> ## Documentation Index
> Fetch the complete documentation index at: https://nixtla-old-docs.mintlify.site/llms.txt
> Use this file to discover all available pages before exploring further.
# RNN
Elman proposed this classic recurrent neural network
([`RNN`](https://nixtlaverse.nixtla.io/neuralforecast/models.rnn.html#rnn))
in 1990, where each layer uses the following recurrent transformation:
$\mathbf{h}^{l}_{t} = \mathrm{Activation}([\mathbf{y}_{t},\mathbf{x}^{(h)}_{t},\mathbf{x}^{(s)}] W^{\intercal}_{ih} + b_{ih} + \mathbf{h}^{l}_{t-1} W^{\intercal}_{hh} + b_{hh})$
where $\mathbf{h}^{l}_{t}$, is the hidden state of RNN layer $l$ for
time $t$, $\mathbf{y}_{t}$ is the input at time $t$ and
$\mathbf{h}_{t-1}$ is the hidden state of the previous layer at $t-1$,
$\mathbf{x}^{(s)}$ are static exogenous inputs, $\mathbf{x}^{(h)}_{t}$
historic exogenous, $\mathbf{x}^{(f)}_{[:t+H]}$ are future exogenous
available at the time of the prediction. The available activations are
`tanh`, and `relu`. The predictions are obtained by transforming the
hidden states into contexts $\mathbf{c}_{[t+1:t+H]}$, that are decoded
and adapted into $\mathbf{\hat{y}}_{[t+1:t+H],[q]}$ through MLPs.
**References** -[Jeffrey L. Elman (1990). “Finding Structure in
Time”.](https://onlinelibrary.wiley.com/doi/10.1207/s15516709cog1402_1)
-[Cho, K., van Merrienboer, B., Gülcehre, C., Bougares, F., Schwenk, H.,
& Bengio, Y. (2014). Learning phrase representations using RNN
encoder-decoder for statistical machine
translation.](http://arxiv.org/abs/1406.1078) Figure 1. Single Layer Elman RNN with MLP
decoder.
***
source
### RNN
> ```text theme={null}
> RNN (h:int, input_size:int=-1, inference_input_size:Optional[int]=None,
> h_train:int=1, encoder_n_layers:int=2, encoder_hidden_size:int=128,
> encoder_activation:str='tanh', encoder_bias:bool=True,
> encoder_dropout:float=0.0, context_size:Optional[int]=None,
> decoder_hidden_size:int=128, decoder_layers:int=2,
> futr_exog_list=None, hist_exog_list=None, stat_exog_list=None,
> exclude_insample_y=False, recurrent=False, loss=MAE(),
> valid_loss=None, max_steps:int=1000, learning_rate:float=0.001,
> num_lr_decays:int=-1, early_stop_patience_steps:int=-1,
> val_check_steps:int=100, batch_size=32,
> valid_batch_size:Optional[int]=None, windows_batch_size=128,
> inference_windows_batch_size=1024, start_padding_enabled=False,
> step_size:int=1, scaler_type:str='robust', random_seed=1,
> drop_last_loader=False, alias:Optional[str]=None, optimizer=None,
> optimizer_kwargs=None, lr_scheduler=None, lr_scheduler_kwargs=None,
> dataloader_kwargs=None, **trainer_kwargs)
> ```
\*RNN
Multi Layer Elman RNN (RNN), with MLP decoder. The network has `tanh` or
`relu` non-linearities, it is trained using ADAM stochastic gradient
descent. The network accepts static, historic and future exogenous data.
**Parameters:** `h`: int, forecast horizon. `input_size`: int,
maximum sequence length for truncated train backpropagation. Default -1
uses 3 \* horizon `inference_input_size`: int, maximum sequence
length for truncated inference. Default None uses input\_size
history. `h_train`: int, maximum sequence length for truncated train
backpropagation. Default 1. `encoder_n_layers`: int=2, number of
layers for the RNN. `encoder_hidden_size`: int=200, units for the
RNN’s hidden state size. `encoder_activation`: str=`tanh`, type of
RNN activation from `tanh` or `relu`. `encoder_bias`: bool=True,
whether or not to use biases b\_ih, b\_hh within RNN units.
