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"""DR-TS-AE: Structured Autoencoder for Time Series Decomposition.
This module implements a neural network approach to decompose time series into
trend, seasonal, and residual components using specialized decoder branches.
Architecture:
- 1D Conv Encoder → Latent embeddings (z_T for trend, z_S for seasonal)
- Trend Decoder: Low-pass / smooth reconstruction branch
- Seasonal Decoder: Periodic / narrow-band reconstruction branch
- Residual is computed as: r = x - trend - seasonal
Training Objective:
L = ReconstructionLoss + α_T*TrendSmoothness + α_S*SeasonalPeriodicity
"""
from __future__ import annotations
from dataclasses import dataclass, field
from pathlib import Path
from typing import Any, Dict, List, Optional, Tuple
import numpy as np
try:
import torch
import torch.nn as nn
import torch.nn.functional as F
from torch.utils.data import DataLoader, TensorDataset
_HAS_TORCH = True
except ImportError:
_HAS_TORCH = False
torch = None
nn = None
@dataclass
class DRTSAEConfig:
"""Configuration for DR-TS-AE model.
Attributes
----------
latent_dim : int
Dimension of latent space for each branch.
hidden_channels : List[int]
Channel sizes for encoder conv layers.
kernel_size : int
Kernel size for conv layers.
alpha_T : float
Weight for trend smoothness regularization.
alpha_S : float
Weight for seasonal periodicity regularization.
period : int
Expected seasonal period (for regularization).
learning_rate : float
Learning rate for training.
n_epochs : int
Number of training epochs.
batch_size : int
Batch size for training.
"""
latent_dim: int = 16
hidden_channels: List[int] = field(default_factory=lambda: [32, 64])
kernel_size: int = 7
alpha_T: float = 10.0
alpha_S: float = 5.0
period: int = 32
learning_rate: float = 1e-3
n_epochs: int = 100
batch_size: int = 32
if _HAS_TORCH:
class StructuredAE(nn.Module):
"""Structured Autoencoder for time series decomposition.
The model has:
- Shared 1D conv encoder
- Two latent vectors: z_trend and z_seasonal
- Two decoder branches producing trend and seasonal components
"""
def __init__(
self,
input_length: int,
latent_dim: int = 16,
hidden_channels: Optional[List[int]] = None,
kernel_size: int = 7,
):
super().__init__()
if hidden_channels is None:
hidden_channels = [32, 64]
self.input_length = input_length
self.latent_dim = latent_dim
self.hidden_channels = hidden_channels
# Encoder layers
enc_layers = []
in_ch = 1
for out_ch in hidden_channels:
enc_layers.extend([
nn.Conv1d(in_ch, out_ch, kernel_size, padding=kernel_size // 2),
nn.BatchNorm1d(out_ch),
nn.ReLU(),
nn.MaxPool1d(2),
])
in_ch = out_ch
self.encoder = nn.Sequential(*enc_layers)
# Calculate encoded length after pooling
self.encoded_length = input_length // (2 ** len(hidden_channels))
self.flat_dim = hidden_channels[-1] * self.encoded_length
# Latent projections
self.fc_trend = nn.Linear(self.flat_dim, latent_dim)
self.fc_seasonal = nn.Linear(self.flat_dim, latent_dim)
# Trend decoder (smooth, low-pass)
self.trend_fc = nn.Linear(latent_dim, self.flat_dim)
trend_dec = []
in_ch = hidden_channels[-1]
for i, out_ch in enumerate(reversed(hidden_channels[:-1])):
trend_dec.extend([
nn.Upsample(scale_factor=2, mode='linear', align_corners=False),
nn.Conv1d(in_ch, out_ch, kernel_size, padding=kernel_size // 2),
nn.BatchNorm1d(out_ch),
