Tian2 田二
Research Mentoring · 研究指导

Selected Project Archetypes.

A view of the research we guide — from a first question to a defended paper — across pure mathematics, physics, chemistry and materials, biology, computer science, and applied data. Shown by field and method, never by name.

Students' identities are withheld. Every project below is described only by its field and method. No names, schools, or internal documents appear anywhere on this page.

Project Archetypes

Field · Method · Result · Venue
I

Pure Mathematics

纯数学
Fractional calculus

An estimate for the Riemann–Liouville fractional integral of Lipschitz functions

An original analysis result developed into a complete manuscript, framed toward a Yau / PRIMES-level paper under close advisory supervision.

VenueS.-T. Yau Science Award · PRIMES track
Applied analysis · EPQ

A survey of optimization algorithms in deep-network training

A structured review paper synthesizing first-order and adaptive methods, scoped and written to the extended-project assessment criteria.

VenueEPQ · Independent extended project
II

Physics

物理
Computational plasma physics

A discontinuous-Galerkin scheme for Hall magnetic reconnection

An extended-MHD solver implemented and validated on a reconnection problem — a thesis, poster, and slide defense developed at a level advanced for high school.

VenueRegeneron ISEF track
Quantum field theory

An analytic result in quantum field theory

A theoretical derivation written up as a formatted journal-style article, the argument carried through review-ready structure.

VenueJournal submission
III

Chemistry & Materials

化学与材料
Electrocatalysis

Electrocatalytic ammonia synthesis by nitrate reduction

Tuning the nitrogen-intermediate pathway on a designed catalyst, with materials characterization, a written paper, and a competed regional-to-state showing.

VenueRegional / State Science Fair → ISEF
Environmental materials

A graphene-oxide / PLA composite for water filtration

A biodegradable adsorbent characterized and modeled with Langmuir isotherms (≈197 mg/g capacity) — a coherent three-layer poster, presentation, and analysis.

VenueRegeneron ISEF track
IV

Biology & Medicine

生物与医学
Cancer immunology · epigenetics

An m6A demethylase target in anti-PD-1 immunotherapy response

A computational target analysis linking RNA-methylation machinery to checkpoint-blockade response in lung cancer, developed through several rounds of independent review.

VenueISEF · S.-T. Yau tracks
Causal ML · epidemiology

Causal discovery of disease-risk factors in national health-survey data

A constraint-based (PC-algorithm) causal-structure study over a large public health-survey corpus, evaluated against held-out predictive performance, shown as a competed poster.

VenueScience Fair → ISEF
V

Computer Science & Machine Learning

计算机与机器学习
ML · astronomy

Exoplanet transit detection on Kepler / TESS light curves

A transformer-and-ensemble classifier for transit signals, evaluated with ROC and confusion-matrix analysis — slides and results competed at a regional science fair.

VenueRegional SEF → ISEF track
Computer vision

Real-time semantic segmentation for autonomous driving

A segmentation pipeline trained on an urban-scenes benchmark and tuned past real-time throughput (>30 fps), written as a conference-template paper draft.

VenueCV conference / preprint
Document AI

An engineering-drawing parser from oriented detection and a vision-language model

Oriented-object detection combined with a document-understanding model over a purpose-built dataset of 1,300+ technical drawings — implementation plus a paper in progress.

VenueJournal / conference
VI

Applied Data & Modeling

应用数据与建模
Agent-based modeling

A crowd-evacuation simulation from social-force and floor-field dynamics

A pedestrian-evacuation model built from coupled social-force and floor-field rules, with original code, a poster, and a slide defense.

VenueRegeneron ISEF track
Data science

Participant clustering in on-chain prediction markets

An end-to-end ETL over public prediction-market data with unsupervised clustering (K-Means / GMM) to profile participant behavior — model and poster drafts.

VenueScience competition · academic submission
Civil engineering

A random finite-element model for cold-region pavement rutting

A stochastic FEM simulating rut formation under cold-climate loading, carried through successive manuscript revisions toward peer review.

VenuePeer-reviewed journal

How Mentoring Works

Question → Method → Artifact → Defense
I

Question

提出问题

We begin by finding a question that is real, tractable, and the student's own — narrow enough to finish, open enough to matter.

II

Method

方法

Then the method: the model, the experiment, or the proof, built and debugged week by week until the result holds up to scrutiny.

III

Artifact

成果

The work becomes an artifact — a paper, a poster, a thesis, a slide deck — written and typeset to the standard real review expects.

IV

Defense

答辩

Finally the defense: rehearsing the questions a Grand Award judge actually asks, so the student can stand behind every line.

From a first question to a defended paper.