Hexapod Control
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Shuheng Zhang
I am a PhD student in Mechanical and Aerospace Engineering (MAE) at UC San Diego. My work moves between mathematical biology, control and systems theory, deep learning, network theory, documentary filmmaking, and essay writing.
See Research, Film, Photography, Writing, and Life.
Before joining UC San Diego, I received my BSc in mathematics from the Chinese University of Hong Kong (Shenzhen) and an MSc with Distinction in mathematics from University of Oxford.
I am interested in building a practice that lets formal analysis, complex systems, and field-based creative work inform each other.
News
| 2026-09 | Two live projects join this site: Hexapod Control and Investment Research. |
| 2026-08 | Placeholder. |
Research
My research sits at the intersection of analysis, dynamical systems, and complex adaptive behaviour. Areas of interest: mathematical biology, control and systems theory, deep learning, and network theory. Two projects carry this into practice and run live on this site: a hexapod robot learning to walk under closed-loop control, and an investment research society.
Predictor Feedback for an Age-Structured Population Model with Input Delay
Stabilization of a nonlinear age-structured population model whose control input — the dilution rate — reaches the plant only after a pure delay. A normalized spectral functional splits the PDE into a scalar amplitude ODE, the only place the delay enters, and an autonomous integral delay equation for the shape, which decays on its own. That cascade admits a predictor state feedback; PDE backstepping and Lyapunov analysis then give exponential stability of the closed loop, with a decay rate explicit in the actuator delay.
Random Vortex Method for 2D Incompressible Flows
A probabilistic numerical scheme for the two-dimensional Navier–Stokes equations: vorticity is carried by random vortex particles whose stochastic trajectories reproduce the viscous flow, and velocity is recovered through the Biot–Savart law. The dissertation develops the method on the unbounded plane and then on domains with no-slip boundaries — a half-plane, a corner, and an infinite belt.Read paper →
Hierarchical Feature-Based Synthesis of a Brain Module
A generative pipeline for synthetic brain networks built on the Drosophila connectome. Flow-based community detection, Hodge decomposition, PageRank centrality and Gaussian mixture models are combined to reconstruct modules that preserve the structural, spatial and hierarchical properties of the original system — giving an interpretable null model against which real connectomes can be tested.
Film
I create documentary and creative films exploring themes of nature, identity, and human experience.
Echos
Echos
An ethnomusicographic film set in the mountainous regions of Yunnan Province, funded by the University of Oxford. Through fieldwork, it explores how sound is intertwined with the land, while reflecting on how economic development, cultural change, and tourism shape these musical traditions.
Current
A short documentary developed on behalf of the University of Southern California, following the journey of an Uber driver in Los Angeles and mirroring the filmmaker's own experiences.
Plant Pears for Your Heirs
A 17-minute award-winning documentary focusing on the lives of construction workers building a university campus and drawing attention to the shared space between students and workers, experienced at different times.
Photography
Selected photographs. More coming soon.
Writing
Essays, reflections, and small thought experiments published on Medium.
Bullshit, Knowledge, and Language
A Medium essay on the relationship between language, knowledge, and the kinds of empty confidence that language can sometimes produce.
From Age-Structured Models to Artificial Life
A piece that starts from age-structured equations and moves toward a broader question: why living systems seem to learn so effectively without ever being explicitly trained.
Graph Theory Kindergarten
A daydream about education that began during fieldwork in the mountains of China, when a child's game suddenly echoed the language of graph theory.
The Dumpling Dream of Oxford
A playful essay about defining what a dumpling is, and about the strange kind of imagination that can emerge from living and thinking with mathematicians.
Life
I am drawn to ways of living that are simple, intentional, and close to the road, the landscape, and the rhythms of everyday work.
This part of the site holds van life, travel, and personal reflections on community, friendship, and home.
Van life — building out a Chevy Express →
