University of California, Los Angeles

Jiayi Liwei

Undergraduate in Applied Mathematics

I am interested in nonlinear dynamics, differential equations, and scientific computing. My current work uses numerical simulations to study how energy moves through nonlinear oscillator chains.

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Research

Finite-Time Dynamics in FPUT and Toda Lattices

January 2026–Present

Independent research following UCLA MATH 134

I study energy redistribution in Fermi–Pasta–Ulam–Tsingou (FPUT) oscillator chains using fourth-order Yoshida symplectic integration in Python. I compare spectral entropy, finite-time Lyapunov estimates, and the drift of a selected Toda integral to examine how these diagnostics describe dynamics over finite observation windows.

Current work includes numerical sensitivity checks and FPUT–Toda switching experiments with paired FPUT controls, examining how intermediate Toda evolution affects subsequent FPUT dynamics.

Research code on GitHub

3D Reconstruction

Manuscript in preparation

Collaborative research · Second author

I contribute literature review and manuscript writing to a collaborative 3D reconstruction project. I reviewed and synthesized related work and drafted the introduction, literature review, preliminaries, and conclusion.

Teaching

UCLA Olga Radko Endowed Math Circle

2025–2026 academic year

Instructor

I taught weekly problem-solving classes for students preparing for the AMC 10/12 and AIME.

Academic Activities

Women in Math Mentorship Program, UCLA

Fall 2026–Present

Mentee