> ## 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.

> Time-series Dense Encoder (`TiDE`) is a MLP-based univariate time-series forecasting model. `TiDE` uses Multi-layer Perceptrons (MLPs) in an encoder-decoder model for long-term time-series forecasting. In addition, this model can handle exogenous inputs.

# TiDE

<figure>
  <img src="https://mintcdn.com/nixtla-old-docs/SxdTUKdxfJcIbFeU/neuralforecast/imgs_models/tide.png?fit=max&auto=format&n=SxdTUKdxfJcIbFeU&q=85&s=71a44b45840f9a8700e3dae7d30718a0" alt="Figure 1. TiDE architecture." width="2380" height="1800" data-path="neuralforecast/imgs_models/tide.png" />

  <figcaption aria-hidden="true">Figure 1. TiDE architecture.</figcaption>
</figure>

## 1. Auxiliary Functions

## 1.1 MLP residual

An MLP block with a residual connection.

***

<a href="https://github.com/Nixtla/neuralforecast/blob/main/neuralforecast/models/tide.py#L17" target="_blank" style={{ float: "right", fontSize: "smaller" }}>source</a>

### MLPResidual

> ```text theme={null}
>  MLPResidual (input_dim, hidden_size, output_dim, dropout, layernorm)
> ```

*MLPResidual*

## 2. Model

***

<a href="https://github.com/Nixtla/neuralforecast/blob/main/neuralforecast/models/tide.py#L51" target="_blank" style={{ float: "right", fontSize: "smaller" }}>source</a>

### TiDE

> ```text theme={null}
>  TiDE (h, input_size, hidden_size=512, decoder_output_dim=32,
>        temporal_decoder_dim=128, dropout=0.3, layernorm=True,
>        num_encoder_layers=1, num_decoder_layers=1, temporal_width=4,
>        futr_exog_list=None, hist_exog_list=None, stat_exog_list=None,
>        exclude_insample_y=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:int=32,
>        valid_batch_size:Optional[int]=None, windows_batch_size=1024,
>        inference_windows_batch_size=1024, start_padding_enabled=False,
>        step_size:int=1, scaler_type:str='identity', random_seed:int=1,
>        drop_last_loader:bool=False, alias:Optional[str]=None,
>        optimizer=None, optimizer_kwargs=None, lr_scheduler=None,
>        lr_scheduler_kwargs=None, dataloader_kwargs=None, **trainer_kwargs)
> ```

\*TiDE

Time-series Dense Encoder
([`TiDE`](https://nixtlaverse.nixtla.io/neuralforecast/models.tide.html#tide))
is a MLP-based univariate time-series forecasting model.
[`TiDE`](https://nixtlaverse.nixtla.io/neuralforecast/models.tide.html#tide)
uses Multi-layer Perceptrons (MLPs) in an encoder-decoder model for
long-term time-series forecasting.

**Parameters:**<br /> `h`: int, forecast horizon.<br /> `input_size`: int,
considered autorregresive inputs (lags), y=\[1,2,3,4] input\_size=2 ->
lags=\[1,2].<br /> `hidden_size`: int=1024, number of units for the dense
MLPs.<br /> `decoder_output_dim`: int=32, number of units for the output
of the decoder.<br /> `temporal_decoder_dim`: int=128, number of units for
the hidden sizeof the temporal decoder.<br /> `dropout`: float=0.0,
dropout rate between (0, 1) .<br /> `layernorm`: bool=True, if True uses
Layer Normalization on the MLP residual block outputs.<br />
`num_encoder_layers`: int=1, number of encoder layers.<br />
`num_decoder_layers`: int=1, number of decoder layers.<br />
`temporal_width`: int=4, lower temporal projected dimension.<br />
`futr_exog_list`: str list, future exogenous columns.<br />
`hist_exog_list`: str list, historic exogenous columns.<br />
`stat_exog_list`: str list, static exogenous columns.<br />\
`exclude_insample_y`: bool=False, whether to exclude the target variable
from the historic exogenous data.<br /> `loss`: PyTorch module,
instantiated train loss class from [losses
collection](https://nixtla.github.io/neuralforecast/losses.pytorch.html).<br />
`valid_loss`: PyTorch module=`loss`, instantiated valid loss class from
[losses
collection](https://nixtla.github.io/neuralforecast/losses.pytorch.html).<br />
`max_steps`: int=1000, maximum number of training steps.<br />
`learning_rate`: float=1e-3, Learning rate between (0, 1).<br />
`num_lr_decays`: int=-1, Number of learning rate decays, evenly
distributed across max\_steps.<br /> `early_stop_patience_steps`: int=-1,
Number of validation iterations before early stopping.<br />
`val_check_steps`: int=100, Number of training steps between every
validation loss check.<br /> `batch_size`: int=32, number of different
series in each batch.<br /> `valid_batch_size`: int=None, number of
different series in each validation and test batch.<br />
`windows_batch_size`: int=1024, number of windows to sample in each
training batch, default uses all.<br /> `inference_windows_batch_size`:
int=1024, number of windows to sample in each inference batch, -1 uses
all.<br /> `start_padding_enabled`: bool=False, if True, the model will
pad the time series with zeros at the beginning, by input size.<br />
`step_size`: int=1, step size between each window of temporal data.<br />
`scaler_type`: str=‘identity’, type of scaler for temporal inputs
normalization see [temporal
scalers](https://nixtla.github.io/neuralforecast/common.scalers.html).<br />
`random_seed`: int=1, random\_seed for pytorch initializer and numpy
generators.<br /> `drop_last_loader`: bool=False, if True
`TimeSeriesDataLoader` drops last non-full batch.<br /> `alias`: str,
optional, Custom name of the model.<br /> `optimizer`: Subclass of
‘torch.optim.Optimizer’, optional, user specified optimizer instead of
the default choice (Adam).<br /> `optimizer_kwargs`: dict, optional, list
of parameters used by the user specified `optimizer`.<br />
`lr_scheduler`: Subclass of ‘torch.optim.lr\_scheduler.LRScheduler’,
optional, user specified lr\_scheduler instead of the default choice
(StepLR).<br /> `lr_scheduler_kwargs`: dict, optional, list of parameters
used by the user specified `lr_scheduler`.<br /> `dataloader_kwargs`:
dict, optional, list of parameters passed into the PyTorch Lightning
dataloader by the `TimeSeriesDataLoader`. <br /> `**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).<br />