`encoder_dropout`: float=0., dropout regularization applied to RNN
outputs. `context_size`: deprecated. `decoder_hidden_size`:
int=200, size of hidden layer for the MLP decoder. `decoder_layers`:
int=2, number of layers for the MLP decoder. `futr_exog_list`: str
list, future exogenous columns. `hist_exog_list`: str list, historic
exogenous columns. `stat_exog_list`: str list, static exogenous
columns. `exclude_insample_y`: bool=False, whether to exclude the
target variable from the historic exogenous data. `recurrent`:
bool=False, whether to produce forecasts recursively (True) or direct
(False). `loss`: PyTorch module, instantiated train loss class from
[losses
collection](https://nixtla.github.io/neuralforecast/losses.pytorch.html).
`valid_loss`: PyTorch module=`loss`, instantiated valid loss class from
[losses
collection](https://nixtla.github.io/neuralforecast/losses.pytorch.html).
`max_steps`: int=1000, maximum number of training steps.
`learning_rate`: float=1e-3, Learning rate between (0, 1).
`num_lr_decays`: int=-1, Number of learning rate decays, evenly
distributed across max\_steps. `early_stop_patience_steps`: int=-1,
Number of validation iterations before early stopping.
`val_check_steps`: int=100, Number of training steps between every
validation loss check. `batch_size`: int=32, number of
differentseries in each batch. `valid_batch_size`: int=None, number
of different series in each validation and test batch.
`windows_batch_size`: int=128, number of windows to sample in each
training batch, default uses all. `inference_windows_batch_size`:
int=1024, number of windows to sample in each inference batch, -1 uses
all. `start_padding_enabled`: bool=False, if True, the model will
pad the time series with zeros at the beginning, by input size.
`step_size`: int=1, step size between each window of temporal
data. \
`scaler_type`: str=‘robust’, type of scaler for temporal inputs
normalization see [temporal
scalers](https://nixtla.github.io/neuralforecast/common.scalers.html).
`random_seed`: int=1, random\_seed for pytorch initializer and numpy
generators. `drop_last_loader`: bool=False, if True
`TimeSeriesDataLoader` drops last non-full batch. `alias`: str,
optional, Custom name of the model. `optimizer`: Subclass of
‘torch.optim.Optimizer’, optional, user specified optimizer instead of
the default choice (Adam). `optimizer_kwargs`: dict, optional, list
of parameters used by the user specified `optimizer`.
`lr_scheduler`: Subclass of ‘torch.optim.lr\_scheduler.LRScheduler’,
optional, user specified lr\_scheduler instead of the default choice
(StepLR). `lr_scheduler_kwargs`: dict, optional, list of parameters
used by the user specified `lr_scheduler`. \
`dataloader_kwargs`: dict, optional, list of parameters passed into the
PyTorch Lightning dataloader by the `TimeSeriesDataLoader`.
`**trainer_kwargs`: int, keyword trainer arguments inherited from
[PyTorch Lighning’s
trainer](https://pytorch-lightning.readthedocs.io/en/stable/api/pytorch_lightning.trainer.trainer.Trainer.html?highlight=trainer). \*
***
### RNN.fit
> ```text theme={null}
> RNN.fit (dataset, val_size=0, test_size=0, random_seed=None,
> distributed_config=None)
> ```
\*Fit.
The `fit` method, optimizes the neural network’s weights using the
initialization parameters (`learning_rate`, `windows_batch_size`, …) and
the `loss` function as defined during the initialization. Within `fit`
we use a PyTorch Lightning `Trainer` that inherits the initialization’s
`self.trainer_kwargs`, to customize its inputs, see [PL’s trainer
arguments](https://pytorch-lightning.readthedocs.io/en/stable/api/pytorch_lightning.trainer.trainer.Trainer.html?highlight=trainer).
