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Example Notebooks

Jupyter notebooks in notebooks/ covering dataset exploration and training workflows.

Dataset Exploration

These notebooks generate a dataset, report its statistics, and visualize samples — the right starting point for understanding what the flow is being asked to learn.

  • Poisson Dataset — EDA

    Source → solution pairs for \(\nabla^2 u = f\): generation, statistics, and sample visualization.

  • Poisson

    An end-to-end 2D Poisson workflow, from dataset generation to learned solutions.

  • Burgers Dataset — EDA

    Initial-condition → final-state pairs, with trajectory rollouts.

  • Darcy Dataset — EDA

    Log-normal coefficient fields \(\kappa\), sources \(f\), and the solutions they produce — including the noisy, partially observed inverse setup.

Training and Analysis

  • Burgers

    Training a flow on the Burgers equation and inspecting the results.

  • Darcy

    Variable-coefficient Poisson, \(-\nabla \cdot (\kappa \nabla u) = f\) — the setting where the inverse problem has a genuinely non-degenerate posterior.

On the Poisson source distribution

The Poisson dataset currently ships an "easy" variant — 3 sine terms at wavenumbers 1–3 (source_num_terms, source_max_mode). That is a low-dimensional subspace and produces optimistic errors. Restore a harder source distribution before reporting operator-learning results.

Running Locally

pip install -e ".[data]" jupyterlab
jupyter lab notebooks/

Detailed ablations and benchmark configurations are in the project report. The notebooks remain the public, runnable examples for the library.