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A Appendix
Reproducibility
All code and data used to train and evaluate Presto will be made available upon publication, and
the code is currently available at https://github.com/nasaharvest/presto . In addition, we
discuss specific implementation details in Appendices A.1 and A.4. We have strived to make the
Presto codebase accessible to other practitioners; to this end, we include a demo Jupyter notebook
demonstrating how Presto can be applied to a new downstream task, which is available at https:
//github.com/nasaharvest/presto/blob/main/downstream_task_demo.ipynb .
A.1 Pre-training details
We outline training hyperparameters below:
•Training length : We train the model for 20 epochs, with a batch size of 4096 (resulting in 5950
batches per epoch). On a single NVIDIA V100 GPU, this takes 431
4hours.
•Optimizer and learning rate : We train the model with an AdamW optimizer. We use a cosine
annealing schedule for our learning rate, with a maximum learning rate of 0.001 at the 2ndepoch.
We apply a weight decay of 0.05, and βs of (0.9, 0.95).
•Masking : We use a masking ratio of 0.75, randomly selecting (for each instance) a masking
strategy from the ones described in Section 3.3. If the masking strategy cannot mask the right
number of tokens, we randomly mask additional tokens to achieve the correct masking ratio.
A.1.1 Pre-training data
Figure 6: The distribution of the pre-training dataset described in Section 3.1.
Remote sensing models can be deployed in a wide range of geographies, with few labelled datapoints
available at fine-tuning time (Kerner et al., 2020; Böhm et al., 2022). We therefore aim to collect
a globally representative pre-training dataset. We achieve this by following the sampling strategy
used by Dynamic World (Brown et al., 2022). We divide the Earth into three regions: the Western
Hemisphere and two regions in the Eastern Hemisphere. These regions are further divided into
ecoregions, and stratified samples are gathered from each region using land cover classes as sampling
strata. Figure 6 shows the resulting geographical distribution. Each sample represents a 510×510
pixel tile with a spatial resolution of 10 meter per pixel. To obtain pixel-timeseries we grid-sample
2,500 pixels from each sample, yielding a total of 21,535,000 pixel samples (each with 24 one-month
timesteps).
A.1.2 Input data
We leverage the following data products when pre-training Presto:
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Table 9: Model sizes and FLOPs required to encode a single EuroSat image (or pixel, for Presto), as
measured by the thop library. When plotting results in Table 5, we multiply the FLOPs for Presto by
the number of pixels encoded for an image. At its highest resolution, EuroSAT images are 64×64,
so Presto FLOPs for a full resolution image can be obtained by multiplying the per-pixel FLOPs by
4,096. We include this value in brackets for completeness.
Model Backbone Params (M) MegaFlops
SatMAE (RGB) (Cong et al., 2022) ViT-Large 303.10 59,685.69
SatMAE (MS) (Cong et al., 2022) ViT-Large 305.96 535,515.25
ScaleMAE (Reed et al., 2022) ViT-Large 303.10 59,685.69
ConvMAE (Gao et al., 2022) ConvMAE-Large 88.78 23,315.58
SeCo (Manas et al., 2021) ResNet-18 11.69 149.37
GASSL (Ayush et al., 2021) ResNet-18 11.69 149.37
Presto RGB pixel (image) Presto 0.40 0.79 (3,235.84)
Presto MS pixel (image) Presto 0.40 2.37 (9,707.52)
•Sentinel-1 Synthetic Aperture Radar observations (S1): The VV (emit and receive at vertical
polarization) and VH (emit at vertical and receive at horizontal polarization) bands: 2 real-valued
dynamic values per monthly timestep.
•Sentinel-2 Multispectral images (S2): We removed the 60m resolution bands, yielding bands
with 10m and 20m resolution with channels in the visible, near-infrared and short-wave infrared
range: 10 real-valued dynamic values per timestep.
•ERA5 Climate Reanalysis Meteorological data (ERA5): Monthly total precipitation and temper-
ature at 2 metres above the ground: 2 real-valued dynamic values per timestep.
•NDVI (Rouse et al., 1974): Computed from the red (B4) and near-infrared (B8) Sentinel-2 bands:
1 real-valued dynamic value per timestep.
•Dynamic World Land Cover classes (DW, Brown et al., 2022): Land cover classes produced for
every non-cloudy Sentinel-2 image: 1 dynamic categorical value from the set of possible classes V
per timestep. We took the mode of classes for all timesteps within a month.
•Topography data (TG), from the Shuttle Radar Topography Mission’s Digital Elevation Model:
The elevation and slope of each pixel, real-valued and static in time.
•Coordinates (Loc): 3D static in time Cartesian coordinates computed from the latitude and longi-
tude of the pixel’s geographical location: sLoc= [cos( lat)×cos(lon),cos(lat)×sin(lon),sin(lat)].
A.1.3 Channel Groups
As described in Section 3.2, we transform the pixel timeseries xinto a number of tokens, where each
token is a linear transformation of a subset of the input channels. We group together channels which