Forecasting El Niño-Southern Oscillation (ENSO)

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 NAs 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:

grb  read_stars(
  file.path(grb_dir, map(readLines("information", warn = FALSE), basename)), alongside = "time") %>%
  st_set_dimensions(3,
                    values = seq(as.Date("1891-01-01"), as.Date("2020-12-01"), by = "months"),
                    names = "time"
                    )

grb

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:

ggplot() +
  geom_stars(knowledge = grb %>% filter(between(time, as.Date("2020-01-01"), as.Date("2020-12-01"))), alpha = 0.8) +
  facet_wrap("time") +
  scale_fill_viridis() +
  coord_equal() +
  theme_map() +
  theme(legend.place = "none")

Monthly sea surface temperatures, 2020/01/01 - 2020/01/12.

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).

nino  read_table2("ONI_NINO34_1854-2020.txt", skip = 9) %>%
  mutate(month = as.Date(paste0(YEAR, "-", `MON/MMM`, "-01"))) %>%
  choose(month, NINO34_MEAN, PHASE) %>%
  filter(between(month, as.Date("1891-01-01"), as.Date("2020-08-01"))) %>%
  mutate(phase_code = as.numeric(as.issue(PHASE)))

nrow(nino)

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.

sst  grb %>% filter(between(y,-55, 60))

dim(sst)

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.

train_mean  imply(sst_train, na.rm = TRUE)
train_sd  sd(sst_train, na.rm = TRUE)

sst_train  (sst_train - train_mean) / train_sd

sst_valid  (sst_valid - train_mean) / train_sd

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.

sst_train[is.na(sst_train)]  0
sst_valid[is.na(sst_valid)]  0

Goal

The goal knowledge are break up analogously. Let’s test although: Are phases (categorizations) distributedly equally in each units?

nino_train  nino %>% filter(month  as.Date("1990-01-01"))
nino_valid  nino %>% filter(month >= as.Date("1990-01-01"))

nino_train %>% 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       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 and peak 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 – dataloaders, 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.

web  mannequin(
  channels_in = 1,
  convlstm_hidden = c(16, 16, 32),
  convlstm_kernel = c(3, 3, 5),
  convlstm_layers = 3
)

system  torch_device(if (cuda_is_available()) "cuda" else "cpu")

web  web$to(system = system)
web

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 …

web$eval()

pred_index  c()
pred_phase  c()

coro::loop(for (b in valid_dl) {

  output  web(b$x$to(system = system))

  pred_index  c(pred_index, output[[2]]$to(system = "cpu"))
  pred_phase  rbind(pred_phase, as.matrix(output[[3]]$to(system = "cpu")))

})

… 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()

Nino 3.4 Index: Ground truth vs. predictions (validation set).

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
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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)
      
  }
    
)

Ham, Yoo-Geun, Jeong-Hwan Kim, and Jing-Jia Luo. 2019b. “Deep studying for multi-year ENSO forecasts” 573 (7775): 568–72. https://doi.org/10.1038/s41586-019-1559-7.

———. 2019a. “Deep studying for multi-year ENSO forecasts” 573 (7775): 568–72. https://doi.org/10.1038/s41586-019-1559-7.

Forecasting El Niño-Southern Oscillation (ENSO)

Enter: Sea Floor Temperatures

Goal: Niño 3.4 Index

Enter

Goal

A1: Checklist of GRB information

A2: `convlstm` code

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Forecasting El Niño-Southern Oscillation (ENSO)

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A2: convlstm code

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A2: `convlstm` code