- University of Texas at Austin
- Ph.D. Candidate in Department of Physics
- Center for Theoretical and Computational Neuroscience
- Contact Information
- luyan.yu [at] utexas.edu
- NHB 4.362, 100 E 24TH ST
- Austin, Texas 78712, USA

I’m currently a 5^{th} year Ph.D. student in physics at UT Austin receiving Provost’s graduate excellence fellowship. Recently, I joined the center for theoretical and computational neuroscience as a research assistant under the supervision of Dr. Thibaud Taillefumier. The two main focuses of my interests in the field of computational neuroscience, broadly speaking, are:

- to understand how the biological neural networks actually work; and
- to inspire the development and improvement of neural-network-based machine learning algorithms.

Here’s a list of my past and ongoing projects.

I use mathematical tools such as stochastic calculus and functional differential equation to study the behavior and extract properties of neural networks; and tropical algebra to study problems in bioinformatics such as phylogenetic trees. Meanwhile, for the second part, I’m also looking into the optimization over tensor networks that has a wide range of applications emerging in machine learning.

I enjoy using computational tools to solve problems either from research or in life. As a passionate believer and active advocate of Wolfram Mathematica, I use it almost daily for research and pleasure. I also use (C++ | Python | Rust) when they best suit my needs. I’m also into parallel computing, more specifically, CUDA for GPU computing. As a side hobby, I casually do web development; for example, this site and Jazzify.AI.

Metastable spiking networks in the replica-mean-field limit

Extreme rays of the $\ell^\infty$-nearest ultrametric tropical polytope

Replica-mean-field limit of spiking neural networks

Tensor Networks in Machine Learning

Topological phase transitions in antiferromagnet and topological insulator trilayer structure

Topological Quantum Computation

Tools for customizing the colors of your figures in Mathematica.

Mathematica package for managing personal utility functions.

Replica simulator for generic neural networks.