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Weinan Wang

Assistant Professor · Department of Mathematics · University of Oklahoma

My name is Weinan Wang and I am a tenure-track Assistant Professor in the Department of Mathematics at the University of Oklahoma. I obtained my PhD in Applied Math from the University of Southern California (USC) under the supervision of Igor Kukavica in August 2020. After that, I worked as a postdoctoral fellow at the MSRI and a postdoctoral associate at the University of Arizona mentored by Christopher Henderson. In summer 2023, I was a MSRI research member.

Research Profiles

Google Scholar arXiv ORCID Erdős Number: 3 Einstein Number: 5

Positions

Assistant ProfessorUniversity of Oklahoma, Fall 2023–present
Affiliated Faculty MemberData Institute for Societal Challenges, University of Oklahoma, Spring 2026–present
SLMath Research MemberSimons Laufer Mathematical Sciences Institute, 2023
MSRI Postdoctoral FellowMathematical Sciences Research Institute, 2021
Postdoctoral AssociateUniversity of Arizona, 2020–2023

Research Grants

SEC Visiting Faculty Travel GrantUniversity of Oklahoma, 2025–2026
Simons Foundation MPS-TSM Grant (No. 0007730)Simons Foundation, 2024–2029
AIM SQuaRE GrantAmerican Institute of Mathematics, 2024–2027
Postdoctoral Collaborative Research GrantUniversity of Arizona, 2023
Postdoctoral Collaborative Research GrantUniversity of Arizona, 2022
AMS-Simons Travel GrantAmerican Mathematical Society, 2021–2023

Honors & Awards

Sigma Xi MemberSigma Xi Honor Society, 2025
Junior Faculty FellowUniversity of Oklahoma, 2025
IAS Summer Collaborators AwardInstitute for Advanced Study, Princeton, 2024
MSRI Research MemberMathematical Sciences Research Institute, Berkeley, 2023
MSRI Postdoctoral FellowshipMathematical Sciences Research Institute, Berkeley, 2021
Edward and Dolores Blum Graduate Research PrizeUniversity of Southern California, 2020
Departmental FellowshipUniversity of Southern California, 2019

Research

Operator Learning · AI for Mathematics · PDEs

Research Interests

Applied mathematics; operator learning; AI for Math; scientific AI agent design; Lean formalization; data science; applied optimal transport; Bayesian inverse problems; fluid and kinetic models; mathematical biology/biostatistics; uncertainty quantification; applied probability and statistics; machine learning in scientific computing; optimal control; stochastic processes

Research Overview

A schematic view of my research program: AI4Math, AI4Science, and Lean formalization built on a rigorous mathematical core in PDE analysis, inverse problems, stochastic analysis, mathematical biology and modeling, optimal control, and mean-field games.

Operator Learning, AI, & Data Science

Operator learning for the 2D incompressible Navier-Stokes equations: a conformal prediction approach in the data-scarce regime (with Hao Deng* and Bowen Gang), submitted, 2026.
Neural-network learning and identifiability for mobility-based SEAIR epidemic models, submitted, 2026.
Thresholds and traps in AI reliance: an ODE and network model with relational capital, submitted, 2026.
Sobolev training for neural operator learning: optimal weighting and regularity dependence, submitted, 2026.
Bayesian sequential inference for a stochastic SEIR model with latent transmission dynamics (with Wen Feng), submitted, 2026.

Inverse Problems

A Calderón type inverse problem for the active scalar equations with fractional dissipation (with Li Li), Inverse Problems & Imaging, 22 (2026), no. 1, pp. 53–64.
A remark on the linearized inverse problem for time-separable potentials in vortex dipole dynamics, Applied Mathematics Letters, 179 (2026), Paper No. 109962, 7 pp.
The Calderón problem for fractional space-time parabolic operators with drift, Analysis and Mathematical Physics, 16 (2026), article no. 79.
Recovery of a general analytic Hamiltonian and running costs in mean field games, Communications in Mathematical Sciences, 24 (2026), no. 7, 1999–2022.
On a partial data inverse problem for the semi-linear wave equations (with Boya Liu), submitted, 2025.
An inverse problem for fractional drift-diffusion equations with potentials, submitted, 2025.
Quantitative unique continuation for Robin boundary value problems on C^1,1 domains (with Zongyuan Li), Indiana University Mathematics Journal, 72 (2023), no. 4, 1429–1460.

Math Biology, AI4Science, & Numerical Modeling

Optimal control of a reaction-diffusion epidemic model with noncompliance (with Marcelo Bongarti and Christian Parkinson), European Journal of Applied Mathematics, 37 (2026), no. 2, 313–338.
Learning contact policies for SEIR epidemics on networks: A mean-field game approach, Mathematical Biosciences & Engineering, 23 (2026), no. 7, 2083–2109. DOI: 10.3934/mbe.2026076.
Optimal control in SIR models with noncompliance as a social contagion (with Chloe Ngo and Christian Parkinson), submitted, 2025.
Analysis of a reaction-diffusion SIR epidemic model with noncompliant behavior (with Christian Parkinson), SIAM Journal on Applied Mathematics, 82 (2023), no. 5, 1969–2002.

