The FEDformer model tackles the challenge of finding reliable dependencies on intricate temporal patterns of long-horizon forecasting.

The architecture has the following distinctive features: - In-built progressive decomposition in trend and seasonal components based on a moving average filter. - Frequency Enhanced Block and Frequency Enhanced Attention to perform attention in the sparse representation on basis such as Fourier transform. - Classic encoder-decoder proposed by Vaswani et al. (2017) with a multi-head attention mechanism.

The FEDformer model utilizes a three-component approach to define its embedding: - It employs encoded autoregressive features obtained from a convolution network. - Absolute positional embeddings obtained from calendar features are utilized.

References
- Zhou, Tian, Ziqing Ma, Qingsong Wen, Xue Wang, Liang Sun, and Rong Jin.. “FEDformer: Frequency enhanced decomposed transformer for long-term series forecasting”

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1. Auxiliary functions

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AutoCorrelationLayer

 AutoCorrelationLayer (correlation, hidden_size, n_head, d_keys=None,
                       d_values=None)

*Base class for all neural network modules.

Your models should also subclass this class.

Modules can also contain other Modules, allowing to nest them in a tree structure. You can assign the submodules as regular attributes::

import torch.nn as nn
import torch.nn.functional as F

class Model(nn.Module):
    def __init__(self):
        super().__init__()
        self.conv1 = nn.Conv2d(1, 20, 5)
        self.conv2 = nn.Conv2d(20, 20, 5)

    def forward(self, x):
        x = F.relu(self.conv1(x))
        return F.relu(self.conv2(x))

Submodules assigned in this way will be registered, and will have their parameters converted too when you call :meth:to, etc.

.. note:: As per the example above, an __init__() call to the parent class must be made before assignment on the child.

:ivar training: Boolean represents whether this module is in training or evaluation mode. :vartype training: bool*

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LayerNorm

 LayerNorm (channels)

Special designed layernorm for the seasonal part

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SeriesDecomp

 SeriesDecomp (kernel_size)

Series decomposition block

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MovingAvg

 MovingAvg (kernel_size, stride)

Moving average block to highlight the trend of time series

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Decoder

 Decoder (layers, norm_layer=None, projection=None)

FEDformer decoder

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DecoderLayer

 DecoderLayer (self_attention, cross_attention, hidden_size, c_out,
               conv_hidden_size=None, MovingAvg=25, dropout=0.1,
               activation='relu')

FEDformer decoder layer with the progressive decomposition architecture

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Encoder

 Encoder (attn_layers, conv_layers=None, norm_layer=None)

FEDformer encoder

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EncoderLayer

 EncoderLayer (attention, hidden_size, conv_hidden_size=None,
               MovingAvg=25, dropout=0.1, activation='relu')

FEDformer encoder layer with the progressive decomposition architecture

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FourierCrossAttention

 FourierCrossAttention (in_channels, out_channels, seq_len_q, seq_len_kv,
                        modes=64, mode_select_method='random',
                        activation='tanh', policy=0)

*Base class for all neural network modules.

Your models should also subclass this class.

Modules can also contain other Modules, allowing to nest them in a tree structure. You can assign the submodules as regular attributes::

import torch.nn as nn
import torch.nn.functional as F

class Model(nn.Module):
    def __init__(self):
        super().__init__()
        self.conv1 = nn.Conv2d(1, 20, 5)
        self.conv2 = nn.Conv2d(20, 20, 5)

    def forward(self, x):
        x = F.relu(self.conv1(x))
        return F.relu(self.conv2(x))

Submodules assigned in this way will be registered, and will have their parameters converted too when you call :meth:to, etc.

.. note:: As per the example above, an __init__() call to the parent class must be made before assignment on the child.

:ivar training: Boolean represents whether this module is in training or evaluation mode. :vartype training: bool*

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FourierBlock

 FourierBlock (in_channels, out_channels, seq_len, modes=0,
               mode_select_method='random')

*Base class for all neural network modules.

Your models should also subclass this class.

Modules can also contain other Modules, allowing to nest them in a tree structure. You can assign the submodules as regular attributes::

import torch.nn as nn
import torch.nn.functional as F

class Model(nn.Module):
    def __init__(self):
        super().__init__()
        self.conv1 = nn.Conv2d(1, 20, 5)
        self.conv2 = nn.Conv2d(20, 20, 5)

    def forward(self, x):
        x = F.relu(self.conv1(x))
        return F.relu(self.conv2(x))

Submodules assigned in this way will be registered, and will have their parameters converted too when you call :meth:to, etc.

.. note:: As per the example above, an __init__() call to the parent class must be made before assignment on the child.

