At present, we use the convLSTM launched in a earlier put up to foretell El Niño-Southern Oscillation (ENSO).
ENSO refers to a altering sample of sea floor temperatures and sea-level pressures occurring within the equatorial Pacific. From its three general states, most likely the best-known is El Niño. El Niño happens when floor water temperatures within the jap Pacific are increased than regular, and the robust winds that usually blow from east to west are unusually weak. The other situations are termed La Niña. All the things in-between is assessed as regular.
ENSO has nice impression on the climate worldwide, and routinely harms ecosystems and societies by way of storms, droughts and flooding, probably leading to famines and financial crises. The very best societies can do is attempt to adapt and mitigate extreme penalties. Such efforts are aided by correct forecasts, the additional forward the higher.
Right here, deep studying (DL) can doubtlessly assist: Variables like sea floor temperatures and pressures are given on a spatial grid – that of the earth – and as we all know, DL is nice at extracting spatial (e.g., picture) options. For ENSO prediction, architectures like convolutional neural networks (Ham, Kim, and Luo (2019a)) or convolutional-recurrent hybrids are habitually used. One such hybrid is simply our convLSTM; it operates on sequences of options given on a spatial grid. At present, thus, we’ll be coaching a mannequin for ENSO forecasting. This mannequin may have a convLSTM for its central ingredient.
Earlier than we begin, a be aware. Whereas our mannequin suits effectively with architectures described within the related papers, the identical can’t be mentioned for quantity of coaching knowledge used. For causes of practicality, we use precise observations solely; consequently, we find yourself with a small (relative to the duty) dataset. In distinction, analysis papers have a tendency to utilize local weather simulations, leading to considerably extra knowledge to work with.
From the outset, then, we don’t count on stellar efficiency. Nonetheless, this could make for an fascinating case research, and a helpful code template for our readers to use to their very own knowledge.
We’ll try to predict month-to-month common sea floor temperature within the Niño 3.4 area, as represented by the Niño 3.4 Index, plus categorization as considered one of El Niño, La Niña or impartial. Predictions can be primarily based on prior month-to-month sea floor temperatures spanning a big portion of the globe.
On the enter facet, public and ready-to-use knowledge could also be downloaded from Tokyo Local weather Heart; as to prediction targets, we receive index and classification right here.
Enter and goal knowledge each are offered month-to-month. They intersect within the time interval starting from 1891-01-01 to 2020-08-01; so that is the vary of dates we’ll be zooming in on.
Enter: Sea Floor Temperatures
Month-to-month sea floor temperatures are offered in a latitude-longitude grid of decision 1°. Particulars of how the information have been processed can be found right here.
Knowledge information can be found in GRIB format; every file accommodates averages computed for a single month. We will both obtain particular person information or generate a textual content file of URLs for obtain. In case you’d prefer to comply with together with the put up, you’ll discover the contents of the textual content file I generated within the appendix. When you’ve saved these URLs to a file, you may have R get the information for you want so:
From R, we are able to learn GRIB information utilizing stars. For instance:
stars object with 2 dimensions and 1 attribute
attribute(s):
sst189101.grb
Min. :-274.9
1st Qu.:-272.8
Median :-259.1
Imply :-260.0
third Qu.:-248.4
Max. :-242.8
NA's :21001
dimension(s):
from to offset delta refsys level values
x 1 360 0 1 Coordinate System importe... NA NULL [x]
y 1 180 90 -1 Coordinate System importe... NA NULL [y]
So on this GRIB file, we’ve got one attribute – which we all know to be sea floor temperature – on a two-dimensional grid. As to the latter, we are able to complement what stars
tells us with more information discovered within the documentation:
The east-west grid factors run eastward from 0.5ºE to 0.5ºW, whereas the north-south grid factors run northward from 89.5ºS to 89.5ºN.
We be aware just a few issues we’ll wish to do with this knowledge. For one, the temperatures appear to be given in Kelvin, however with minus indicators. We’ll take away the minus indicators and convert to levels Celsius for comfort. We’ll even have to consider what to do with the NA
s that seem for all non-maritime coordinates.