Fluid Models

Exponential decay for the 3D Boussinesq equations with Navier boundary conditions (with Wen Feng and Xiang Xu***), submitted, 2026.
2D incompressible inviscid Oldroyd-B equations: ill-posedness, Voigt regularization, and high Weissenberg limit number (with Xin Liu), submitted, 2026.
Quantitative bounds of critically bounded solutions to the three-dimensional Navier-Stokes equations in Lorentz spaces (with Wen Feng and Jiao He), Discrete and Continuous Dynamical Systems Series B, 37 (2026), pp. 175–205. DOI: 10.3934/dcdsb.2026048.
On the global stability for the 3D incompressible MHD equations with anisotropic dissipation (with Wen Feng and Jiahong Wu), submitted, 2025.
Asymptotic stability for the 3D Navier-Stokes equations in L³ and nearby spaces (with Zachary Bradshaw), Proceedings of the American Mathematical Society, 153 (2025), no. 9, pp. 3867–3881.
On the space-time analyticity of the inhomogeneous heat equation on the half space with Neumann boundary conditions (with Elie Abdo), Applicable Analysis, 103 (2024), no. 16, 3017–3028.
Stability for a system of the 2D incompressible MHD equations with fractional dissipation (with Wen Feng and Jiahong Wu), Journal of Mathematical Fluid Mechanics, 26 (2024), no. 4, paper no. 57.
On the global well-posedness and analyticity of some electrodiffusion models in ideal fluids and porous media (with Elie Abdo and Fizay-Noah Lee), SIAM Journal on Mathematical Analysis, 55 (2023), no. 6, 6838–6866.
Nonlinear stability for the 2D incompressible MHD system with fractional dissipation in the horizontal direction (with Wen Feng and Jiahong Wu), Journal of Evolution Equations, 23 (2023), no. 2, paper No. 32, 37 pp.
On the analyticity and Gevrey regularity of solutions to the three-dimensional inviscid Boussinesq equations in a half space. Communications in Mathematical Sciences, 20 (2022), no. 2, 479–493.
Global existence and stability for the 2D Oldroyd-B model with mixed partial dissipation (with Wen Feng and Jiahong Wu), Proceedings of the American Mathematical Society, 150 (2022), no. 12, 5321–5334.
On the global stability of large solutions for the Boussinesq equations with Navier boundary conditions, Archiv der Mathematik, 116 (2021), no. 4, 445–456.
Norm inflation for the Boussinesq system (with Zongyuan Li), Discrete and Continuous Dynamical Systems Series B, 26 (2021), no. 10, 5449–5463.
Global Sobolev persistence for the fractional Boussinesq equations with zero diffusivity (with Igor Kukavica), Pure and Applied Functional Analysis, 5 (2020), no. 1, 27–45.
Long time behavior of solutions to the 2D Boussinesq equations with zero diffusivity (with Igor Kukavica), Journal of Dynamics and Differential Equations, 32 (2020), no. 4, 2061–2077.
On the global regularity for a 3D Boussinesq model without thermal diffusion, Zeitschrift für Angewandte Mathematik und Physik, 70 (2019), no. 6, paper 174.

Kinetic Models

A note on relativistic kinetic Schauder estimates, submitted, 2026.
Several counterexamples to kinetic Schauder estimates (with Hongjie Dong), submitted, 2026.
On the axi-symmetric solutions to the Landau-Fermi-Dirac equations, submitted, 2025.
A kinetic Nash inequality and precise boundary behavior of the kinetic Fokker-Planck equation (with Christopher Henderson and Giacomo Lucertini**), submitted, 2024.
Kinetic Schauder estimates with time-irregular coefficients and uniqueness for the Landau equation (with Christopher Henderson), Discrete and Continuous Dynamical Systems, 44 (2024), no. 4, 1026–1072.
Local well-posedness for the Boltzmann equation with very soft potential and polynomially decaying initial data (with Christopher Henderson), SIAM Journal on Mathematical Analysis, 54 (2022), no. 3, 2845–2875.

Stochastic Processes

A stochastic compartmental model for epidemiology with human behavior (with Christian Parkinson), Mathematical Biosciences, 392 (2026), paper No. 109588.
Global well-posedness and enhanced dissipation for the 2D stochastic Nernst-Planck-Navier-Stokes equations with transport noise (with Quyuan Lin and Rongchang Liu), Stochastic Processes and their Applications, 184 (2025), paper no. 104603.
Global existence for the stochastic Boussinesq equations with transport noise and small rough data (with Quyuan Lin and Rongchang Liu), SIAM Journal on Mathematical Analysis, 56 (2024), no. 1, 501–528.
Almost sure existence of global weak solutions to the Boussinesq equations (with Haitian Yue), Dynamics of PDEs, 17 (2020), no. 2, 165–183.

Interdisciplinary Research

Adaptive Disinformation Diffusion on Networks with Heterogeneous Node and Link Dynamics (with Alice Nanyanzi, Sridhar Radhakrishnan, Kash Barker, Venu Sirisanagandla), IEEE Transactions on Computational Social Systems, Early Access, pp. 1–21, published online May 12, 2026. DOI: 10.1109/TCSS.2026.3686750.

AI Lab

Interactive AI Tools for Science & Mathematics

AI Research Infrastructure. I design, evaluate, and deploy AI systems for mathematical research — domain-specialized language models, autonomous research AI agents, agent RL for reward-trained ranking, and interactive scientific simulations. My newest direction is multi-agent system (MAS) design: small specialist agents hand work to one another, critique intermediate outputs, and expose their conversation so users can see how a statistical or numerical analysis is assembled.

Interactive Lab Banner

Interactive Cloth Lab Weinan Wang AI Lab

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Large Language Models (LLMs) for Research

Domain-specialized language models developed by Weinan Wang (2025-present), fine-tuned for technical research across mathematical biology, applied mathematics, operations research, and optimal control. Unlike general-purpose chatbots, these models are trained to reason with research-level terminology, notation, and technical depth.

Training and evaluation were supported in part by computational resources from the University of Oklahoma Supercomputing Center for Education & Research (OSCER) and the Data Institute for Societal Challenges (DISC).

