Applied Mathematics · Machine Learning · Computational Geometry

Dengyuhan Dai

戴 邓语涵

Optimization, structure, and the mathematics behind learning.

I work at the boundary of mathematical theory and machine learning - studying how iterative algorithms become differentiable architectures, and how geometry gives structure to data. UCLA Applied Math '26 · Incoming INRIA Researcher · Imperial MSc AI '27.

Explainable ML Algorithm Unrolling Computational Geometry Reinforcement Learning 3D Vision
Dengyuhan Dai
01 · About

About

I'm a final-year Applied Mathematics student at UCLA, with a background in analysis, convex optimization, numerical methods, and algorithms. My core interest is understanding machine learning from the inside - not treating models as black boxes, but tracing how their behavior follows from mathematical structure.

This summer I join INRIA TITANE (Sophia Antipolis) as a research intern, working on variational mesh reconstruction from 3D point clouds using reinforcement learning and graph neural networks, supervised by Pierre Alliez.

In autumn I begin an MSc in AI at Imperial College London, where I plan to deepen work on principled model understanding - connecting optimization theory to interpretable, reliable learning systems.

Outside of research: I write suspense fiction, play souls-like games, and hold a JLPT N2 in Japanese.

Current UCLA Applied Math
Next Imperial MSc AI '27
Summer INRIA TITANE
Location LA → London
GitHub TomoriNa0
Languages EN · ZH · JP
02 · Experience

Experience

Education
UCLA
Sep 2022 - Jun 2026
Los Angeles, CA
University of California, Los Angeles
B.S. Applied Mathematics
Key Courses  ·  Algorithms  ·  Machine Learning  ·  ODE  ·  Real Analysis  ·  Numerical Methods
Internship
INRIA
Jul - Sep 2026
Sophia Antipolis, France
INRIA TITANE
Research Intern · Geometric Modeling & Computer Vision
Key Work  ·  RL-based 3D mesh reconstruction  ·  GNN + GAT geometric feature modeling  ·  DINOv2 image encoding  ·  A2C multi-agent policy optimization
Upcoming
Imperial College London
Sep 2026 - Sep 2027
London, UK
Imperial College London
MSc Artificial Intelligence
03 · Research

Research

Research · Ongoing
TSP Point Art
Image-to-TSP generative pipeline converting image signals into large-scale Euclidean TSP instances. Density field construction, adaptive sampling (brightness / edge / multilayer), Floyd-Steinberg dithering, and LLM-agent auto-configuration of solver parameters.
Combinatorial Optimization Generative Art LLM Agent
Research · Algorithm Unrolling
Topology Optimization
Algorithm unrolling applied to structural topology optimization: iterative level-set updates become differentiable network layers, retaining mathematical guarantees while enabling learned descent. Full FEM pipeline with SIMP and Level-set frameworks, adjoint sensitivity analysis.
Algorithm Unrolling FEM Level-set Methods
Research · Theory
Stochastic Processes & ML
Guided reading on Markov chains, Poisson processes, and random walks (Prof. Vadim Markel, 2023). Traced their appearance in modern ML: SGD as a discrete-time stochastic process, Bernoulli dropout in attention mechanisms.
Stochastic Processes Theory
Publication · 2023
Linear Regression Analysis
Published paper examining factors affecting linear regression model performance. DOI: 10.1145/3653724.3653734
Statistics Published
Skills
Languages
  • Python
  • C++
  • Java
  • MATLAB
  • Lua
  • LaTeX
Frameworks
  • PyTorch
  • TensorFlow
  • NumPy
  • SciPy
  • FastAPI
  • FreeFEM++
Research Areas
  • Algorithm Unrolling
  • Topology Optimization
  • Computational Geometry
  • Variational Methods
  • Reinforcement Learning
  • 3D Point Clouds
Human Languages
  • Chinese
  • English
  • Japanese
04 · Projects

Projects

Project · Bayesian Systems
Movie Estimator
Bayesian estimation system for movie viewing counts. FastAPI backend, session state machines, Beta-Binomial Bayesian correction, weighted sampling from Top-250 pool, and LLM semantic correction layer.
Bayesian Inference FastAPI LLM Integration
Project · Dynamical Systems
Population Dynamics Modeling
Lotka-Volterra system analysis with real ecological time-series data. Equilibrium analysis, linear stability, phase portraits, parameter estimation via numerical integration, and model extension for carrying capacity, seasonality, and functional responses.
Dynamical Systems Numerical Methods MATLAB
View Report
05 · Beyond the Equations
The Hound - Namterre Luo
Art by Dollllls
Original Novel

The Hound  /  恶犬

Namterre Luo · 骆南洮
In Film & Literature

My favourite director is Shunji Iwai, whose films move between tenderness and quiet devastation with an unhurried grace I find irreplaceable.

In literature I return most often to Yukio Mishima - drawn to his obsession with beauty, discipline, and the fatal coherence of an ideal.

The Hound is my current novel-in-progress - a suspense work written with classical restraint: slow-burn tension, precise prose, and psychological depth over spectacle. It is a novel about the architecture of a criminal mind, not born of passion or madness, but of cold structural logic applied to human behavior.

Namterre Luo · 骆南洮

A physics student with no emotional affect and exceptional intelligence. The Hound follows her slow, deliberate transformation - how someone who feels nothing comes to act with total, precise intention. She does not break rules out of rage or trauma; she simply decides, with perfect clarity, that they do not apply to her, and then acts accordingly.

"The evil that men do lives after them; The good is oft interred with their bones."

06 · Contact