MAFIA

MAFIA is used to construct the mean and precision matrix of a 3D Gaussian Markov Random Field (GMRF) in a specific volume in the Trondheimsfjord for intelligent ocean sampling using Autonomous Underwater Vehicles (AUVs). The GMRFs are approximated through a Stochastic Partial differential equation with the matérn covariance function as its stationary solution. We have parameterized three different models; A stationary model with vertical-lateral anisotropy, a similar Non-stationary, and a Non-stationary model with bidirectional anisotropy, and have fit them to a field approximation from a complex numerical ocean model (SINMOD). The precision matrix is found in ./models/SINMOD-SA.npy, ./models/SINMOD-NI.npy, and ./models/SINMOD-NA.npy respectively, and the standard devitation of Gaussian white noise in the field and the measurement noise of the AUV is found in ./models/sigma.npy.

It is implemented as a class so it can simply loaded with:

from spde import spde

To load the different models simply specify it in the class constructor:

Stationary model with vertical-laterial anisotropy

mod = spde(model == 1)

Non-Stationary model with vertical-laterial anisotropy

mod = spde(model == 2)

Non-Stationary model with vertical-laterial anisotropy

mod = spde(model == 3)

General functionalities

To sample from the model do the call:

mod.sample(n=1)

where n specifies the number of realizations of the entire field.

To estimate the marginal variance of the precision matrix:

mod.mvar()

This is estimated empricically with the samples from the model.

To get the candidate variance given that you have sampled in a point pos within the field:

mod.candidate(pos = [xi,yi,zi])

This can be used to find the points which are most informative.

When the AUV has sampled a point it can update the field with:

mod.search_path_from_trees(rel=measurement, pos=[xi, yi, zi])

This updates the mean and precision matrix of the field within the class and returns nothing.

To get attributees from the class

mod.mu  # the mean of the field (20250) vector
mod.Q  # the precision matrix of the field (20250x20250) sparse matrix
mod.sigma  # gaussian noise of the field (mod.sigma[1]) and the measurement noise of the AUV (mod.sigma[0])
mod.Q_fac  # the choleksy factorized Q. This is a object returned from the C library cholmod
mod.lats  # latitude boundary of the field
mod.lons  # longitude boundary of the field
mod.X_START  # x boundary of the field
mod.Y_START  # y boundary of the field

HITL of MAFIA

Open 4 iterfaces either through tmux or Ctrl+Alt+T. —

SINMOD salinity field