MathBio AI (7B)

Fine-tuned from Qwen2.5-Math-7B on 27,000 arXiv examples covering epidemic modeling, PDEs, operator learning, and mathematical biology.

Open MathBio Agent →

Tornado AI (How to use AI to predict tornadoes?)

Tornado-focused AI/LLM for interpreting Oklahoma severe-weather observations and short-term convective regimes.

Open Tornado AI →

RESEARCH MODEL OptimAI (7B)

Fine-tuned Qwen2.5-Math-7B for operations research and optimal control. Formulates, solves, and explains LP/IP, network flow, inventory, queuing, and LQR problems.

RESEARCH GRADE MathBio AI (72B)

Larger model trained on the OU Schooner supercomputer. Achieves 0.738 overall on the math-bio benchmark. Evaluation release in progress.

Embed a live MathBio demo ↓

Open the full MathBio app →

LeanPilot AI

A formal-mathematics AI track developed by Weinan Wang (2025-present), connecting domain-specialized LLM reasoning with Lean 4 verification. The project is designed for translating research mathematics into Lean statements, drafting proof skeletons, debugging proof states, and building reusable formalization workflows for PDEs, operator learning, and mathematical biology.

LEANPILOT AI LeanPilot AI Assistant

Developed by Weinan Wang as an LLM assistant for theorem formalization, Lean 4 statement drafting, proof-state interpretation, and Mathlib-aware proof repair.

Open LeanPilot AI →

Agentic AI

Research AI systems by Weinan Wang, including agentic literature tools, scientific-computing assistants, and reward-trained ranking components where feedback data is available.

Math Research AI Agent (by Weinan Wang, 2026-present) — AI research assistant that turns a mathematician's arXiv record into a structured map of papers, themes, reading paths, first steps, and possible project directions. Open Math Research AI Agent
Google Scholar AI Agent (by Weinan Wang, 2026-present) — Citation and literature radar that works from Google Scholar alert files, research interests, and paper metadata to rank scholarly items and produce citation-quality briefings. Open Google Scholar AI Agent
arXiv AI Agent (by Weinan Wang, 2026-present) — Interactive arXiv AI agent for exploring recent papers by research interests, keywords, and arXiv categories, with an RL-trained paper-ranking component trained from research-memory reward signals. Open arXiv AI Agent
AI for Math Biology (by Weinan Wang, 2026-present) — LLM-powered research AI agent for ODE/SDE/PDE epidemic models with real-time parameter estimation, stochastic simulation, and optimal control. MathBio AI Agent
AI for Fluid Dynamics & Weather (by Weinan Wang, 2025-present) — Neural surrogate training (Fourier Neural Operator), automated regime discovery, and LLM experiment planning over a real-time fluid dynamics solver with the National Weather Center (Norman, OK) data integration. Fluid&Weather AI Agent
AI for Human Behavior in Epidemics (by Weinan Wang, 2025-present) — Agent-based simulation comparing 6 behavioral adaptation mechanisms (prevalence-dependent, media/awareness, game-theoretic, policy threshold, fatigue). HumanBehavior AI Agent

Multi-Agent System

These systems are built as a connected scientific AI ecosystem, not separate chat boxes. Each run follows a shared protocol — question, assumptions, method choice, Python/R/MATLAB code, diagnostics, critique, and final memo — while specialized agents exchange artifacts, relay packets, judge scores, and human-gated memory candidates across statistics, numerical analysis, decision optimization, and self-improvement.

AI for Statistics

From messy data to statistical memo

Data-Cleaning, Statistician, Visualization, and Report agents talk through dataset quality, variable roles, assumptions, model choice, plots, Python/R/MATLAB drafts, and cautious interpretation. The shared engine adds judge scores, staged memory, and relay packets for numerical-analysis or decision-model follow-up.

Shared protocolPython + R + MATLABStats-numerics relay

Designed and developed by Weinan Wang.

Shared Protocoldata, code, plots, memo

Data-Cleaningaudit + repair

diagnostics

Statisticianassumptions + model

model brief

Visualizationplots + patterns

figure notes

Reportmemo + code

revision

Agent conversation: each robot sends an artifact into the shared workspace, then receives critique from the next specialist.

Conversation replay

Data-Cleaning: Dataset audit complete: missingness and variable types are documented.

clean data

Open AI for Statistics

AI for Numerical Analysis

From PDE/ODE prompt to computational evidence

Classifier, formulation, method-design, stability, implementation, benchmark, visualization, paper, and reproducibility agents coordinate schemes, Python/R/MATLAB solver drafts, convergence checks, and research-note guardrails. The shared engine turns convergence tables into statistics-side uncertainty and decision-model handoffs.

Shared protocolPython + R + MATLABStatistics relay

Designed and developed by Weinan Wang.

Numerical Labscheme, solver, evidence, notes

ClassifierPDE/ODE type

Formulationvariables + domain

Methodsolver design

Stabilityerror + CFL

CodePy/R/MATLAB

Benchmarkconvergence

Visualizationtables + plots

Reproducibilitynotes + limits

problem scheme stability code evidence figures archive limits

Agent conversation: the orbit makes the feedback loop visible: formulation shapes the method, stability constrains code, and benchmarks push revisions back into the lab.

Conversation replay

Classifier: Classified as a parabolic PDE with mixed boundary data.

problem class

Open AI for Numerical Analysis

AI for Optimal Control + OR

From decision problem to audited operating plan

Gateway, Formulator, Constraint Modeler, Method Selector, Solver Architect, Verifier, Simulation, Visualization, and Decision Memo agents coordinate states, controls, constraints, solver choices, Python/R/MATLAB drafts, feasibility checks, trajectories, and a cautious recommendation under the same shared protocol.

