# CAREER: Fluctuation estimate, Selection principle and Transition paths for multiscale interacting dynamics on complex structure

> **NSF 01002526DB NSF RESEARCH & RELATED ACTIVIT** · Purdue University (IN) · $518,920

## Abstract

Interactive dynamics, where individuals or particles influence each other and the overall system, are important in fields like biology, physics, materials science, and social sciences. These dynamics often involve rare events that can have large impacts, such as changes in protein structures or genetic evolution. Inaccurate predictions of these events can hinder our understanding of biological processes, drug design, and our ability to prepare for extreme events. This project seeks to improve our ability to predict and control these rare but critical events by identifying key patterns in energy landscapes and developing new methods for estimating fluctuations and controlling extreme events in complex spaces. The insights gained will not only help in predicting extreme events but also improve our understanding of various interactive behaviors, such as material design and social opinions. Educational initiatives will promote interdisciplinary learning and advance the growth of applied mathematics and related fields.

This project aims to predict and control rare, significant events in interactive dynamics on complex configuration spaces. The goal is to advance the theoretical understanding of Hamilton-Jacobi equations (HJEs) and control theory for multiscale interactions by addressing key challenges, including non-uniqueness of stationary solutions, fluctuation estimates in multiscale interactions, and singular optimal control in probability spaces. Theoretical developments w

## Key facts

- **NSF award ID:** 2440651
- **Awardee organization:** Purdue University (IN)
- **SAM.gov UEI:** YRXVL4JYCEF5
- **PI:** Yuan Gao
- **Primary program:** 01002526DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** CAREER-Faculty Erly Career Dev
- **Estimated total:** $518,920
- **Funds obligated:** $56,177
- **Transaction type:** Continuing Grant
- **Period:** 06/01/2025 → 05/31/2030

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2440651

## Citation

> US National Science Foundation, Award 2440651, CAREER: Fluctuation estimate, Selection principle and Transition paths for multiscale interacting dynamics on complex structure. Retrieved via AI Analytics 2026-06-08 from https://api.ai-analytics.org/grant/nsf/2440651. Licensed CC0.

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