Shuheng Zhang 章书恒

Shuheng Zhang

I am a PhD student in Mechanical and Aerospace Engineering (MAE) at UC San Diego. I was trained as a mathematician, and my research now lies at the intersection of mathematics, control, artificial intelligence, and robotics — on how intelligent systems learn, act, and organize themselves.

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.

Outside research, I am building a campervan, making films, taking photographs, and writing. Mathematics, science, and cinema are different languages for uncovering hidden structures in the world and making them visible.

News

2026-12 Upcoming: presenting at the IEEE Conference on Decision and Control, Honolulu, 15–18 December.
2026-10 ShellChat opens to collaborators: a conversation system that listens for where research comes from.
2026-09 New essay: Truths as Opinions.
2026-09 Hexapod — Survival Is the Only Task and Longview are running live.
2026-07 Predictor Feedback for an Age-Structured Population Model with Input Delay accepted to CDC 2026.
2026-07 Presented at the inaugural African Control Systems Symposium at AIMS Mbour, Senegal.
2025-04 Presented Current at the Fisheye International Film Festival, High Wycombe, UK.

Projects

I was trained in mathematics and now work between control, artificial intelligence, and robotics, on how intelligent systems learn, act, and organize themselves. Four threads run through it: control of infinite-dimensional systems such as PDEs; how a learning system can choose for itself what to study next; robots whose behaviour follows their own survival rather than a human task; and one architecture that holds network science, language models, reinforcement learning, motion planning, and classical control together instead of treating them as separate tools. Three projects carry this into practice and run live on this site: a language agent that has to work out how to walk a body it was told nothing about, an autonomous investment research society, and a conversation system that listens for where research comes from.

ShellChat — Where Research Comes FromOpen site →

Conversation system · 2026 – present · live at chat.shzhang.com (login required)

A quiet place to talk: about research, about who to work with, about everyday things. A model listens, keeps what is worth pursuing as a written outline, and lets the rest go. The aim is plain: better conversations, and a shorter path from an idea to work worth doing.

A chat between two people: endless small talk, of which three offhand complaints about buses, traffic and queues flow into the ShellChat mark, which writes an outline titled why things bunch up and lets the rest go.
Three complaints in passing — buses in threes, a jam with no accident, the slowest queue — turn out to be one question. The listener keeps that one and lets the rest of the small talk go.

Hexapod — Survival Is the Only TaskOpen console →

Embodied-agent experiment · 2026 · console at hexapod.shzhang.com (login required)

A language agent is sealed in a container and handed a body it knows nothing about — a simulated hexapod reachable only over HTTP — with a one-page datasheet and a single instruction: stay alive. That it has six legs, how to stand, how to walk, and that fruit stops the battery draining are all things it must find out by experiment. There is no training. Its workspace persists after it dies, so each new instance inherits whatever the last one wrote down; the question is whether experience compiles into files.

The simulated hexapod mid-stride on rough undulating ground, its two stalked eyes turned toward the camera, coloured fruit spheres scattered across the floor.
Run 3, life 22, mid-stride on the roughest ground any life was given. A MuJoCo render replayed from the episode's ground truth: the pose is logged, only the camera chosen. The two stalks are its eyes.

Longview — An Autonomous Investment Research SocietyOpen site →

Multi-agent research system · 2026 – present · live at longview.shzhang.com (login required)

Four persistent identities — an actor, a critic, a steward and a doctor — share one world graph and are built to disagree, preserving the disagreement rather than resolving it. They read primary filings rather than prices, and every claim enters the graph as an edge with the document behind it: a thesis is admitted only with the fact that supports it and the filing that would falsify it. The horizon is deliberately long; its only edge is time, not speed. Nothing here is advice, and the system never trades.

A close view of the world graph with three unrelated nodes lit across the frame — Qualcomm, US drug pricing policy and OpenAI — each with its labelled edges to neighbours such as Apple, Merck and AMD, over a pale field of the rest of the graph.
Three unrelated corners lit together — Qualcomm, US drug pricing policy, OpenAI — each with the edges it carries. Solid edges are evidence-backed, dashed ones seeded and unverified. Behind them, the rest: 277 nodes, 467 edges.

Predictor Feedback for an Age-Structured Population Model with Input Delay

With Mamadou Diagne and Miroslav Krstic · UC San Diego · Accepted, 2026 IEEE Conference on Decision and Control

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.

Population density over time and age under three control strategies: nominal, naive feedback, and predictor feedback.
The population density f(t, a) under actuator delay τ = 1.5: (a) the nominal control misses the equilibrium, (b) delay-blind feedback oscillates, (c) the predictor settles onto f*. Dashed red is the initial profile, green the equilibrium.

Random Vortex Method for 2D Incompressible Flows

M.Sc. dissertation · University of Oxford · 2025
Supervised by Prof. Zhongmin Qian

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 →

Simulated streamlines at t = 12 in three wall-bounded domains: the upper half-plane, a corner, and a belt.
Streamlines and vorticity at t = 12 in the three wall-bounded geometries, reconstructed from the random vortex particles: the upper half-plane and the corner at ν = 0.1, the belt ℝ × [0, 6] at ν = 0.05.

Hierarchical Feature-Based Synthesis of a Brain Module

Network science research project · University of Oxford · 2025

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.

Three-view projections of two Infomap modules within the Drosophila connectome.
Three-view projections of two second-level Infomap modules inside the fly brain. Module 1 (left) is asymmetric on its own; Module 5 (right) is strongly bilaterally symmetric.

Film

I create documentary and creative films exploring themes of nature, identity, and human experience.

Echos

Echos

2025 · Yunnan, China · Director, cinematographer, editor

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 poster

Current

2024 · Los Angeles, CA, USA · Director, producer, editor

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.

Watch trailer

Plant Pears for Your Heirs poster

Plant Pears for Your Heirs

2022 · Shenzhen, China · Production manager, cinematographer, editor

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.

Watch film

Photography

Selected photographs. More coming soon.

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Writing

Essays, reflections, and small thought experiments published on Medium.

Truths as Opinions

Sep 2026

When enough people believe an opinion, we call it truth. Mathematics is no exception: proof became authority by persuading everyone, and now a benchmark persuades too.

Bullshit, Knowledge, and Language

Mar 2026

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

Feb 2026

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

Oct 2025

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

Jun 2025

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 →

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