Shared protocolPython + R + MATLABDecision handoffs

Designed and developed by Weinan Wang.

Decision Labmodel, solver, audit, memo

Gatewayproblem route

Formulatorstates + controls

MethodLP/MILP/MPC

Solvercode artifacts

Verifierfeasibility

Simulationstress path

Visualizationplots + slack

Memooperating plan

scope model method code audit stress figures memo

Decision conversation: optimization agents pass a structured plan around the orbit, so constraints, solver code, feasibility, simulation, and the final memo can critique one another before the recommendation lands.

Conversation replay

Gateway: Routed the request to a constrained dynamic-control workflow.

decision scope

Open AI for Optimal Control + OR

Self-Improving Agents

From one run to a better next run

An OpenClaw-style gateway, Hermes-compatible backend lane, critic, benchmark, and memory agents turn each scientific answer into a scored revision loop for statistics, numerical analysis, and optimal-control/OR tasks. The export bundle includes Python/R/MATLAB adapter sketches, staged memory, and a human approval gate before promotion.

Shared protocolHuman approval gatePython + R + MATLAB

Designed and developed by Weinan Wang.

Learning Loopanswer, critique, score, memory

GatewayOpenClaw-style route

route

ReasonerHermes lane

draft

Criticflags + fixes

critique

Benchmarkscore + gate

score

Memorylessons kept

lesson

Reportnext-run plan

Self-improvement loop: the first answer is not the endpoint; critics, benchmarks, and memory convert it into a more disciplined next run.

Conversation replay

Gateway: Routed the scientific request and attached the prior run context.

run context

Open Self-Improving Agents

Publications

Key: * = undergrad | ** = grad student | *** = postdoc mentee | † = non-alphabetical authorship

Google Scholar arXiv

43.
A note on relativistic kinetic Schauder estimates
submitted, 2026
Submitted
42.
*** Exponential decay for the 3D Boussinesq equations with Navier boundary conditions
with Wen Feng and Xiang Xu*** · submitted, 2026
SubmittedPostdoc Mentee
41.
Several counterexamples to kinetic Schauder estimates
with Hongjie Dong · submitted, 2026
Submitted
40.
†* Operator learning for the 2D incompressible Navier-Stokes equations: a conformal prediction approach in the data-scarce regime
with Hao Deng* and Bowen Gang · submitted, 2026
SubmittedUndergrad
39.
2D incompressible inviscid Oldroyd-B equations: ill-posedness, Voigt regularization, and high Weissenberg limit number
with Xin Liu · submitted, 2026
Submitted
38.
Neural-network learning and identifiability for mobility-based SEAIR epidemic models
submitted, 2026
Submitted
37.
†* Adaptive Disinformation Diffusion on Networks with Heterogeneous Node and Link Dynamics
with Alice Nanyanzi, Sridhar Radhakrishnan, Kash Barker, Venu Sirisanagandla · IEEE Transactions on Computational Social Systems, Early Access, pp. 1–21, published online May 12, 2026. DOI: 10.1109/TCSS.2026.3686750
PublishedGrad Student
36.
Sobolev training for neural operator learning: optimal weighting and regularity dependence
submitted, 2026
Submitted
35.
A Calderón type inverse problem for the active scalar equations with fractional dissipation
with Li Li · Inverse Problems & Imaging, 22 (2026), no. 1, pp. 53–64
Published
34.
A remark on the linearized inverse problem for time-separable potentials in vortex dipole dynamics
Applied Mathematics Letters, 179 (2026), Paper No. 109962, 7 pp.
Published
33.
A compartmental model for epidemiology with human behavior and stochastic effects
with Christian Parkinson · Mathematical Biosciences, 392 (2026), paper No. 109588
Published
32.
The Calderón problem for fractional space-time parabolic operators with drift
Analysis and Mathematical Physics, 16 (2026), article no. 79
Published
31.
Quantitative bounds of critically bounded solutions to the three-dimensional Navier-Stokes equations in Lorentz spaces
with Wen Feng and Jiao He · Discrete and Continuous Dynamical Systems Series B, 37 (2026), pp. 175–205. DOI: 10.3934/dcdsb.2026048
Published
30.
Recovery of a general analytic Hamiltonian and running costs in mean field games
Communications in Mathematical Sciences, 24 (2026), no. 7, 1999–2022
Published
29.
Optimal control of a reaction-diffusion epidemic model with noncompliance
with Marcelo Bongarti and Christian Parkinson · European Journal of Applied Mathematics, 37 (2026), no. 2, 313–338
Published
28.
Thresholds and traps in AI reliance: an ODE and network model with relational capital
submitted, 2026
Submitted
27.
Bayesian sequential inference for a stochastic SEIR model with latent transmission dynamics
with Wen Feng · submitted, 2026
Submitted
26.
Learning contact policies for SEIR epidemics on networks: A mean-field game approach
Mathematical Biosciences & Engineering, 23 (2026), no. 7, 2083–2109. DOI: 10.3934/mbe.2026076
Published
25.
On a partial data inverse problem for the semi-linear wave equations
with Boya Liu · submitted, 2025
Submitted

24.
* Optimal control in SIR models with noncompliance as a social contagion
with Chloe Ngo* and Christian Parkinson · submitted, 2025
SubmittedUndergrad
23.
An inverse problem for fractional drift-diffusion equations with potentials
submitted, 2025
Submitted
22.
On the global stability for the 3D incompressible MHD equations with anisotropic dissipation
with Wen Feng and Jiahong Wu · submitted, 2025
Submitted
21.
On the axi-symmetric solutions to the Landau-Fermi-Dirac equations
submitted, 2025
Submitted
20.
Global well-posedness and enhanced dissipation for the 2D stochastic Nernst-Planck-Navier-Stokes equations with transport noise
with Quyuan Lin and Rongchang Liu · Stochastic Processes and their Applications, 184 (2025), paper no. 104603
Published
19.
Asymptotic stability for the 3D Navier-Stokes equations in L³ and nearby spaces
with Zachary Bradshaw · Proceedings of the American Mathematical Society, 153 (2025), no. 9, pp. 3867–3881
Published