nn.ReLU(),
])
in_ch = out_ch
# Final layer
trend_dec.extend([
nn.Upsample(scale_factor=2, mode='linear', align_corners=False),
nn.Conv1d(in_ch, 1, kernel_size * 2 - 1, padding=(kernel_size * 2 - 1) // 2),
])
self.trend_decoder = nn.Sequential(*trend_dec)
# Seasonal decoder (periodic-aware)
self.seasonal_fc = nn.Linear(latent_dim, self.flat_dim)
seasonal_dec = []
in_ch = hidden_channels[-1]
for i, out_ch in enumerate(reversed(hidden_channels[:-1])):
seasonal_dec.extend([
nn.Upsample(scale_factor=2, mode='linear', align_corners=False),
nn.Conv1d(in_ch, out_ch, kernel_size, padding=kernel_size // 2),
nn.BatchNorm1d(out_ch),
nn.ReLU(),
])
in_ch = out_ch
seasonal_dec.extend([
nn.Upsample(scale_factor=2, mode='linear', align_corners=False),
nn.Conv1d(in_ch, 1, kernel_size, padding=kernel_size // 2),
])
self.seasonal_decoder = nn.Sequential(*seasonal_dec)
def encode(self, x: torch.Tensor) -> Tuple[torch.Tensor, torch.Tensor]:
"""Encode input to latent representations."""
# x: (batch, 1, length)
h = self.encoder(x)
h_flat = h.view(h.size(0), -1)
z_trend = self.fc_trend(h_flat)
z_seasonal = self.fc_seasonal(h_flat)
return z_trend, z_seasonal
def decode_trend(self, z: torch.Tensor) -> torch.Tensor:
"""Decode trend latent to trend component."""
h = self.trend_fc(z)
h = h.view(h.size(0), self.hidden_channels[-1], self.encoded_length)
trend = self.trend_decoder(h)
# Ensure output matches input length
if trend.size(-1) != self.input_length:
trend = F.interpolate(trend, size=self.input_length, mode='linear', align_corners=False)
return trend
def decode_seasonal(self, z: torch.Tensor) -> torch.Tensor:
"""Decode seasonal latent to seasonal component."""
h = self.seasonal_fc(z)
h = h.view(h.size(0), self.hidden_channels[-1], self.encoded_length)
seasonal = self.seasonal_decoder(h)
if seasonal.size(-1) != self.input_length:
seasonal = F.interpolate(seasonal, size=self.input_length, mode='linear', align_corners=False)
return seasonal
def forward(self, x: torch.Tensor) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
"""Forward pass returning trend, seasonal, and reconstruction."""
z_trend, z_seasonal = self.encode(x)
trend = self.decode_trend(z_trend)
seasonal = self.decode_seasonal(z_seasonal)
recon = trend + seasonal
return trend, seasonal, recon
def _second_diff_loss(x: "torch.Tensor") -> "torch.Tensor":
"""Compute second-order difference penalty for smoothness."""
if x.size(-1) < 3:
return torch.tensor(0.0, device=x.device)
diff2 = x[..., 2:] - 2 * x[..., 1:-1] + x[..., :-2]
return torch.mean(diff2 ** 2)
def _seasonal_lag_loss(x: "torch.Tensor", period: int) -> "torch.Tensor":
"""Compute seasonal periodicity penalty."""
if period >= x.size(-1) or period < 1:
return torch.tensor(0.0, device=x.device)
diff = x[..., period:] - x[..., :-period]
return torch.mean(diff ** 2)
def train_structured_ae(
series_list: List[np.ndarray],
config: Optional[DRTSAEConfig] = None,
device: str = 'cpu',
verbose: bool = False,
) -> "StructuredAE":
"""Train a StructuredAE model on a list of time series.
Parameters
----------
series_list : List[np.ndarray]
List of 1D numpy arrays (training data).
config : DRTSAEConfig, optional
Model and training configuration.
device : str
Device to train on ('cpu' or 'cuda').
verbose : bool
Whether to print training progress.
Returns
-------
StructuredAE
Trained model.
