"""
Implementation of ``nn.Modules`` for N-Beats model.
"""
from typing import Tuple
import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
[docs]def linear(input_size, output_size, bias=True, dropout: int = None):
lin = nn.Linear(input_size, output_size, bias=bias)
if dropout is not None:
return nn.Sequential(nn.Dropout(dropout), lin)
else:
return lin
[docs]def linspace(backcast_length: int, forecast_length: int, centered: bool = False) -> Tuple[np.ndarray, np.ndarray]:
if centered:
norm = max(backcast_length, forecast_length)
start = -backcast_length
stop = forecast_length - 1
else:
norm = backcast_length + forecast_length
start = 0
stop = backcast_length + forecast_length - 1
lin_space = np.linspace(start / norm, stop / norm, backcast_length + forecast_length, dtype=np.float32)
b_ls = lin_space[:backcast_length]
f_ls = lin_space[backcast_length:]
return b_ls, f_ls
[docs]class NBEATSBlock(nn.Module):
def __init__(
self,
units,
thetas_dim,
num_block_layers=4,
backcast_length=10,
forecast_length=5,
share_thetas=False,
dropout=0.1,
):
super().__init__()
self.units = units
self.thetas_dim = thetas_dim
self.backcast_length = backcast_length
self.forecast_length = forecast_length
self.share_thetas = share_thetas
fc_stack = [
nn.Linear(backcast_length, units),
nn.ReLU(),
]
for _ in range(num_block_layers - 1):
fc_stack.extend([linear(units, units, dropout=dropout), nn.ReLU()])
self.fc = nn.Sequential(*fc_stack)
if share_thetas:
self.theta_f_fc = self.theta_b_fc = nn.Linear(units, thetas_dim, bias=False)
else:
self.theta_b_fc = nn.Linear(units, thetas_dim, bias=False)
self.theta_f_fc = nn.Linear(units, thetas_dim, bias=False)
[docs] def forward(self, x):
return self.fc(x)
[docs]class NBEATSSeasonalBlock(NBEATSBlock):
def __init__(
self,
units,
thetas_dim=None,
num_block_layers=4,
backcast_length=10,
forecast_length=5,
nb_harmonics=None,
min_period=1,
dropout=0.1,
):
if nb_harmonics:
thetas_dim = nb_harmonics
else:
thetas_dim = forecast_length
self.min_period = min_period
super().__init__(
units=units,
thetas_dim=thetas_dim,
num_block_layers=num_block_layers,
backcast_length=backcast_length,
forecast_length=forecast_length,
share_thetas=True,
dropout=dropout,
)
backcast_linspace, forecast_linspace = linspace(backcast_length, forecast_length, centered=False)
p1, p2 = (thetas_dim // 2, thetas_dim // 2) if thetas_dim % 2 == 0 else (thetas_dim // 2, thetas_dim // 2 + 1)
s1_b = torch.tensor(
[np.cos(2 * np.pi * i * backcast_linspace) for i in self.get_frequencies(p1)], dtype=torch.float32
) # H/2-1
s2_b = torch.tensor(
[np.sin(2 * np.pi * i * backcast_linspace) for i in self.get_frequencies(p2)], dtype=torch.float32
)
self.register_buffer("S_backcast", torch.cat([s1_b, s2_b]))
s1_f = torch.tensor(
[np.cos(2 * np.pi * i * forecast_linspace) for i in self.get_frequencies(p1)], dtype=torch.float32
) # H/2-1
s2_f = torch.tensor(
[np.sin(2 * np.pi * i * forecast_linspace) for i in self.get_frequencies(p2)], dtype=torch.float32
)
self.register_buffer("S_forecast", torch.cat([s1_f, s2_f]))
[docs] def forward(self, x) -> Tuple[torch.Tensor, torch.Tensor]:
x = super().forward(x)
amplitudes_backward = self.theta_b_fc(x)
backcast = amplitudes_backward.mm(self.S_backcast)
amplitudes_forward = self.theta_f_fc(x)
forecast = amplitudes_forward.mm(self.S_forecast)
return backcast, forecast
def get_frequencies(self, n):
return np.linspace(0, (self.backcast_length + self.forecast_length) / self.min_period, n)
[docs]class NBEATSTrendBlock(NBEATSBlock):
def __init__(
self,
units,
thetas_dim,
num_block_layers=4,
backcast_length=10,
forecast_length=5,
dropout=0.1,
):
super().__init__(
units=units,
thetas_dim=thetas_dim,
num_block_layers=num_block_layers,
backcast_length=backcast_length,
forecast_length=forecast_length,
share_thetas=True,
dropout=dropout,
)
backcast_linspace, forecast_linspace = linspace(backcast_length, forecast_length, centered=True)
norm = np.sqrt(forecast_length / thetas_dim) # ensure range of predictions is comparable to input
coefficients = torch.tensor([backcast_linspace**i for i in range(thetas_dim)], dtype=torch.float32)
self.register_buffer("T_backcast", coefficients * norm)
coefficients = torch.tensor([forecast_linspace**i for i in range(thetas_dim)], dtype=torch.float32)
self.register_buffer("T_forecast", coefficients * norm)
[docs] def forward(self, x) -> Tuple[torch.Tensor, torch.Tensor]:
x = super().forward(x)
backcast = self.theta_b_fc(x).mm(self.T_backcast)
forecast = self.theta_f_fc(x).mm(self.T_forecast)
return backcast, forecast
[docs]class NBEATSGenericBlock(NBEATSBlock):
def __init__(
self,
units,
thetas_dim,
num_block_layers=4,
backcast_length=10,
forecast_length=5,
dropout=0.1,
):
super().__init__(
units=units,
thetas_dim=thetas_dim,
num_block_layers=num_block_layers,
backcast_length=backcast_length,
forecast_length=forecast_length,
dropout=dropout,
)
self.backcast_fc = nn.Linear(thetas_dim, backcast_length)
self.forecast_fc = nn.Linear(thetas_dim, forecast_length)
[docs] def forward(self, x):
x = super().forward(x)
theta_b = F.relu(self.theta_b_fc(x))
theta_f = F.relu(self.theta_f_fc(x))
return self.backcast_fc(theta_b), self.forecast_fc(theta_f)