Research collaboration board

Projects for collaborators, junior researchers, and students

Browse open directions in numerical PDEs, entropy-stable schemes, AI-assisted solvers, and scientific computing education. Each item is designed to be concrete enough to start a conversation.

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Project Board

Showing all projects

Good first projectPython/MATLAB

Reproduce a scalar conservation law benchmark

Build a clean experiment for linear advection or Burgers equation and compare numerical diffusion across schemes.

  • Deliverable: plots, error table, short note
  • Skills: CFL condition, grids, convergence
Discuss Project
ResearchValidation

Entropy-stable method comparison suite

Create reproducible tests comparing stability, resolution, and computational cost for selected entropy-aware schemes.

  • Deliverable: benchmark repository
  • Skills: finite volume methods, stability
Collaborate
AIScientific ML

Learning numerical viscosity without losing structure

Explore how learned viscosity can support robust solvers while respecting conservation and stability constraints.

  • Deliverable: prototype and ablation study
  • Skills: PyTorch, PDE benchmarks, metrics
Start Conversation
Student friendlyTeaching

Mini lecture notes for numerical PDE beginners

Turn core numerical PDE ideas into short notes and matching YouTube explainers for junior researchers.

  • Deliverable: notes + short videos
  • Skills: LaTeX, examples, communication
Contribute
Quantum-inspiredExploratory

Quantum-inspired perspectives on numerical schemes

Map useful quantum-algorithm concepts to classical numerical workflows and identify realistic research questions.

  • Deliverable: survey note or pilot experiment
  • Skills: algorithms, numerical analysis
Explore
Open educationYouTube

Code walkthrough playlist

Prepare short videos that explain one numerical experiment at a time: setup, method, plot, interpretation.

  • Deliverable: code + video script
  • Skills: MATLAB/Python, teaching
Open Channel

How to Start

For junior researchers

  1. Pick one small benchmark from the board.
  2. Reproduce one figure or one error table.
  3. Write a one-page note explaining what you observed.
  4. Email the note with your code link and one clear question.

For collaborators

  • Send a short problem statement and where your expertise connects.
  • Include any preprint, code, dataset, or benchmark you want to discuss.
  • Suggest a concrete first step: experiment, reading group, note, or joint seminar.

YouTube Lecture Roadmap

Connect projects with public learning

The YouTube channel can become a bridge between research code, lecture notes, and junior researcher onboarding.

Open YouTube Channel Suggest Topic
Numerical PDE basics: CFL, stability, convergence Research code walkthroughs: plots and benchmark design Scientific ML: learned viscosity and hybrid solvers Paper-reading sessions for junior researchers