Earlier than we get there although, we have to mix knowledge from all information right into a single knowledge body. This provides an extra dimension, time, starting from 1891/01/01 to 2020/01/12:
stars object with 3 dimensions and 1 attribute
attribute(s), abstract of first 1e+05 cells:
sst189101.grb
Min. :-274.9
1st Qu.:-273.3
Median :-258.8
Imply :-260.0
third Qu.:-247.8
Max. :-242.8
NA's :33724
dimension(s):
from to offset delta refsys level values
x 1 360 0 1 Coordinate System importe... NA NULL [x]
y 1 180 90 -1 Coordinate System importe... NA NULL [y]
time 1 1560 NA NA Date NA 1891-01-01,...,2020-12-01
Let’s visually examine the spatial distribution of month-to-month temperatures for one 12 months, 2020:

Determine 1: Month-to-month sea floor temperatures, 2020/01/01 – 2020/01/12.
Goal: Niño 3.4 Index
For the Niño 3.4 Index, we obtain the month-to-month knowledge and, among the many offered options, zoom in on two: the index itself (column NINO34_MEAN
) and PHASE
, which may be E
(El Niño), L
(La Niño) or N
(impartial).
1556
Subsequent, we take a look at find out how to get the information right into a format handy for coaching and prediction.
Enter
First, we take away all enter knowledge for deadlines the place floor fact knowledge are nonetheless lacking.
Subsequent, as is finished by e.g. Ham, Kim, and Luo (2019b), we solely use grid factors between 55° south and 60° north. This has the extra benefit of decreasing reminiscence necessities.
360, 115, 1560
As already alluded to, with the little knowledge we’ve got we are able to’t count on a lot when it comes to generalization. Nonetheless, we put aside a small portion of the information for validation, since we’d like for this put up to function a helpful template for use with greater datasets.
From right here on, we work with R arrays.
sst_train as.tbl_cube.stars(sst_train)$mets[[1]]
sst_valid as.tbl_cube.stars(sst_valid)$mets[[1]]
Conversion to levels Celsius shouldn’t be strictly crucial, as preliminary experiments confirmed a slight efficiency enhance attributable to normalizing the enter, and we’re going to do this anyway. Nonetheless, it reads nicer to people than Kelvin.
sst_train sst_train + 273.15
quantile(sst_train, na.rm = TRUE)
0% 25% 50% 75% 100%
-1.8000 12.9975 21.8775 26.8200 34.3700
By no means surprisingly, international warming is clear from inspecting temperature distribution on the validation set (which was chosen to span the final thirty-one years).
sst_valid sst_valid + 273.15
quantile(sst_valid, na.rm = TRUE)
0% 25% 50% 75% 100%
-1.800 13.425 22.335 27.240 34.870
The subsequent-to-last step normalizes each units in response to coaching imply and variance.
Lastly, what ought to we do concerning the NA
entries? We set them to zero, the (coaching set) imply. That might not be sufficient of an motion although: It means we’re feeding the community roughly 30% deceptive knowledge. That is one thing we’re not completed with but.
Goal
The goal knowledge are break up analogously. Let’s test although: Are phases (categorizations) distributedly equally in each units?
# A tibble: 3 x 4
# Teams: phase_code [3]
phase_code PHASE rely avg
1 1 E 301 27.7
2 2 L 333 25.6
3 3 N 554 26.7
nino_valid %>% group_by(phase_code, PHASE) %>% summarise(rely = n(), avg = imply(NINO34_MEAN))
# A tibble: 3 x 4
# Teams: phase_code [3]
phase_code PHASE rely avg
1 1 E 93 28.1
2 2 L 93 25.9
3 3 N 182 27.2
This doesn’t look too unhealthy. After all, we once more see the general rise in temperature, regardless of part.
Lastly, we normalize the index, similar as we did for the enter knowledge.
train_mean_nino imply(nino_train$NINO34_MEAN)
train_sd_nino sd(nino_train$NINO34_MEAN)
nino_train nino_train %>% mutate(NINO34_MEAN = scale(NINO34_MEAN, heart = train_mean_nino, scale = train_sd_nino))
nino_valid nino_valid %>% mutate(NINO34_MEAN = scale(NINO34_MEAN, heart = train_mean_nino, scale = train_sd_nino))
On to the torch
dataset.
The dataset is chargeable for appropriately matching up inputs and targets.
Our purpose is to take six months of worldwide sea floor temperatures and predict the Niño 3.4 Index for the next month. Enter-wise, the mannequin will count on the next format semantics:
batch_size * timesteps * width * peak * channels
, the place
-
batch_size
is the variety of observations labored on in a single spherical of computations, -
timesteps
chains consecutive observations from adjoining months, -
width
andpeak
collectively represent the spatial grid, and -
channels
corresponds to accessible visible channels within the “picture.”
