai-analytics.org/grant/nsf/2505605. Licensed CC0.

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