datide

Data assimilation routines for Gaussian process regression, built to connect with gptide and gpvecchia.

Please see the examples for particular use cases.

Documentation

Documentation is available on read the docs.

Installation

pip

pip install datide

To install a local development version

pip install -e ./

To install latest from github

pip install git+https://github.com/tide-itrh/datide.git

Features

• Gaussian process regression posterior mean, marginal likelihood, posterior covariance and conditional sampling, given an observation operator H, prior covariance B and observation error covariance R.
• Three solvers sharing the same interface: DAdense (dense linear algebra), DAsparse (dask + sparse, for much larger problems) and DAblock (batches many independent problems, e.g. one per harmonic constituent).
• MultiscaleGP, for combining multiple additive latent-process scales (e.g. a large-scale and a small-scale field) into one Gaussian process posterior, with an optional Woodbury-identity fast path for low-rank scales.
• Pluggable prior covariance representations in datide.scales (dense, sparse, low-rank, or delegated to an external Vecchia-approximation evaluator) consumed by both DAdense and MultiscaleGP.
• datide.synthetic, for generating synthetic Gaussian random fields to test against a known truth.

Quick Usage

import numpy as np
from datide import DAdense

rng = np.random.default_rng(0)

n_obs, n_state = 20, 5
H = rng.normal(size=(n_obs, n_state))          # observation operator
B = np.eye(n_state)                             # prior state covariance
R = 0.1 * np.eye(n_obs)                         # observation error covariance

x_true = rng.normal(size=n_state)
y = H @ x_true + rng.normal(scale=0.1, size=n_obs)  # noisy observations

model = DAdense(H, B, R)
x_est = model(y)  # posterior mean estimate of x_true

See the examples for a worked multiscale interpolation use case.

Citing

If you use datide in your research, please cite it -- see CITATION.cff for citation metadata (also available via GitHub's "Cite this repository" button).