In .getitem()
, we choose the consecutive observations, beginning at a given index, and stack them in dimension one. (One, not two, as batches will solely begin to exist as soon as the dataloader
comes into play.)
Now, what concerning the goal? Our final purpose was – is – predicting the Niño 3.4 Index. Nonetheless, as you see we outline three targets: One is the index, as anticipated; an extra one holds the spatially-gridded sea floor temperatures for the prediction month. Why? Our major instrument, probably the most distinguished constituent of the mannequin, can be a convLSTM, an structure designed for spatial prediction. Thus, to coach it effectively, we wish to give it the chance to foretell values on a spatial grid. Thus far so good; however there’s yet another goal, the part/class. This was added for experimentation functions: Perhaps predicting each index and part helps in coaching?
Lastly, right here is the code for the dataset. In our experiments, we primarily based predictions on inputs from the previous six months (n_timesteps ). It is a parameter you would possibly wish to play with, although.
n_timesteps 6
enso_dataset dataset(
title = "enso_dataset",
initialize = operate(sst, nino, n_timesteps) {
self$sst sst
self$nino nino
self$n_timesteps n_timesteps
},
.getitem = operate(i) {
x torch_tensor(self$sst[, , i:(n_timesteps + i - 1)]) # (360, 115, n_timesteps)
x x$permute(c(3,1,2))$unsqueeze(2) # (n_timesteps, 1, 360, 115))
y1 torch_tensor(self$sst[, , n_timesteps + i])$unsqueeze(1) # (1, 360, 115)
y2 torch_tensor(self$nino$NINO34_MEAN[n_timesteps + i])
y3 torch_tensor(self$nino$phase_code[n_timesteps + i])$squeeze()$to(torch_long())
listing(x = x, y1 = y1, y2 = y2, y3 = y3)
},
.size = operate() {
nrow(self$nino) - n_timesteps
}
)
valid_ds enso_dataset(sst_valid, nino_valid, n_timesteps)
After the customized dataset, we create the – fairly typical – dataloader
s, making use of a batch dimension of 4.
batch_size 4
train_dl train_ds %>% dataloader(batch_size = batch_size, shuffle = TRUE)
valid_dl valid_ds %>% dataloader(batch_size = batch_size)
Subsequent, we proceed to mannequin creation.
The mannequin’s major ingredient is the convLSTM launched in a prior put up. For comfort, we reproduce the code within the appendix.
In addition to the convLSTM, the mannequin makes use of three convolutional layers, a batchnorm layer and 5 linear layers. The logic is the next.
First, the convLSTM job is to foretell the following month’s sea floor temperatures on the spatial grid. For that, we nearly simply return its last state, – nearly: We use self$conv1
to cut back the quantity channels to at least one.
For predicting index and part, we then must flatten the grid, as we require a single worth every. That is the place the extra conv layers are available. We do hope they’ll help in studying, however we additionally wish to cut back the variety of parameters a bit, downsizing the grid (strides = 2
and strides = 3
, resp.) a bit earlier than the upcoming torch_flatten()
.
As soon as we’ve got a flat construction, studying is shared between the duties of index and part prediction (self$linear
), till lastly their paths break up (self$cont
and self$cat
, resp.), they usually return their separate outputs.
(The batchnorm? I’ll touch upon that within the Dialogue.)
