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time-series
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benchmark
component-recovery
symbolic-regression
icml-2026
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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 | |
| 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, | |
| ) | |