:ivar training: Boolean represents whether this module is in training or evaluation mode. :vartype training: bool*

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get_frequency_modes

 get_frequency_modes (seq_len, modes=64, mode_select_method='random')

Get modes on frequency domain: ‘random’ for sampling randomly ‘else’ for sampling the lowest modes;

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2. Model

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FEDformer

 FEDformer (h:int, input_size:int, stat_exog_list=None,
            hist_exog_list=None, futr_exog_list=None,
            decoder_input_size_multiplier:float=0.5,
            version:str='Fourier', modes:int=64, mode_select:str='random',
            hidden_size:int=128, dropout:float=0.05, n_head:int=8,
            conv_hidden_size:int=32, activation:str='gelu',
            encoder_layers:int=2, decoder_layers:int=1,
            MovingAvg_window:int=25, loss=MAE(), valid_loss=None,
            max_steps:int=5000, learning_rate:float=0.0001,
            num_lr_decays:int=-1, early_stop_patience_steps:int=-1,
            start_padding_enabled=False, val_check_steps:int=100,
            batch_size:int=32, valid_batch_size:Optional[int]=None,
            windows_batch_size=1024, inference_windows_batch_size=1024,
            step_size:int=1, scaler_type:str='identity',
            random_seed:int=1, num_workers_loader:int=0,
            drop_last_loader:bool=False, optimizer=None,
            optimizer_kwargs=None, **trainer_kwargs)

*FEDformer

The FEDformer model tackles the challenge of finding reliable dependencies on intricate temporal patterns of long-horizon forecasting.

The architecture has the following distinctive features: - In-built progressive decomposition in trend and seasonal components based on a moving average filter. - Frequency Enhanced Block and Frequency Enhanced Attention to perform attention in the sparse representation on basis such as Fourier transform. - Classic encoder-decoder proposed by Vaswani et al. (2017) with a multi-head attention mechanism.

The FEDformer model utilizes a three-component approach to define its embedding: - It employs encoded autoregressive features obtained from a convolution network. - Absolute positional embeddings obtained from calendar features are utilized.

Parameters:
h: int, forecast horizon.
input_size: int, maximum sequence length for truncated train backpropagation. Default -1 uses all history.
futr_exog_list: str list, future exogenous columns.
hist_exog_list: str list, historic exogenous columns.
stat_exog_list: str list, static exogenous columns.
decoder_input_size_multiplier: float = 0.5, .
version: str = ‘Fourier’, version of the model.
modes: int = 64, number of modes for the Fourier block.
mode_select: str = ‘random’, method to select the modes for the Fourier block.
hidden_size: int=128, units of embeddings and encoders.
dropout: float (0, 1), dropout throughout Autoformer architecture.
n_head: int=8, controls number of multi-head’s attention.
conv_hidden_size: int=32, channels of the convolutional encoder.
activation: str=GELU, activation from [‘ReLU’, ‘Softplus’, ‘Tanh’, ‘SELU’, ‘LeakyReLU’, ‘PReLU’, ‘Sigmoid’, ‘GELU’].
encoder_layers: int=2, number of layers for the TCN encoder.
decoder_layers: int=1, number of layers for the MLP decoder.
MovingAvg_window: int=25, window size for the moving average filter.
loss: PyTorch module, instantiated train loss class from losses collection.
valid_loss: PyTorch module, instantiated validation loss class from losses collection.
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 different series in each batch.
valid_batch_size: int=None, number of different series in each validation and test batch, if None uses batch_size.
windows_batch_size: int=1024, 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.
start_padding_enabled: bool=False, if True, the model will pad the time series with zeros at the beginning, by input size.
scaler_type: str=‘robust’, type of scaler for temporal inputs normalization see temporal scalers.
random_seed: int=1, random_seed for pytorch initializer and numpy generators.
num_workers_loader: int=os.cpu_count(), workers to be used by TimeSeriesDataLoader.
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.
**trainer_kwargs: int, keyword trainer arguments inherited from PyTorch Lighning’s trainer.
*

import numpy as np
import pandas as pd
import pytorch_lightning as pl
import matplotlib.pyplot as plt

from neuralforecast import NeuralForecast
from neuralforecast.models import MLP
from neuralforecast.losses.pytorch import MQLoss, DistributionLoss, MSE
from neuralforecast.tsdataset import TimeSeriesDataset
from neuralforecast.utils import AirPassengers, AirPassengersPanel, AirPassengersStatic, augment_calendar_df

AirPassengersPanel, calendar_cols = augment_calendar_df(df=AirPassengersPanel, freq='M')

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

model = FEDformer(h=12,
                 input_size=24,
                 modes=64,
                 hidden_size=64,
                 conv_hidden_size=128,
                 n_head=8,
                 loss=MAE(),
                 futr_exog_list=calendar_cols,
                 scaler_type='robust',
                 learning_rate=1e-3,
                 max_steps=500,
                 batch_size=2,
                 windows_batch_size=32,
                 val_check_steps=50,
                 early_stop_patience_steps=2)

nf = NeuralForecast(
    models=[model],
    freq='M',
)
nf.fit(df=Y_train_df, static_df=None, val_size=12)
forecasts = nf.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])

if model.loss.is_distribution_output:
    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['FEDformer-median'], c='blue', label='median')
    plt.fill_between(x=plot_df['ds'][-12:], 
                    y1=plot_df['FEDformer-lo-90'][-12:].values, 
                    y2=plot_df['FEDformer-hi-90'][-12:].values,
                    alpha=0.4, label='level 90')
    plt.grid()
    plt.legend()
    plt.plot()
else:
    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['FEDformer'], c='blue', label='Forecast')
    plt.legend()
    plt.grid()