mannequin nn_module(
initialize = operate(channels_in,
convlstm_hidden,
convlstm_kernel,
convlstm_layers) {
self$n_layers convlstm_layers
self$convlstm convlstm(
input_dim = channels_in,
hidden_dims = convlstm_hidden,
kernel_sizes = convlstm_kernel,
n_layers = convlstm_layers
)
self$conv1
nn_conv2d(
in_channels = 32,
out_channels = 1,
kernel_size = 5,
padding = 2
)
self$conv2
nn_conv2d(
in_channels = 32,
out_channels = 32,
kernel_size = 5,
stride = 2
)
self$conv3
nn_conv2d(
in_channels = 32,
out_channels = 32,
kernel_size = 5,
stride = 3
)
self$linear nn_linear(33408, 64)
self$b1 nn_batch_norm1d(num_features = 64)
self$cont nn_linear(64, 128)
self$cat nn_linear(64, 128)
self$cont_output nn_linear(128, 1)
self$cat_output nn_linear(128, 3)
},
ahead = operate(x) {
ret self$convlstm(x)
layer_last_states ret[[2]]
last_hidden layer_last_states[[self$n_layers]][[1]]
next_sst last_hidden %>% self$conv1()
c2 last_hidden %>% self$conv2()
c3 c2 %>% self$conv3()
flat torch_flatten(c3, start_dim = 2)
frequent self$linear(flat) %>% self$b3() %>% nnf_relu()
next_temp frequent %>% self$cont() %>% nnf_relu() %>% self$cont_output()
next_nino frequent %>% self$cat() %>% nnf_relu() %>% self$cat_output()
listing(next_sst, next_temp, next_nino)
}
)
Subsequent, we instantiate a fairly small-ish mannequin. You’re greater than welcome to experiment with bigger fashions, however coaching time in addition to GPU reminiscence necessities will enhance.
An `nn_module` containing 2,389,605 parameters.
── Modules ───────────────────────────────────────────────────────────────────────────────
● convlstm: #182,080 parameters
● conv1: #801 parameters
● conv2: #25,632 parameters
● conv3: #25,632 parameters
● linear: #2,138,176 parameters
● b1: #128 parameters
● cont: #8,320 parameters
● cat: #8,320 parameters
● cont_output: #129 parameters
● cat_output: #387 parameters
Now we have three mannequin outputs. How ought to we mix the losses?
On condition that the primary purpose is predicting the index, and the opposite two outputs are primarily means to an finish, I discovered the next mixture relatively efficient:
# weight for sea floor temperature prediction
lw_sst
The coaching course of follows the sample seen in all torch
posts thus far: For every epoch, loop over the coaching set, backpropagate, test efficiency on validation set.
However, once we did the pre-processing, we have been conscious of an imminent drawback: the lacking temperatures for continental areas, which we set to zero. As a sole measure, this strategy is clearly inadequate. What if we had chosen to make use of latitude-dependent averages? Or interpolation? Each could also be higher than a worldwide common, however each have their issues as effectively. Let’s a minimum of alleviate unfavourable penalties by not utilizing the respective pixels for spatial loss calculation. That is taken care of by the next line beneath:
sst_loss nnf_mse_loss(sst_output[sst_target != 0], sst_target[sst_target != 0])
Right here, then, is the whole coaching code.
optimizer optim_adam(web$parameters, lr = 0.001)
num_epochs 50
train_batch operate(b) {
optimizer$zero_grad()
output web(b$x$to(system = system))
sst_output output[[1]]
sst_target b$y1$to(system = system)
sst_loss nnf_mse_loss(sst_output[sst_target != 0], sst_target[sst_target != 0])
temp_loss nnf_mse_loss(output[[2]], b$y2$to(system = system))
nino_loss nnf_cross_entropy(output[[3]], b$y3$to(system = system))
loss lw_sst * sst_loss + lw_temp * temp_loss + lw_nino * nino_loss
loss$backward()
optimizer$step()
listing(sst_loss$merchandise(), temp_loss$merchandise(), nino_loss$merchandise(), loss$merchandise())
}
valid_batch operate(b) {
output web(b$x$to(system = system))
sst_output output[[1]]
sst_target b$y1$to(system = system)
sst_loss nnf_mse_loss(sst_output[sst_target != 0], sst_target[sst_target != 0])
temp_loss nnf_mse_loss(output[[2]], b$y2$to(system = system))
nino_loss nnf_cross_entropy(output[[3]], b$y3$to(system = system))
loss
lw_sst * sst_loss + lw_temp * temp_loss + lw_nino * nino_loss
listing(sst_loss$merchandise(),
temp_loss$merchandise(),
nino_loss$merchandise(),
loss$merchandise())
}
for (epoch in 1:num_epochs) {
web$prepare()
train_loss_sst c()
train_loss_temp c()
train_loss_nino c()
train_loss c()
coro::loop(for (b in train_dl) {
losses train_batch(b)
