# ERI: Advancing Design of Highly Chaotic Systems with Higher-Dimensional Analysis and Human-in-the-Loop Reinforced Learning

> **NSF 01002526DB NSF RESEARCH & RELATED ACTIVIT** · Embry-Riddle Aeronautical University (FL) · $200,000

## Abstract

This Engineering Research Initiation (ERI) project supports research that aims to establish a new foundation for the analysis and design of chaotic systems by investigating how higher-dimensional representations and topological modeling can fundamentally alter the way engineers perceive and interact with complex dynamics. Many critical engineering challenges, such as trajectory design for space missions, occur within chaotic regimes where small changes in initial conditions can lead to vastly different outcomes. Traditional approaches often reduce these systems to oversimplified, low-dimensional representations that obscure their full complexity, leading to inefficiencies and blind spots in design. To address these challenges, this project seeks to answer two research questions – 1) how can expanding the dimensionality of the problem space, while incorporating topological methods from knot theory, enhance the analysis, visualization, and design of complex chaotic systems to reveal previously unattainable solutions? 2) how does knot theory-informed reinforcement learning with human-in-the-loop interactions enhance design quality, guidance, and decision efficiency and accuracy? This project hypothesizes that by expanding the dimensionality of the design space and integrating human-in-the-loop learning with mathematical insights from knot theory, it is possible to reveal new solutions and guide users toward more efficient, accurate, and interpretable design decisions. This work 

## Key facts

- **NSF award ID:** 2501408
- **Awardee organization:** Embry-Riddle Aeronautical University (FL)
- **SAM.gov UEI:** U5MMBAC9XAM5
- **PI:** David Canales Garcia
- **Primary program:** 01002526DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** Complex Systems, System Design and Simulation, WOMEN, MINORITY, DISABLED, NEC, RESEARCH INITIATION AWARD
- **Estimated total:** $200,000
- **Funds obligated:** $200,000
- **Transaction type:** Standard Grant
- **Period:** 06/01/2025 → 05/31/2027

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2501408

## Citation

> US National Science Foundation, Award 2501408, ERI: Advancing Design of Highly Chaotic Systems with Higher-Dimensional Analysis and Human-in-the-Loop Reinforced Learning. Retrieved via AI Analytics 2026-06-08 from https://api.ai-analytics.org/grant/nsf/2501408. Licensed CC0.

---

*[NSF Awards dataset](/datasets/nsf-awards) · CC0 1.0*