"""
if not _HAS_TORCH:
raise ImportError("PyTorch is required for DR-TS-AE.")
cfg = config or DRTSAEConfig()
# Determine input length (use most common length or pad)
lengths = [len(s) for s in series_list]
input_length = max(lengths)
# Pad/truncate series to same length
data = []
for s in series_list:
s = np.asarray(s, dtype=np.float32).ravel()
if len(s) < input_length:
s = np.pad(s, (0, input_length - len(s)), mode='edge')
elif len(s) > input_length:
s = s[:input_length]
# Normalize
s_mean, s_std = s.mean(), s.std() + 1e-8
s = (s - s_mean) / s_std
data.append(s)
X = np.stack(data, axis=0)[:, np.newaxis, :] # (N, 1, L)
X_tensor = torch.tensor(X, dtype=torch.float32)
dataset = TensorDataset(X_tensor)
loader = DataLoader(dataset, batch_size=cfg.batch_size, shuffle=True)
# Build model
model = StructuredAE(
input_length=input_length,
latent_dim=cfg.latent_dim,
hidden_channels=cfg.hidden_channels,
kernel_size=cfg.kernel_size,
).to(device)
optimizer = torch.optim.Adam(model.parameters(), lr=cfg.learning_rate)
model.train()
for epoch in range(cfg.n_epochs):
total_loss = 0.0
for (batch,) in loader:
batch = batch.to(device)
optimizer.zero_grad()
trend, seasonal, recon = model(batch)
# Reconstruction loss
recon_loss = F.mse_loss(recon, batch)
# Regularization
trend_smooth_loss = _second_diff_loss(trend)
seasonal_period_loss = _seasonal_lag_loss(seasonal, cfg.period)
loss = recon_loss + cfg.alpha_T * trend_smooth_loss + cfg.alpha_S * seasonal_period_loss
loss.backward()
optimizer.step()
total_loss += loss.item() * batch.size(0)
if verbose and (epoch + 1) % 20 == 0:
avg_loss = total_loss / len(X)
print(f"Epoch {epoch+1}/{cfg.n_epochs}, Loss: {avg_loss:.6f}")
model.eval()
return model
def decompose_with_ae(
y: np.ndarray,
model: "StructuredAE",
device: str = 'cpu',
) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
"""Decompose a single series using a trained StructuredAE.
Parameters
----------
y : np.ndarray
Input time series.
model : StructuredAE
Trained model.
device : str
Device to run inference on.
Returns
-------
trend : np.ndarray
seasonal : np.ndarray
residual : np.ndarray
"""
if not _HAS_TORCH:
raise ImportError("PyTorch is required for DR-TS-AE.")
y_arr = np.asarray(y, dtype=np.float32).ravel()
n = len(y_arr)
input_length = model.input_length
# Store normalization params
y_mean, y_std = y_arr.mean(), y_arr.std() + 1e-8
y_norm = (y_arr - y_mean) / y_std
# Pad/truncate
if n < input_length:
y_padded = np.pad(y_norm, (0, input_length - n), mode='edge')
elif n > input_length:
y_padded = y_norm[:input_length]
else:
y_padded = y_norm
x_tensor = torch.tensor(y_padded[np.newaxis, np.newaxis, :], dtype=torch.float32).to(device)
model.eval()
with torch.no_grad():
trend_t, seasonal_t, _ = model(x_tensor)
trend = trend_t.cpu().numpy().squeeze()
seasonal = seasonal_t.cpu().numpy().squeeze()
# Truncate/pad back to original length
if n < input_length:
trend = trend[:n]
seasonal = seasonal[:n]
elif n > input_length:
# Extrapolate by repeating edge
trend = np.pad(trend, (0, n - input_length), mode='edge')
seasonal = np.pad(seasonal, (0, n - input_length), mode='edge')
# Denormalize
trend = trend * y_std + y_mean * (trend.mean() / (trend.mean() + 1e-8) if abs(trend.mean()) > 1e-8 else 0)
# Keep seasonal zero-mean
seasonal = seasonal * y_std
# Adjust to ensure reconstruction
# trend should capture the mean/level, seasonal should be zero-mean
trend_offset = y_arr.mean() - (trend + seasonal).mean()
trend = trend + trend_offset
residual = y_arr - trend - seasonal
return trend, seasonal, residual
# Global model cache
_MODEL_CACHE: Dict[str, "StructuredAE"] = {}
def dr_ts_ae_decompose(
y: np.ndarray,
config: Optional[Dict[str, Any]] = None,
fs: float = 1.0,
meta: Optional[Dict[str, Any]] = None,
) -> "DecompResult":
"""DR-TS-AE decomposition using a structured autoencoder.
