qlroms — quantized-local reduced-order models

The state space is partitioned into charts by k-means, each chart gets its own local POD basis, and an exact shared atlas stitches the charts into one global coordinate system. On that geometry, this package advances the local dynamics with qlGalerkin: an intrusive projection of the governing equations, one quadratic reduced system \(\dot{\bm{a}} = \bm{b}_k + \mathbf{A}_k\bm{a} + \mathsf{B}_k(\bm{a},\bm{a})\) per chart, plus the transition maps that carry coordinates across chart boundaries.

Schematic of a quantized-local ROM

A quantized-local ROM cuts the attractor into \(K\) regimes, gives each one its own low-dimensional coordinate system, and advances whichever one the trajectory is currently in.

Where to go

Getting started — install, the five-line quickstart, where caches live.
Theory — why one global basis is not enough, charts, the exact atlas, the intrusive step.
Config-driven builds — one YAML per model, python -m qlroms.utils.builder.
API reference — qlroms (charts, atlas, transitions, the shared step(apod) surface, operators), qlroms.intrusive_qlroms (qlGalerkin + data pipelines; cases: ks1d, ks2d, pinball), qlroms.utils (case registry, builder, metrics, diagnosis, figures).
Live demos — move \(K\) and \(r\) with a slider and watch the charts, the forecast and the predictability time change: a travelling wave of the 2-D Kuramoto–Sivashinsky equation, the most intuitive case, and the chaotic 1-D Kuramoto–Sivashinsky equation.
Tutorials — the executed notebooks 0–4, exported to HTML.

References

If you use this package, please cite the papers the method comes from:

Colanera, A., & Magri, L. (2025). Quantized local reduced-order modeling in time (ql-ROM). Computer Methods in Applied Mechanics and Engineering, 447, 118393.
Colanera, A., & Magri, L. (2026). Towards extreme event prediction of turbulent flows with quantized local reduced-order models. Journal of Physics: Conference Series, 3230(1), 012003. IOP Publishing.

Acknowledgements

This work is funded by Schmidt Sciences, LLC, and by the European Research Council (ERC) Starting Grant 949388.