**References:**<br /> - [Das, Abhimanyu, Weihao Kong, Andrew Leach, Shaan
Mathur, Rajat Sen, and Rose Yu (2024). “Long-term Forecasting with TiDE:
Time-series Dense Encoder.”](http://arxiv.org/abs/2304.08424)\*

***

### TiDE.fit

> ```text theme={null}
>  TiDE.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:**<br /> `dataset`: NeuralForecast’s
[`TimeSeriesDataset`](https://nixtlaverse.nixtla.io/neuralforecast/tsdataset.html#timeseriesdataset),
see
[documentation](https://nixtla.github.io/neuralforecast/tsdataset.html).<br />
`val_size`: int, validation size for temporal cross-validation.<br />
`random_seed`: int=None, random\_seed for pytorch initializer and numpy
generators, overwrites model.\_\_init\_\_’s.<br /> `test_size`: int, test
size for temporal cross-validation.<br />\*

***

### TiDE.predict

> ```text theme={null}
>  TiDE.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:**<br /> `dataset`: NeuralForecast’s
[`TimeSeriesDataset`](https://nixtlaverse.nixtla.io/neuralforecast/tsdataset.html#timeseriesdataset),
see
[documentation](https://nixtla.github.io/neuralforecast/tsdataset.html).<br />
`test_size`: int=None, test size for temporal cross-validation.<br />
`step_size`: int=1, Step size between each window.<br /> `random_seed`:
int=None, random\_seed for pytorch initializer and numpy generators,
overwrites model.\_\_init\_\_’s.<br /> `quantiles`: list of floats,
optional (default=None), target quantiles to predict. <br />
`**data_module_kwargs`: PL’s TimeSeriesDataModule args, see
[documentation](https://pytorch-lightning.readthedocs.io/en/1.6.1/extensions/datamodules.html#using-a-datamodule).\*

## 3. Usage Examples

```python theme={null}
import pandas as pd
import matplotlib.pyplot as plt

from neuralforecast import NeuralForecast
from neuralforecast.models import TiDE
from neuralforecast.losses.pytorch import GMM
from neuralforecast.utils import AirPassengersPanel, AirPassengersStatic

Y_train_df = AirPassengersPanel[AirPassengersPanel.ds<AirPassengersPanel['ds'].values[-12]] # 132 train
Y_test_df = AirPassengersPanel[AirPassengersPanel.ds>=AirPassengersPanel['ds'].values[-12]].reset_index(drop=True) # 12 test

fcst = NeuralForecast(
    models=[
            TiDE(h=12,
                input_size=24,
                loss=GMM(n_components=7, return_params=True, level=[80,90], weighted=True),
                max_steps=100,
                scaler_type='standard',
                futr_exog_list=['y_[lag12]'],
                hist_exog_list=None,
                stat_exog_list=['airline1'],
                ),     
    ],
    freq='ME'
)
fcst.fit(df=Y_train_df, static_df=AirPassengersStatic)
forecasts = fcst.predict(futr_df=Y_test_df)

# Plot quantile predictions
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['TiDE-median'], c='blue', label='median')
plt.fill_between(x=plot_df['ds'][-12:], 
                 y1=plot_df['TiDE-lo-90'][-12:].values,
                 y2=plot_df['TiDE-hi-90'][-12:].values,
                 alpha=0.4, label='level 90')
plt.legend()
plt.grid()
```