train_loss_sst c(train_loss_sst, losses[[1]])
train_loss_temp c(train_loss_temp, losses[[2]])
train_loss_nino c(train_loss_nino, losses[[3]])
train_loss c(train_loss, losses[[4]])
})
cat(
sprintf(
"nEpoch %d, coaching: loss: %3.3f sst: %3.3f temp: %3.3f nino: %3.3f n",
epoch, imply(train_loss), imply(train_loss_sst), imply(train_loss_temp), imply(train_loss_nino)
)
)
web$eval()
valid_loss_sst c()
valid_loss_temp c()
valid_loss_nino c()
valid_loss c()
coro::loop(for (b in valid_dl) {
losses valid_batch(b)
valid_loss_sst c(valid_loss_sst, losses[[1]])
valid_loss_temp c(valid_loss_temp, losses[[2]])
valid_loss_nino c(valid_loss_nino, losses[[3]])
valid_loss c(valid_loss, losses[[4]])
})
cat(
sprintf(
"nEpoch %d, validation: loss: %3.3f sst: %3.3f temp: %3.3f nino: %3.3f n",
epoch, imply(valid_loss), imply(valid_loss_sst), imply(valid_loss_temp), imply(valid_loss_nino)
)
)
torch_save(web, paste0(
"model_", epoch, "_", spherical(imply(train_loss), 3), "_", spherical(imply(valid_loss), 3), ".pt"
))
}
After I ran this, efficiency on the coaching set decreased in a not-too-fast, however steady method, whereas validation set efficiency saved fluctuating. For reference, complete (composite) losses regarded like this:
Epoch Coaching Validation
10 0.336 0.633
20 0.233 0.295
30 0.135 0.461
40 0.099 0.903
50 0.061 0.727
Considering of the scale of the validation set – thirty-one years, or equivalently, 372 knowledge factors – these fluctuations might not be all too shocking.
Now losses are typically summary; let’s see what truly will get predicted. We receive predictions for index values and phases like so …
… and mix these with the bottom fact, stripping off the primary six rows (six was the variety of timesteps used as predictors):
valid_perf knowledge.body(
actual_temp = nino_valid$NINO34_MEAN[(batch_size + 1):nrow(nino_valid)] * train_sd_nino + train_mean_nino,
actual_nino = issue(nino_valid$phase_code[(batch_size + 1):nrow(nino_valid)]),
pred_temp = pred_index * train_sd_nino + train_mean_nino,
pred_nino = issue(pred_phase %>% apply(1, which.max))
)
For the part, we are able to generate a confusion matrix:
yardstick::conf_mat(valid_perf, actual_nino, pred_nino)
Reality
Prediction 1 2 3
1 70 0 43
2 0 47 10
3 23 46 123
This seems higher than anticipated (primarily based on the losses). Phases 1 and a pair of correspond to El Niño and La Niña, respectively, and these get sharply separated.
What concerning the Niño 3.4 Index? Let’s plot predictions versus floor fact:
valid_perf valid_perf %>%
choose(precise = actual_temp, predicted = pred_temp) %>%
add_column(month = seq(as.Date("1990-07-01"), as.Date("2020-08-01"), by = "months")) %>%
pivot_longer(-month, names_to = "Index", values_to = "temperature")
ggplot(valid_perf, aes(x = month, y = temperature, colour = Index)) +
geom_line() +
scale_color_manual(values = c("#006D6F", "#B2FFFF")) +
theme_classic()

Determine 2: Nino 3.4 Index: Floor fact vs. predictions (validation set).
This doesn’t look unhealthy both. Nonetheless, we have to remember the fact that we’re predicting only a single time step forward. We most likely mustn’t overestimate the outcomes. Which leads on to the dialogue.
When working with small quantities of knowledge, lots may be realized by quick-ish experimentation. Nonetheless, when on the similar time, the duty is advanced, one needs to be cautious extrapolating.
For instance, well-established regularizers resembling batchnorm and dropout, whereas meant to enhance generalization to the validation set, could prove to severely impede coaching itself. That is the story behind the one batchnorm layer I saved (I did strive having extra), and additionally it is why there isn’t a dropout.
One lesson to study from this expertise then is: Ensure that the quantity of knowledge matches the complexity of the duty. That is what we see within the ENSO prediction papers printed on arxiv.
If we must always deal with the outcomes with warning, why even publish the put up?
For one, it exhibits an software of convLSTM to real-world knowledge, using a fairly advanced structure and illustrating strategies like customized losses and loss masking. Comparable architectures and techniques needs to be relevant to a variety of real-world duties – principally, each time predictors in a time-series drawback are given on a spatial grid.
