This package implements a method for equation discovery over 2D periodic spatial fields using interleaved linear regression and symbolic regression with spatial differential operators on residuals. This approach allows us to discover parsimonious symbolic relationships between spatial fields using high-order differential terms -- as well as weighted sums of such terms, even if they have significantly different orders of magnitude.
The library is closely integrated with pyqg, a simulator of quasigeostrophic fluid dynamics, though the symbolic regression method can be run independently.
Below we show a basic example of how to run symbolic regression on a dataset, then interpret the learned expression as a parameterization within pyqg, and use it to run a parameterized fluid dynamics simulation:
import eqn_disco
terms_by_iter, parameterizations_by_iter = eqn_disco.hybrid_symbolic.hybrid_symbolic_regression(
dataset,
max_iters=3,
target='fancy_subgrid_forcing',
base_features=['velocity', 'potential_vorticity'],
base_functions=['mul', 'add'],
spatial_functions=['ddx', 'ddy', 'laplacian', 'advected'],
**gplearn_arguments
)
parameterization = parameterizations_by_iter[-1]
pyqg_run = parameterization.run_online(**pyqg_arguments)For more details, see notebooks showcasing this approach on datasets generated from pyqg or constructed independently.
To install, clone the repository, and run pip install -e ..
The code in this repository was originally developed by Andrew Ross and Pavel Perezhogin, in this repository, for use in the publication: Benchmarking of machine learning ocean parameterizations in an idealized model (published in JAMES, https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2022MS003258).
It is currently being worked on by Jim Denholm and Andrew Ross, along with other members of the ICCS and M2LInES.
The work is available under an MIT License; see the license.