romda — real-time reduced-order modelling and bias-aware data assimilation

romda is an open-source Python package for real-time data assimilation with reduced-order models: ensemble Kalman filters (including the regularized bias-aware EnKF), physical and data-driven forecast models (ESN, POD-ESN), bias estimators, and POD/SPOD decompositions — with applications to thermoacoustics and fluid flows.

📖 Documentation: https://andreanovoa.github.io/real-time-bias-aware-DA/

This repository was formerly the real-time-DA package. The code used in the papers listed below is preserved at the release tags v1.0, v1.1 and v2.1.

🚀 Getting started

1. Install from PyPI

pip install romda

or, to work on the source, clone and install in editable mode:

git clone https://github.com/andreanovoa/real-time-bias-aware-DA
cd real-time-bias-aware-DA
conda create -n romda python=3.12 && conda activate romda
pip install -e ".[dev,notebooks]" --use-pep517   # dev = pytest, notebooks = jupyter

2. (Optional) Run the test suite

python -m pytest tests/                 # unit and integration tests
python -m pytest scripts/tutorials/test_tutorials.py    # execute the tutorial notebooks

Quick example — bias-aware state and parameter estimation on a Van der Pol twin experiment:

import numpy as np
from romda.bias_estimators import ConstantBias
from romda.estimators import rBA_EnKF
from romda.models.physical import VdP
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')
Cdd = np.diag((0.05 * np.max(abs(truth.y_obs), axis=0)) ** 2)

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)     # advance model (and bias) to the observation time
    ensemble.analysis_step(d=d, Cdd=Cdd)  # Bayesian update

(The ensemble forecast runs in a multiprocessing pool, so in a script keep this under if __name__ == "__main__":.)

Check out the Tutorials folder, which includes several jupyter notebooks aiming to ease the understanding of the repository.

🌟 What is available?

Data assimilation methods romda.estimators

• EnKF — ensemble Kalman filter
• EnSRKF — ensemble square-root Kalman filter
• rBA-EnKF — regularized bias-aware EnKF
• KalmanFilter — the classical (linear) Kalman filter

Physical models romda.models.physical (from the dynamodels package)

• Rijke tube model (dimensional with Galerkin projection)
• Van der Pol oscillator
• Lorenz 63
• Lorenz 96
• Azimuthal thermoacoustics model
• Kuramoto-Sivashinsky equation

Data-driven models romda.models.data_driven

• ESN_model — Echo State Network as a forecasting model
• POD_ESN — POD dimensionality reduction + ESN forecaster
• LinearModel — linear map with process noise (Kalman-filter tutorials)
• Projectors (autoencoders/): POD, SPOD — (Spectral) Proper Orthogonal Decomposition (Sieber 2016, Towne 2018)

Reservoir core: EchoStateNetwork — from the external echostatenetwork package, re-exported by romda.models.data_driven; pod_utils (in autoencoders/) — standalone POD/SPOD algorithms

Bias estimators romda.bias_estimators

• Echo State Network
• Constant bias
• No bias (unbiased limit)

📂 Structure

.
├── data/                        # Dataset files
├── docs/                        # Documentation site sources + media used in the notebooks
├── results/                     # Generated results
├── scripts/
│   └── tutorials/               # Teaching notebooks + notebook execution tests
├── src/                         # Source code (the romda package: `from romda... import ...`)
│   ├── observations.py          # Truth / observation generation
│   ├── data_assimilation.py     # run_da_loop: the shared sequential DA driver
│   ├── utils.py
│   ├── estimators/              # Estimator hierarchy (the DA layer)
│   │   ├── base.py              # Estimator base class (forecast_step, bias wiring)
│   │   ├── ensembles.py         # EnsembleEstimator: EnKF, EnSRKF, rBA_EnKF
│   │   ├── deterministic.py     # DeterministicEstimator: KalmanFilter
│   │   └── inflation.py         # Covariance inflation
│   ├── bias_estimators/         # Bias model classes
│   │   ├── bias.py              # Bias base class
│   │   ├── esn.py               # ESN_bias
│   │   └── constantbias.py      # ConstantBias, NoBias
│   ├── models/                  # Model layer
│   │   ├── __init__.py          # re-exports the dynamodels package (Model base,
│   │   │                        #   integrators, physical models) + pickle aliases
│   │   └── data_driven/         # ESN_model, POD_ESN, LinearModel, esn_config
│   │       └── autoencoders/    # Projector hierarchy: POD, SPOD (+ pod_utils)
│   └── plotting/                # Visualization helpers
├── tests/                       # Unit and integration test suite
├── mkdocs.yml                   # Documentation site configuration
├── pyproject.toml               # Package setup
└── README.md                    # This file

📚 Main publications from this repository

Journal papers

• Nóvoa, Noiray, Dawson & Magri (2024). A real-time digital twin of azimuthal thermoacoustic instabilities. Journal of Fluid Mechanics. Published paper | 🏷️ v1.0.
• Nóvoa, Racca & Magri (2023). Inferring unknown unknowns. Computer Methods in Applied Mechanics and Engineering. Published paper | Legacy repository.
• Nóvoa & Magri (2022). Real-time thermoacoustic data assimilation. Journal of Fluid Mechanics. Published paper | Legacy repository.

Conference papers and proceedings

• Nóvoa & Magri (2025). Online model learning with data-assimilated reservoir computers. Preprint | 🏷️ v1.1.
• Nóvoa & Magri (2024). Real-time digital twins of multiphysics and turbulent flows. Paper.
• Nóvoa & Magri (2022). Bias-aware thermoacoustic data assimilation. In_ 51st International Congress and Exposition on Noise Control Engineering. Paper. | Legacy repository.

PhD thesis

• Nóvoa (2024). Real-time data assimilation in nonlinear dynamcal systems. University of Cambridge. Thesis.

🤝 Contributing

Contributions, bug reports, and feature requests are welcome! Please open an issue or submit a pull request. For questions or collaborations, please reach out to A. Nóvoa.