# Nonlinear Partial Differential Equations and Applications

> **NSF 01002526DB NSF RESEARCH & RELATED ACTIVIT** · University of Chicago (IL) · $200,000

## Abstract

This project develops methods for the qualitative and quantitative study of nonlinear first- and second-order partial differential equations (PDE) set in finite and/or infinite dimensional state spaces arising in science and engineering, and some of their applications. The emphasis is on (i) the theory of mean field games (MFG) and the techniques associated to them including the well-posedeness of nonlinear PDE in infinite dimensional spaces and applications to mean field limits, large deviations of random matrices, filtering, information acquisition, deep learning and economics; and (ii) viscosity solutions techniques to study traffic models and  goal-based stochastic control of portfolio selection with time inconsistency and mental accounting. The project aims at creating a multifaceted platform for theoretical advances across the areas of mean field games, PDE set in infinite dimensional spaces, large deviations of random matrices, mean field limits of interacting particle systems with singular interactions, deep learning, filtering and control of partial information, robust control, time-inconsistent stochastic optimization, and the modeling for applications in asset pricing, traffic management, information acquisition, personalized goal-setting optimization and mental accounting. The analysis of the proposed applications will first require a deeper theoretical understanding that will prompt the formulation of new mathematical questions and their study. It will also gener

## Key facts

- **NSF award ID:** 2452972
- **Awardee organization:** University of Chicago (IL)
- **SAM.gov UEI:** ZUE9HKT2CLC9
- **PI:** Panagiotis E Souganidis
- **Primary program:** 01002526DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** Machine Learning Theory
- **Estimated total:** $200,000
- **Funds obligated:** $200,000
- **Transaction type:** Standard Grant
- **Period:** 08/15/2025 → 07/31/2028

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2452972

## Citation

> US National Science Foundation, Award 2452972, Nonlinear Partial Differential Equations and Applications. Retrieved via AI Analytics 2026-06-07 from https://api.ai-analytics.org/grant/nsf/2452972. Licensed CC0.

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