18.
** A kinetic Nash inequality and precise boundary behavior of the kinetic Fokker-Planck equation
with Christopher Henderson and Giacomo Lucertini** · submitted, 2024
SubmittedGrad Student
17.
** On the space-time analyticity of the inhomogeneous heat equation on the half space with Neumann boundary conditions
with Elie Abdo** · Applicable Analysis, 103 (2024), no. 16, 3017–3028
PublishedGrad Student
16.
Global existence for the stochastic Boussinesq equations with transport noise and small rough data
with Quyuan Lin and Rongchang Liu · SIAM Journal on Mathematical Analysis, 56 (2024), no. 1, 501–528
Published
15.
Kinetic Schauder estimates with time-irregular coefficients and uniqueness for the Landau equation
with Christopher Henderson · Discrete and Continuous Dynamical Systems, 44 (2024), no. 4, 1026–1072
Published
14.
Stability for a system of the 2D incompressible MHD equations with fractional dissipation
with Wen Feng and Jiahong Wu · Journal of Mathematical Fluid Mechanics, 26 (2024), no. 4, paper no. 57
Published

13.
Quantitative unique continuation for Robin boundary value problems on C¹·¹ domains
with Zongyuan Li · Indiana University Mathematics Journal, 72 (2023), no. 4, 1429–1460
Published
12.
Analysis of a reaction-diffusion SIR epidemic model with noncompliant behavior
with Christian Parkinson · SIAM Journal on Applied Mathematics, 82 (2023), no. 5, 1969–2002
Published
11.
** On the global well-posedness and analyticity of some electrodiffusion models in ideal fluids and porous media
with Elie Abdo** and Fizay-Noah Lee** · SIAM Journal on Mathematical Analysis, 55 (2023), no. 6, 6838–6866
PublishedGrad Student
10.
Nonlinear stability for the 2D incompressible MHD system with fractional dissipation in the horizontal direction
with Wen Feng and Jiahong Wu · Journal of Evolution Equations, 23 (2023), no. 2, paper No. 32
Published

9.
Local well-posedness for the Boltzmann equation with very soft potential and polynomially decaying initial data
with Christopher Henderson · SIAM Journal on Mathematical Analysis, 54 (2022), no. 3, 2845–2875
Published
8.
On the analyticity and Gevrey regularity of solutions to the three-dimensional inviscid Boussinesq equations in a half space
Communications in Mathematical Sciences, 20 (2022), no. 2, 479–493
Published
7.
Global existence and stability for the 2D Oldroyd-B model with mixed partial dissipation
with Wen Feng and Jiahong Wu · Proceedings of the American Mathematical Society, 150 (2022), no. 12, 5321–5334
Published
6.
On the global stability of large solutions for the Boussinesq equations with Navier boundary conditions
Archiv der Mathematik, 116 (2021), no. 4, 445–456
Published
5.
Norm inflation for the Boussinesq system
with Zongyuan Li · Discrete and Continuous Dynamical Systems Series B, 26 (2021), no. 10, 5449–5463
Published
4.
Almost sure existence of global weak solutions to the Boussinesq equations
with Haitian Yue · Dynamics of PDEs, 17 (2020), no. 2, 165–183
Published
3.
Global Sobolev persistence for the fractional Boussinesq equations with zero diffusivity
with Igor Kukavica · Pure and Applied Functional Analysis, 5 (2020), no. 1, 27–45
Published
2.
Long time behavior of solutions to the 2D Boussinesq equations with zero diffusivity
with Igor Kukavica · Journal of Dynamics and Differential Equations, 32 (2020), no. 4, 2061–2077
Published
1.
On the global regularity for a 3D Boussinesq model without thermal diffusion
Zeitschrift für Angewandte Mathematik und Physik, 70 (2019), no. 6, paper 174
Published

Teaching

University of Oklahoma · Fall 2023–present

Course Notes

AIcademic Advisor

An OU Mathematics advising prototype that turns the 2026-2027 catalog into a deterministic degree audit, prerequisite check, next-course planner, and cited agent handoff.

Pilot scope: Mathematics B.A. Standard Option and B.S. Professional Option.
Advising model: public catalog data first, AI explanations second, human advisor handoff when policy risk appears.
Status: Hugging Face testing deployment for early OU Math experiments.

Launch Hugging Face prototype

Courses at the University of Oklahoma

Math 1914Differential and Integral Calculus IFall 2026
Math 4163Introduction to PDEsSpring 2026
Math 3990Independent StudySpring 2026
Math 3440Mentored Research ExperienceSpring 2026
Math 3423Physical Mathematics IIFall 2025
Math 3980Honors ResearchFall 2025
Math 3440Mentored Research ExperienceSummer 2025
Math 2924Differential and Integral Calculus IISpring 2025
Math 3980Honors ResearchSpring 2025
Math 4433Introduction to Analysis IFall 2024
Math 2934Differential and Integral Calculus III (Honors)Fall 2024
Math 4073Numerical Analysis ISpring 2024
Math 2934Differential and Integral Calculus IIISpring 2024
Math 2443Calculus and Analytic Geometry IVFall 2023

