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Welcome!

I am a Ph.D. candidate in Mathematics at the University of Minnesota, advised by Arnd Scheel. I received my B.S. in Mathematics from the University of California, Los Angeles.

My research lies at the intersection of dynamical systems and partial differential equations. Specifically, I study pattern formation in reaction-diffusion systems with applications to biological phenomena.

Nan Li

Recent Posts

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Why Arclength Continuation?

Why Arclength Continuation?

Overcome fold points and optimize parameter sweeping using arclength continuation

Center Manifold for PDE Dynamics: A Concrete Example

Center Manifold for PDE Dynamics: A Concrete Example

A concrete example of center manifold reduction for PDE

How I Built My Website

How I Built My Website

A tutorial for building a personal website using Astro and Github pages

Recent Projects

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SciML: Allen-Cahn Equation via Modified DeepONet

SciML: Allen-Cahn Equation via Modified DeepONet

Python project that implements a modified Deep Operator Network (DeepONet) to solve the Allen-Cahn equation. The project focuses on using neural networks to approximate the solution operator for this equation.

Demo
SciML: FitzHugh Nagumo Equation via Extended Physics Informed Neural Networks (XPINN)

SciML: FitzHugh Nagumo Equation via Extended Physics Informed Neural Networks (XPINN)

Python project that utilizes Extended Physics Informed Neural Networks (XPINN) to learn the multiple time scale dynamics for the FitzHugh-Nagumo equation.

Demo
SciML: 2D Kuramoto-Sivashinsky Equation via Fourier Neural Networks (FNO)

SciML: 2D Kuramoto-Sivashinsky Equation via Fourier Neural Networks (FNO)

Python project that employs Fourier Neural Networks to learn the solution operator for the 2D Kuramoto-Sivashinsky equation.

Demo
Dynamical Bestiary: Kuramoto-Sivashinsky Equation

Dynamical Bestiary: Kuramoto-Sivashinsky Equation

Python notebook for the Kuramoto-Sivashinsky equation. Explores pattern formations using numerical continuation and direct simulation methods.

Demo
Dynamical Bestiary: Swift-Hohenberg Equation

Dynamical Bestiary: Swift-Hohenberg Equation

Python notebook for the Swift-Hohenberg equation. Explores pattern formations using numerical continuation and direct simulation methods.

Demo
Dynamical Bestiary: Cahn-Hilliard Equation

Dynamical Bestiary: Cahn-Hilliard Equation

Python notebook for the Cahn-Hilliard equation. Explores pattern formations using numerical continuation and direct simulation methods.

Demo

Recent Publications

All publications »
Preprint
2025

Instability of Anchored Spirals in Geometric Flows

A. Cortez, N. Li, N. Mihm, A. Xu, X. Yu, A. Scheel
PDF Paper
London Mathematical Society Lecture Note Series
2024

Anchored Spirals in the Driven Curvature Flow Approximation

N. Li, A. Scheel
PDF Paper
Orbita Mathematicae
2022

Counting Compatible Indexing Systems for $C_{p^n}$

M. Hill, J. Meng, N. Li
PDF Paper