Parameters
----------
y : np.ndarray
Input time series.
config : dict, optional
Configuration with keys: model_path, latent_dim, period, etc.
fs : float
Sampling frequency (not directly used).
meta : dict, optional
Metadata from scenario.
Returns
-------
DecompResult
Decomposition result.
"""
from .decomp_methods import DecompResult
if not _HAS_TORCH:
# Fallback to simple decomposition
y_arr = np.asarray(y, dtype=float).ravel()
n = len(y_arr)
window = max(3, n // 10)
trend = np.convolve(y_arr, np.ones(window) / window, mode='same')
residual = y_arr - trend
seasonal = np.zeros(n)
return DecompResult(
trend=trend,
season=seasonal,
residual=residual,
extra={'method': 'dr_ts_ae', 'fallback': 'no_torch'},
)
y_arr = np.asarray(y, dtype=float).ravel()
cfg = dict(config or {})
model_path = cfg.get('model_path')
device = cfg.get('device', 'cpu')
cache_model = bool(cfg.get('cache_model', True))
cache_key = cfg.get('cache_key')
# Check if we have a pre-trained model
model = None
if model_path and Path(model_path).exists():
path_key = str(model_path)
if path_key not in _MODEL_CACHE:
_MODEL_CACHE[path_key] = torch.load(model_path, map_location=device)
model = _MODEL_CACHE[path_key]
if model is None and cache_model:
if cache_key is None:
period_val = cfg.get('period')
if period_val is None and meta:
period_val = meta.get('primary_period')
period_val = int(period_val) if period_val not in (None, 0) else 32
hidden = cfg.get('hidden_channels', [32, 64])
cache_key = (
f"auto_len{len(y_arr)}_latent{cfg.get('latent_dim', 16)}"
f"_period{period_val}_epochs{cfg.get('n_epochs', 50)}"
f"_kernel{cfg.get('kernel_size', 7)}"
f"_hidden{','.join(str(v) for v in hidden)}"
f"_device{device}"
)
if cache_key in _MODEL_CACHE:
model = _MODEL_CACHE[cache_key]
if model is None:
# Train a quick model on just this series (not ideal but works for single inference)
# In practice, should use a pre-trained model
ae_config = DRTSAEConfig(
latent_dim=int(cfg.get('latent_dim', 16)),
period=int(cfg.get('period', meta.get('primary_period', 32) if meta else 32)),
n_epochs=int(cfg.get('n_epochs', 50)), # Quick training
alpha_T=float(cfg.get('alpha_T', 10.0)),
alpha_S=float(cfg.get('alpha_S', 5.0)),
)
# Train on just this series (multiple copies for batch diversity)
model = train_structured_ae(
[y_arr] * 10, # Replicate for training
config=ae_config,
device=device,
verbose=False,
)
if cache_model and cache_key:
_MODEL_CACHE[cache_key] = model
trend, seasonal, residual = decompose_with_ae(y_arr, model, device=device)
extra = {
'method': 'dr_ts_ae',
'params': cfg,
}
return DecompResult(
trend=trend,
season=seasonal,
residual=residual,
extra=extra,
)