Service & Outreach

Conferences, committees, reviewing, and community engagement

Conferences & Seminars

Organizer, Special Session on Recent Trends in Differential Equations and Optimal Control with Biological Applications, JMM, Chicago, IL, Jan. 12–15, 2027
Organizer, Special Session on Recent Developments in PDEs and Inverse Problems, JMM, Washington DC, Jan. 2026
Organizer, OSU-OU Joint PDE Seminar, OU & OSU, Spring 2026–present
Organizer, Special Session on Recent Developments in PDEs and Related Areas, JMM, Seattle, Jan. 2025
Organizer, Special Session on Dynamics and Regularity of PDEs, JMM, San Francisco, Jan. 2024
Organizer, Analysis Seminar, University of Oklahoma, Fall 2023–present
Organizer, Analysis, Dynamics, and Applications Seminar, University of Arizona, Fall 2022–Spring 2023
Organizer, Early Career Math Colloquium, Online, Spring 2022–Spring 2024
Organizer, AMS Eastern Sectional — Topics in PDEs and Harmonic Analysis, UMass Amherst, Oct. 2022
Organizer, AMS Special Session — Regularity Theory for Linear and Nonlinear PDEs, AMS Western Sectional, May 2021

Editorial Board

Editorial Board Member, Scientific Reports, 2026–present

Review Activities

Reviewer for zbMATH and Mathematical Reviews / MathSciNet. Journal reviewer for:

Advanced Nonlinear Studies
Annals of Applied Statistics (AOAS)
Communications in Statistics - Theory and Methods
Communications on Pure and Applied Analysis
Discrete and Continuous Dynamical Systems-B
Journal of Differential Equations
Journal of Functional Analysis
Journal of Mathematical Analysis & Applications
Journal of Mathematical Fluid Mechanics
Journal of Nonlinear Science
Mathematical Biosciences
Mathematical Biosciences and Engineering
Networks and Heterogeneous Media
Nonlinearity
Physics of Fluids
Potential Analysis
Risk Analysis
SIAM Journal on Mathematical Analysis
Zeitschrift für Angewandte Mathematik und Physik

Committees

2025–2026 Department of Mathematics, University of Oklahoma

Undergraduate Awards Committee
First Year Math Committee
OU Math Day Committee
Undergraduate Committee
Newsletter Committee

2024–2025 Department of Mathematics, University of Oklahoma

OU Math Day Committee
Undergraduate Committee
Syllabi Preparation Committee
Newsletter Committee

2023–2024 Department of Mathematics, University of Oklahoma

Undergraduate Committee
Syllabi Preparation Committee
Newsletter Committee

2022–2023 Department of Mathematics, University of Arizona

Undergraduate Committee
Undergraduate Awards and Scholarship Sub-Committee
Teaching Representative of the Postdoc Committee

2021–2022 Department of Mathematics, University of Arizona

Undergraduate Committee
Undergraduate Awards and Scholarship Sub-Committee
Teaching Representative of the Postdoc Committee

Outreach

Math Alliance mentor for doctoral and pre-doctoral students, Fall 2023–present
Nov 6, 2025 — Co-organized OU Math Day for over 300 high school students.
Apr 22, 2025 — Shared research on applications of differential equations at the OU Math Club.
Nov 7, 2024 — Co-organized OU Math Day for over 400 high school students.
Spring 2023 — Mentored five students on "Non-pharmaceutical Interventions for Disease Spread Mitigation" in Math 485 at UArizona.

Early Career Math Colloquium

Organizers: Rongchang Liu, Christian Parkinson, and Weinan Wang

Goal: To provide junior mathematicians (graduate students, postdocs, assistant professors), especially those from underrepresented groups, with an opportunity to showcase their research. All talks are recorded (with permission) and available on YouTube.

YouTube Channel ResearchSeminars.org Zoom Link

Spring 2024

Thursdays, 2:00–3:00pm CST

Feb 8 Patrick Phelps (Temple University)
Feb 22 Amélie Loher (University of Cambridge)
Feb 29 Xin Liu (Texas A&M University)
Mar 14 Chunyin Siu (Cornell University)
Mar 21 Son Tu (Michigan State University)
Mar 28 Zhongkai Tao (UC Berkeley)
Apr 4 Tommaso Rosati (University of Warwick)
Apr 11 Aurélie Paull (Institut Élie Cartan de Lorraine)
Apr 11 Yongquan Zhang (Stony Brook University)
Apr 18 Jiaxin Jin (Ohio State University)
Apr 25 Yupei Huang (Duke University)
May 2 Yeor Hafouta (University of Florida)

Fall 2023

Mondays, 2:00–3:00pm CST

Sep 18 Daniel McKenzie (Colorado School of Mines)
Sep 25 Albert Ai (University of Wisconsin-Madison)
Oct 2 Margherita Zanella (Polytechnic University of Milan)
Oct 16 Marissa Gee (Cornell University)
Oct 23 Matthew Hernandez (University of Maine)
Oct 30 Bohyun Kim (University of Utah)
Nov 6 Wen Feng (Niagara University)
Nov 13 Jin Tan (Cergy Paris University)
Nov 20 Michele Dolce (EPFL, Switzerland)
Nov 27 Dwight Williams II (Morgan State University)
Dec 4 Antonio Agresti (Delft University of Technology)

Spring 2023

Wednesdays, 2:30–3:30pm Arizona time

Feb 1 Yuzhe Zhu (University of Cambridge)
Feb 8 Sarah Strikwerda (NC State University)
Feb 15 Elliot Cartee (University of Chicago)
Mar 1 Michael Lindstrom (UT Rio Grande Valley)
Mar 15 Yotam Yaniv (UCLA)
Mar 22 Quyuan Lin (UC Santa Barbara)
Mar 29 Mengxuan Yang (UC Berkeley)
Apr 5 Katherine Zhiyuan Zhang (Courant Institute, NYU)
Apr 12 Xueying Yu (University of Washington)
Apr 19 Lucio Galeati (EPFL, Switzerland)
Apr 26 Brennan Sprinkle (Colorado School of Mines)
May 3 Khoa Le (University of Leeds)

