Data source

The remote-sensing data of both ice-shelf velocity and thickness used for the DIFFICE_jax package are available online. The raw velocity data can be downloaded from NASA MEaSUREs Phase-Based Antarctica Ice Velocity Map, Version 1 (NSIDC-0754) with a 450m resolution. The thickness data can be downloaded from NASA MEaSUREs BedMachine Antarctica, Version 2 (NSIDC-0756) with a 500m resolution. These raw datasets are not provided in the package. Instead, the datasets provided in the examples folder are cropped from these raw datasets at the same resolution with no additional processing, and are saved separately for each ice shelf. Additional information required for the PINN training, such as the position of the ice-shelf calving front, is also included in the dataset. The full requirements of the dataset, which ensures the success of PINN training, are provided in the document below. Users should strictly follow these requirements to create datasets for ice shelves that are not currently available in the package.

Data Format

To be successfully loaded by the PINN code in this package, the input data of each ice shelf needs to be organized and named in a particular way as shown in the example dataset in this folder. Users need to strictly follow the same way if you want to create datasets for other ice shelves. The datasets for PINN and XPINN training shares certain similarity, but also contain differences that users need to pay attention to.

First, the filename of the .mat dataset for both PINNs and XPINNs training should be made following the form:

	PINNs	XPINNs
Filename:	data_pinns_#shelfname#.mat	data_xpinns_#shelfname#.mat

Second, quantities with their names, physical meaning, and data types and shapes in the .mat dataset that are required for the PINNs or XPINNs training are listed in the table below:

Variables	meaning	PINNs	XPINNs
xd	x-position of velocity data	2D matrix	cell[2D matrix]
yd	y-position of velocity data	2D matrix	cell[2D matrix]
ud	velocity component along x-direction	2D matrix	cell[2D matrix]
vd	velocity component along y-direction	2D matrix	cell[2D matrix]
xd_h	x-position of thickness data	2D matrix	cell[2D matrix]
yd_h	x-position of thickness data	2D matrix	cell[2D matrix]
hd	thickness data	2D matrix	cell[2D matrix]
xct	x-position of calving front	nx1 array	cell[nx1 array]
yct	y-position of calving front	nx1 array	cell[nx1 array]
nnct	unit normal vector of calving front	nx2 array	cell[nx2 array]

The quantities listed above should be included in the datasets for both PINN and XPINN training. The only difference is that, for XPINNs, each quantity should have a separate matrix for each sub-region, and all of them should be saved in a cell type. Additionally, we note that all the velocity-related quantities (xd, yd, ud and vd) should have the exact same shape, and the same applies to the thickness-related quantities (xd_h, yd_h and h_d). The calving front-related quantities (xct, yct and nnct) should also have the same length.

Apart from the above quantities, below are the additional quantities particularly required for the XPINNs training

Variables	meaning	XPINNs
x_md	x-position of the interface between two sub-regions	cell[nx1 array]
y_md	x-position of the interface between two sub-regions	cell[nx1 array]
Xe	x-position of velocity data for the whole domain	2D matrix
Ye	y-position of velocity data for the whole domain	2D matrix
Xe_h	x-position of thickness data for the whole domain	2D matrix
Ye_h	y-position of thickness data for the whole domain	2D matrix
idxcrop	vertex position of sub-regional velocity data in the whole domain	cell[4x1 array]
idxcrop_h	vertex position of sub-regional thickness data in the whole domain	cell[4x1 array]

x_md and y_md are the positions of the interface between each two consecutive sub-regions, which are required to evaluate the continuity loss for the XPINNs training. The other 6 quantities are the required information to merge the variable of all sub-regions into a large entity matrix, representing the whole domain.