Secondly, the appliance itself – forecasting an atmospheric phenomenon that drastically impacts ecosystems in addition to human well-being – looks like a superb use of deep studying. Functions like these stand out as all of the extra worthwhile as the identical can’t be mentioned of all the pieces deep studying is – and can be, barring efficient regulation – used for.
Thanks for studying!
A1: Checklist of GRB information
To be put right into a textual content file to be used with purrr::stroll( … obtain.file … )
.
https://ds.knowledge.jma.go.jp/tcc/tcc/merchandise/elnino/cobesst/gpvdata/1891-1899/sst189101.grb
https://ds.knowledge.jma.go.jp/tcc/tcc/merchandise/elnino/cobesst/gpvdata/1891-1899/sst189102.grb
https://ds.knowledge.jma.go.jp/tcc/tcc/merchandise/elnino/cobesst/gpvdata/1891-1899/sst189103.grb
https://ds.knowledge.jma.go.jp/tcc/tcc/merchandise/elnino/cobesst/gpvdata/1891-1899/sst189104.grb
https://ds.knowledge.jma.go.jp/tcc/tcc/merchandise/elnino/cobesst/gpvdata/1891-1899/sst189105.grb
https://ds.knowledge.jma.go.jp/tcc/tcc/merchandise/elnino/cobesst/gpvdata/1891-1899/sst189106.grb
https://ds.knowledge.jma.go.jp/tcc/tcc/merchandise/elnino/cobesst/gpvdata/1891-1899/sst189107.grb
https://ds.knowledge.jma.go.jp/tcc/tcc/merchandise/elnino/cobesst/gpvdata/1891-1899/sst189108.grb
https://ds.knowledge.jma.go.jp/tcc/tcc/merchandise/elnino/cobesst/gpvdata/1891-1899/sst189109.grb
https://ds.knowledge.jma.go.jp/tcc/tcc/merchandise/elnino/cobesst/gpvdata/1891-1899/sst189110.grb
https://ds.knowledge.jma.go.jp/tcc/tcc/merchandise/elnino/cobesst/gpvdata/1891-1899/sst189111.grb
https://ds.knowledge.jma.go.jp/tcc/tcc/merchandise/elnino/cobesst/gpvdata/1891-1899/sst189112.grb
https://ds.knowledge.jma.go.jp/tcc/tcc/merchandise/elnino/cobesst/gpvdata/1891-1899/sst189201.grb
https://ds.knowledge.jma.go.jp/tcc/tcc/merchandise/elnino/cobesst/gpvdata/1891-1899/sst189202.grb
https://ds.knowledge.jma.go.jp/tcc/tcc/merchandise/elnino/cobesst/gpvdata/1891-1899/sst189203.grb
https://ds.knowledge.jma.go.jp/tcc/tcc/merchandise/elnino/cobesst/gpvdata/1891-1899/sst189204.grb
https://ds.knowledge.jma.go.jp/tcc/tcc/merchandise/elnino/cobesst/gpvdata/1891-1899/sst189205.grb
https://ds.knowledge.jma.go.jp/tcc/tcc/merchandise/elnino/cobesst/gpvdata/1891-1899/sst189206.grb
https://ds.knowledge.jma.go.jp/tcc/tcc/merchandise/elnino/cobesst/gpvdata/1891-1899/sst189207.grb
https://ds.knowledge.jma.go.jp/tcc/tcc/merchandise/elnino/cobesst/gpvdata/1891-1899/sst189208.grb
https://ds.knowledge.jma.go.jp/tcc/tcc/merchandise/elnino/cobesst/gpvdata/1891-1899/sst189209.grb
https://ds.knowledge.jma.go.jp/tcc/tcc/merchandise/elnino/cobesst/gpvdata/1891-1899/sst189210.grb
https://ds.knowledge.jma.go.jp/tcc/tcc/merchandise/elnino/cobesst/gpvdata/1891-1899/sst189211.grb
https://ds.knowledge.jma.go.jp/tcc/tcc/merchandise/elnino/cobesst/gpvdata/1891-1899/sst189212.grb
https://ds.knowledge.jma.go.jp/tcc/tcc/merchandise/elnino/cobesst/gpvdata/1891-1899/sst189301.grb
https://ds.knowledge.jma.go.jp/tcc/tcc/merchandise/elnino/cobesst/gpvdata/1891-1899/sst189302.grb
https://ds.knowledge.jma.go.jp/tcc/tcc/merchandise/elnino/cobesst/gpvdata/1891-1899/sst189303.grb
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A2: convlstm
code
For an in-depth rationalization of convlstm
, see the weblog put up.