Fall 2022

Organizers: Christian Parkinson and Weinan Wang · Wednesdays, 2:30–3:30pm Arizona time

Sep 7 Austin Christian (Georgia Institute of Technology)
Sep 14 Fizay-Noah Lee (Princeton University)
Sep 21 Samy Wu Fung (Colorado School of Mines)
Oct 12 Marcelo Bongarti (Weierstrass Institute, Germany)
Oct 19 Evan Miller (University of British Columbia)
Oct 26 Hanye Zhu (Brown University)
Nov 2 Jake Brusca (New Jersey Institute of Technology)
Nov 9 Kevin Miller (Oden Institute, UT Austin)
Nov 16 Federico Pasqualotto (Duke University)
Nov 23 Havva Yoldış (Delft University of Technology)
Nov 30 Wen Feng (Niagara University)

Spring 2022

Organizers: Ethan O'Brien and Weinan Wang · Fridays, 12:00–1:00pm Arizona time

Feb 11 Trinh Nguyen (USC)
Feb 25 Stan Palasek (UCLA)
Mar 18 Doug Pfeffer (Berry College)
Mar 25 Jaemin Park (University of Barcelona)
Apr 1 Guher Camliyurt (University of Chicago)
Apr 8 Elie Abdo (Temple University)
Apr 15 Alison Mirin (University of Arizona)
Apr 22 Renato Velozo Ruiz (University of Cambridge)

Computational Labs & Software

Interactive scientific labs and research software from the Wang Lab

Interactive Research Labs

Interactive research demos for inverse problems, epidemic dynamics, incompressible fluids, and kinetic particle models.

Inverse Problems Lab

Epidemic Flow Field

INTERACTIVE RESEARCH LAB

Epidemic Flow Field by Weinan Wang

60 FPS
3,200 AGENTS

Parameters

Transmission β0.35

Recovery γ0.12

Mobility0.45

Intervention0.00

Live Readout

Susceptible3200

Infected0

Recovered0

I(t) over time

Click anywhere to infect · Drag to spread

Agent-based SIR dynamics on a 2D lattice. Each dot is an individual agent following a continuous-time stochastic SIR process with local mobility. Adjust parameters, click to seed an outbreak, and watch the epidemic curve develop.

Fluid Dynamics Lab

Kinetic Equation Lab

R Packages on CRAN

seairmobility: Mobility-Based SEAIR Epidemic Models (Weinan Wang, 2026) — Tools for simulating, analysing, and fitting mobility-based SEAIR compartmental epidemic models with heterogeneous individual mobility. Provides a numerical PDE solver, closed-form computation of the basic reproduction number R₀ and final epidemic size, and a least-squares routine for recovering the mobility distribution from observed aggregate symptomatic time series. Version 0.1.0 · Published 2026-04-28 · License: MIT · DOI: 10.32614/CRAN.package.seairmobility

CRAN Page → install.packages("seairmobility")
npfseir: Nested Particle Filter for Stochastic SEIR Epidemic Models (Weinan Wang, 2026) — Provides online Bayesian inference for stochastic SEIR epidemic models with time-varying transmission. Uses a nested particle filter for joint state and parameter estimation, with utilities for simulation, posterior summarisation, and forecasting. Version 0.2.1 · Published 2026-04-24 · License: MIT · DOI: 10.32614/CRAN.package.npfseir

CRAN Page → install.packages("npfseir")
seirMFG: Mean-Field Game Equilibrium for SEIR Epidemics on Networks (Weinan Wang, 2026) — Implements the forward-backward sweep algorithm for computing Nash equilibrium contact policies in SEIR epidemic mean-field games on heterogeneous contact networks. Supports heterogeneous networks with susceptible contact effort, value functions, epidemic trajectories, and the effective reproduction number R_t. Version 0.1.0 · Published 2026-04-09 · License: MIT · DOI: 10.32614/CRAN.package.seirMFG

CRAN Page → install.packages("seirMFG")

Mentoring

Undergraduate Research · Postdoctoral Mentoring · Collaborative Projects

Mentoring Philosophy

My group works at the intersection of operator learning, applied PDEs, AI for mathematics, inverse problems, statistics/biostatistics, mathematical biology, stochastic processes, and optimal control. Students at every level — first‑year undergraduates through postdoctoral fellows — take on projects that combine mathematical modeling, rigorous analysis, scientific computation, and clear research writing.

Each project is shaped to the student's background and interests. I try to keep the questions concrete enough to make progress on in a semester, and open enough that the work can grow into a poster, a thesis, or a paper. We meet weekly, read together, code together, and write together.

ModelingTranslating questions in biology, epidemiology, and the sciences into PDE / ODE / stochastic models.

AnalysisStability, well‑posedness, regularity, and optimal control of the resulting equations.

ComputationNumerical schemes, operator learning, and data‑driven inference in Python and R.

CommunicationWriting, figure‑making, and presenting at undergraduate research symposia and beyond.

Current Members

PG

Petr Groshenko Undergraduate

OU · Fall 2026–present

AI-for-Math and machine learning.

HRAP — Honors Research Assistant Program

VL

Victor Lu Undergraduate

OU · Spring 2026–present

AI-for-Math, LLM ranking, and machine learning.

