romda

Real-time reduced-order modelling and bias-aware data assimilation.

romda is an open-source Python package for combining low-order forecast models with experimental data in real time. It provides:

• Ensemble data assimilation — the ensemble Kalman filter (EnKF), the ensemble square-root Kalman filter (EnSRKF), and the regularized bias-aware EnKF (r-EnKF) of Nóvoa, Racca & Magri (2023), plus a linear Kalman filter.
• Forecast models — physical low-order models (Rijke tube, azimuthal thermoacoustics, Van der Pol, Lorenz 63/96, Kuramoto–Sivashinsky) and data-driven reduced-order models (Echo State Networks and POD-ESN).
• Bias estimators — interchangeable models of the (unknown) model bias: an ESN estimator, a constant (persistent) bias, and a zero-bias placeholder.
• Modal decompositions — POD and spectral POD (Sieber 2016 and Towne 2018) with an sklearn-style fit / encode / decode interface.

Real-time bias-aware data assimilation: forecast, bias correction, assimilation, and update.

Model choice trades off accuracy against computational cost — from cheap low-order physical models to expensive high-fidelity simulations, with data-driven reduced-order models in between:

The source of model bias: physical models trade fidelity for speed.

Quick example

from romda.estimators.ensembles import rBA_EnKF
from romda.models.physical import VdP
from romda.bias_estimators import ConstantBias
from romda.observations import Observations

truth = Observations(model=VdP, t_start=0.6, t_stop=0.8, Nt_obs=30,
                      add_noise=True, manual_bias='linear')

ensemble = rBA_EnKF(parent_model=VdP(dt=truth.dt),
                     parent_bias=ConstantBias,
                     m=10, std_phi=0.1, std_alpha=dict(zeta=(40., 60.)))

for d, t_d in zip(truth.y_obs, truth.t_obs):
    ensemble.forecast_step(t_end=t_d)
    ensemble.analysis_step(d=d, Cdd=...)

Where to go

• Getting started — install the package and run the first example.
• Experiments — run physical-model and thermoacoustic cases.
• Class hierarchy — how models, estimators, bias estimators and observations relate.
• API reference — browse models, estimators, observations, and bias estimators.
• Tutorials — follow the notebooks from core classes to reduced-order models.
• Sibling packages: dynamodels (the physical models) and ntsa (nonlinear time-series analysis), both usable independently of romda.

Citing

If you use romda in your research, please cite the relevant publications, in particular:

Nóvoa, A., Racca, A., & Magri, L. (2023). Inferring unknown unknowns: Regularized bias-aware ensemble Kalman filter. Computer Methods in Applied Mechanics and Engineering, 418, 116502.