library(torch)
library(torchvision)
convlstm_cell nn_module(
initialize = operate(input_dim, hidden_dim, kernel_size, bias) {
self$hidden_dim hidden_dim
padding kernel_size %/% 2
self$conv nn_conv2d(
in_channels = input_dim + self$hidden_dim,
# for every of enter, overlook, output, and cell gates
out_channels = 4 * self$hidden_dim,
kernel_size = kernel_size,
padding = padding,
bias = bias
)
},
ahead = operate(x, prev_states) {
h_prev prev_states[[1]]
c_prev prev_states[[2]]
mixed torch_cat(listing(x, h_prev), dim = 2) # concatenate alongside channel axis
combined_conv self$conv(mixed)
gate_convs torch_split(combined_conv, self$hidden_dim, dim = 2)
cc_i gate_convs[[1]]
cc_f gate_convs[[2]]
cc_o gate_convs[[3]]
cc_g gate_convs[[4]]
# enter, overlook, output, and cell gates (comparable to torch's LSTM)
i torch_sigmoid(cc_i)
f torch_sigmoid(cc_f)
o torch_sigmoid(cc_o)
g torch_tanh(cc_g)
# cell state
c_next f * c_prev + i * g
# hidden state
h_next o * torch_tanh(c_next)
listing(h_next, c_next)
},
init_hidden = operate(batch_size, peak, width) {
listing(torch_zeros(batch_size, self$hidden_dim, peak, width, system = self$conv$weight$system),
torch_zeros(batch_size, self$hidden_dim, peak, width, system = self$conv$weight$system))
}
)
convlstm nn_module(
initialize = operate(input_dim, hidden_dims, kernel_sizes, n_layers, bias = TRUE) {
self$n_layers n_layers
self$cell_list nn_module_list()
for (i in 1:n_layers) {
cur_input_dim if (i == 1) input_dim else hidden_dims[i - 1]
self$cell_list$append(convlstm_cell(cur_input_dim, hidden_dims[i], kernel_sizes[i], bias))
}
},
# we at all times assume batch-first
ahead = operate(x) {
batch_size x$dimension()[1]
seq_len x$dimension()[2]
peak x$dimension()[4]
width x$dimension()[5]
# initialize hidden states
init_hidden vector(mode = "listing", size = self$n_layers)
for (i in 1:self$n_layers) {
init_hidden[[i]] self$cell_list[[i]]$init_hidden(batch_size, peak, width)
}
# listing containing the outputs, of size seq_len, for every layer
# this is identical as h, at every step within the sequence
layer_output_list vector(mode = "listing", size = self$n_layers)
# listing containing the final states (h, c) for every layer
layer_state_list vector(mode = "listing", size = self$n_layers)
cur_layer_input x
hidden_states init_hidden
# loop over layers
for (i in 1:self$n_layers) {
# each layer's hidden state begins from 0 (non-stateful)
h_c hidden_states[[i]]
h h_c[[1]]
c h_c[[2]]
# outputs, of size seq_len, for this layer
# equivalently, listing of h states for every time step
output_sequence vector(mode = "listing", size = seq_len)
# loop over timesteps
for (t in 1:seq_len) {
h_c self$cell_list[[i]](cur_layer_input[ , t, , , ], listing(h, c))
h h_c[[1]]
c h_c[[2]]
# preserve monitor of output (h) for each timestep
# h has dim (batch_size, hidden_size, peak, width)
output_sequence[[t]] h
}
# stack hs for all timesteps over seq_len dimension
# stacked_outputs has dim (batch_size, seq_len, hidden_size, peak, width)
# similar as enter to ahead (x)
stacked_outputs torch_stack(output_sequence, dim = 2)
# move the listing of outputs (hs) to subsequent layer
cur_layer_input stacked_outputs
# preserve monitor of listing of outputs or this layer
layer_output_list[[i]] stacked_outputs
# preserve monitor of final state for this layer
layer_state_list[[i]] listing(h, c)
}
listing(layer_output_list, layer_state_list)
}
)