Independent Study — Math 3440

HD

Hao Deng Undergraduate

Fall 2025–present · co‑advised with Bowen Gang (University of Alberta)

Operator learning and data analysis for parametric PDE problems.

PaperOperator learning for the 2D incompressible Navier-Stokes equations: a conformal prediction approach in the data-scarce regime (with Hao Deng* and Bowen Gang), submitted, 2026.

Visiting / co‑advised research

XX

Xiang Xu Postdoctoral Fellow

Department of Mathematics, OU · Fall 2025–present

Applied PDEs · analysis of fluid and kinetic equations.

PaperExponential decay for the 3D Boussinesq equations with Navier boundary conditions (with Wen Feng and Xiang Xu), submitted, 2026.

Undergraduate Research Projects

Mathematical Biology · Behavior

Data‑driven epidemic modeling with human behavior

Anubhab Ganguly

Epidemic models in which compliance, awareness, and contact behavior are coupled to the disease dynamics, calibrated against outbreak data.

ODE / PDE modelingData calibrationPython

Optimal Control · Epidemiology

Optimal control of epidemic models

Chloe Ngo (with Christian Parkinson; Michigan State University)

SIR‑type systems with intervention costs, studied via the Pontryagin maximum principle, with noncompliance modeled as a social contagion.

Pontryagin maximum principleOptimal controlNumerical optimization

PaperNgo, Parkinson, Wang — Optimal control in SIR models with noncompliance as a social contagion, submitted 2025.

Next position: Graduate school in the Economics program at Duke University.

AI for Mathematics

Operator learning and data analysis

Hao Deng (with B. Gang, University of Alberta)

Neural surrogates for families of parametric PDE problems, and the data analysis questions surrounding their training and evaluation.

Operator learningPDE surrogatesData analysis

PaperDeng, Gang, Wang — Operator learning for the 2D incompressible Navier-Stokes equations: a conformal prediction approach in the data-scarce regime, submitted 2026.

AI-for-Math · Machine Learning

AI-for-Math and machine learning

Petr Groshenko

Research on machine-learning methods for mathematical reasoning, formalization workflows, and computational tools for research mathematics.

AI-for-MathMachine learningMathematical reasoning

AI-for-Math · Machine Learning · Biology

Machine learning and mathematical biological models

Victor Lu

Independent study (Math 3440) exploring how machine‑learning methods interact with classical mathematical models in biology.

AI-for-MathMachine learningMathematical biologyPython

Mathematical Biology · Data

Data‑driven methodologies for mathematical models in biology

Lorelei Starling (with Christian Parkinson; Michigan State University)

HRAP project on data‑driven approaches to building, calibrating, and analyzing mathematical models in biology.

Mathematical biologyData‑driven modeling

Networks · Epidemiology

Network analysis in epidemic disease modeling

Laila Ruslan

Summer project on how contact‑network structure shapes epidemic thresholds and outbreak size.

Network scienceEpidemic modeling

Research Figures

Animated SIR phase-plane streamlines with a moving intervention band. — Fig. 1 Epidemic intervention schematic SI(R) phase‑plane streamlines with behavior coupling.

Animated optimal-control curve with pulsing switching points. — Fig. 2 Optimal control policies Switching structure of u*(t) for SIR with noncompliance.

Animated operator-learning heat field across changing parameters. — Fig. 3 Operator learning surrogates Predicted PDE solution field across parameter samples.

Animated Boltzmann-type particle cloud with moving velocities and collision highlights. — Fig. 4 Kinetic particle simulations Snapshot of a Boltzmann‑type simulation in a periodic box.

Past Mentees & Outcomes

Spring 2026

Lorelei Starling Undergraduate
HRAP, OU. Co‑mentored with Christian Parkinson. Data‑driven methodologies for mathematical models in biology.
Summer 2025 – Spring 2026

Anubhab Ganguly Undergraduate
Independent Study and Honors Research, partially supported by the Junior Faculty Fellowship, OU. Data‑driven epidemic modeling that couples disease dynamics with human behavior.
Fall 2024 – Fall 2025

Chloe Ngo Undergraduate
HRAP, OU. Co‑mentored with Christian Parkinson. Optimal control of epidemic disease via the Pontryagin maximum principle.

PaperNgo, Parkinson, Wang — Optimal control in SIR models with noncompliance as a social contagion, submitted 2025.

Next position: Graduate school in the Economics program at Duke University.
Summer 2025

Laila Ruslan Undergraduate
Summer Research Assistant, OU. Network analysis in epidemic disease modeling.
Spring 2025

Ava Cimini Undergraduate
HRAP, OU. Optimal control of the SIR model.
Spring 2022

Nathan Gomez Undergraduate
Undergraduate Teaching Assistant Program, University of Arizona.
Spring 2022

Lenox Baloglou Undergraduate
Undergraduate Teaching Assistant Program, University of Arizona.
Fall 2021

Jack Hall Undergraduate
Undergraduate Teaching Assistant Program, University of Arizona.

For Students Interested in Joining

Get in touch.

I am happy to talk with OU undergraduates and graduate students who would like to work on a research project — through HRAP, an Independent Study, an honors thesis, or a summer assistantship. Visiting and remotely co‑advised students are also welcome when there is a clear scientific overlap.

The best first step is a short email (ww@ou.edu) describing the courses you have taken, what you have enjoyed in them, and a few sentences about what kind of question would excite you to work on for a semester. No prior research experience is needed — only curiosity, persistence, and a willingness to write things down carefully.

Good fits include

Applied mathematics & analysis
Partial differential equations
Probability & stochastic processes
Scientific computing
Machine learning & data analysis
Mathematical biology & epidemiology
Optimal control
Lean / formal mathematics