The method is designed to be compatible with SKLearn-like classes and in
particular to be compatible with the StatsForecast library.
By default the `model` is not saving training checkpoints to protect
disk memory, to get them change `enable_checkpointing=True` in
`__init__`.
**Parameters:** `dataset`: NeuralForecast’s
[`TimeSeriesDataset`](https://nixtlaverse.nixtla.io/neuralforecast/tsdataset.html#timeseriesdataset),
see
[documentation](https://nixtla.github.io/neuralforecast/tsdataset.html).
`val_size`: int, validation size for temporal cross-validation.
`random_seed`: int=None, random\_seed for pytorch initializer and numpy
generators, overwrites model.\_\_init\_\_’s. `test_size`: int, test
size for temporal cross-validation. \*
***
### RNN.predict
> ```text theme={null}
> RNN.predict (dataset, test_size=None, step_size=1, random_seed=None,
> quantiles=None, **data_module_kwargs)
> ```
\*Predict.
Neural network prediction with PL’s `Trainer` execution of
`predict_step`.
**Parameters:** `dataset`: NeuralForecast’s
[`TimeSeriesDataset`](https://nixtlaverse.nixtla.io/neuralforecast/tsdataset.html#timeseriesdataset),
see
[documentation](https://nixtla.github.io/neuralforecast/tsdataset.html).
`test_size`: int=None, test size for temporal cross-validation.
`step_size`: int=1, Step size between each window. `random_seed`:
int=None, random\_seed for pytorch initializer and numpy generators,
overwrites model.\_\_init\_\_’s. `quantiles`: list of floats,
optional (default=None), target quantiles to predict.
`**data_module_kwargs`: PL’s TimeSeriesDataModule args, see
[documentation](https://pytorch-lightning.readthedocs.io/en/1.6.1/extensions/datamodules.html#using-a-datamodule).\*
## Usage Example
```python theme={null}
import pandas as pd
import matplotlib.pyplot as plt
from neuralforecast import NeuralForecast
from neuralforecast.models import RNN
from neuralforecast.losses.pytorch import MQLoss
from neuralforecast.utils import AirPassengersPanel, AirPassengersStatic
Y_train_df = AirPassengersPanel[AirPassengersPanel.ds=AirPassengersPanel['ds'].values[-12]].reset_index(drop=True) # 12 test
fcst = NeuralForecast(
models=[RNN(h=12,
input_size=24,
inference_input_size=24,
loss=MQLoss(level=[80, 90]),
valid_loss=MQLoss(level=[80, 90]),
scaler_type='standard',
encoder_n_layers=2,
encoder_hidden_size=128,
decoder_hidden_size=128,
decoder_layers=2,
max_steps=200,
futr_exog_list=['y_[lag12]'],
stat_exog_list=['airline1'],
)
],
freq='ME'
)
fcst.fit(df=Y_train_df, static_df=AirPassengersStatic, val_size=12)
forecasts = fcst.predict(futr_df=Y_test_df)
Y_hat_df = forecasts.reset_index(drop=False).drop(columns=['unique_id','ds'])
plot_df = pd.concat([Y_test_df, Y_hat_df], axis=1)
plot_df = pd.concat([Y_train_df, plot_df])
plot_df = plot_df[plot_df.unique_id=='Airline1'].drop('unique_id', axis=1)
plt.plot(plot_df['ds'], plot_df['y'], c='black', label='True')
plt.plot(plot_df['ds'], plot_df['RNN-median'], c='blue', label='median')
plt.fill_between(x=plot_df['ds'][-12:],
y1=plot_df['RNN-lo-90'][-12:].values,
y2=plot_df['RNN-hi-90'][-12:].values,
alpha=0.4, label='level 90')
plt.legend()
plt.grid()
plt.plot()
```
