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"""
Station Embedding Module for LILITH.
Learns dense representations of weather stations based on:
- Geographic coordinates (lat/lon/elevation)
- Historical observation patterns
- Station characteristics
"""
import math
from typing import Optional
import torch
import torch.nn as nn
import torch.nn.functional as F
class PositionalEncoding3D(nn.Module):
"""
3D positional encoding for geographic coordinates.
Uses spherical harmonics-inspired encoding for lat/lon
and linear encoding for elevation.
"""
def __init__(self, d_model: int, max_freq: int = 10):
super().__init__()
self.d_model = d_model
self.max_freq = max_freq
# Frequencies for sinusoidal encoding
freqs = torch.exp(
torch.arange(0, max_freq) * (-math.log(10000.0) / max_freq)
)
self.register_buffer("freqs", freqs)
# Projection to model dimension
# 2 coords * 2 (sin/cos) * max_freq + elevation features
input_dim = 4 * max_freq + 4
self.proj = nn.Linear(input_dim, d_model)
def forward(
self,
lat: torch.Tensor,
lon: torch.Tensor,
elev: torch.Tensor,
) -> torch.Tensor:
"""
Encode geographic coordinates.
Args:
lat: Latitude in degrees (-90, 90), shape (batch, n_stations)
lon: Longitude in degrees (-180, 180), shape (batch, n_stations)
elev: Elevation in meters, shape (batch, n_stations)
Returns:
Positional encoding of shape (batch, n_stations, d_model)
"""
# Normalize coordinates
lat_norm = lat / 90.0 # [-1, 1]
lon_norm = lon / 180.0 # [-1, 1]
# Convert to radians for spherical encoding
lat_rad = lat_norm * (math.pi / 2)
lon_rad = lon_norm * math.pi
# Sinusoidal encoding for latitude
lat_enc = torch.cat([
torch.sin(lat_rad.unsqueeze(-1) * self.freqs),
torch.cos(lat_rad.unsqueeze(-1) * self.freqs),
], dim=-1)
# Sinusoidal encoding for longitude
lon_enc = torch.cat([
torch.sin(lon_rad.unsqueeze(-1) * self.freqs),
torch.cos(lon_rad.unsqueeze(-1) * self.freqs),
], dim=-1)
# Elevation encoding (normalized and log-scaled)
elev_norm = torch.clamp(elev / 8848.0, -1, 1) # Normalize by Everest height
elev_log = torch.sign(elev) * torch.log1p(torch.abs(elev) / 100.0) / 5.0
elev_enc = torch.stack([
elev_norm,
elev_log,
torch.sin(elev_norm * math.pi),
torch.cos(elev_norm * math.pi),
], dim=-1)
# Concatenate all encodings
encoding = torch.cat([lat_enc, lon_enc, elev_enc], dim=-1)
return self.proj(encoding)
class StationEmbedding(nn.Module):
"""
Embeds weather station observations into a dense vector space.
Combines:
1. Feature embedding (weather variables)
2. Positional embedding (geographic location)
3. Temporal embedding (time features)
Architecture:
Input features → LayerNorm → MLP → + Position Encoding → Output
"""
def __init__(
self,
input_dim: int,
hidden_dim: int = 256,
output_dim: int = 256,
n_layers: int = 2,
dropout: float = 0.1,
use_position: bool = True,
):
"""
Initialize station embedding module.
Args:
input_dim: Number of input weather features
hidden_dim: Hidden dimension of MLP
output_dim: Output embedding dimension
n_layers: Number of MLP layers
dropout: Dropout probability
use_position: Whether to add positional encoding
"""
super().__init__()
self.input_dim = input_dim
self.hidden_dim = hidden_dim
self.output_dim = output_dim
self.use_position = use_position
# Input normalization
self.input_norm = nn.LayerNorm(input_dim)
# Feature embedding MLP
layers = []
in_dim = input_dim
for i in range(n_layers):
out_dim = hidden_dim if i < n_layers - 1 else output_dim
layers.extend([
nn.Linear(in_dim, out_dim),
nn.GELU(),
nn.Dropout(dropout),
])
in_dim = out_dim
# Remove last dropout
self.feature_mlp = nn.Sequential(*layers[:-1])
# Positional encoding
if use_position:
self.pos_encoding = PositionalEncoding3D(output_dim)
# Output normalization
self.output_norm = nn.LayerNorm(output_dim)
# Initialize weights
self._init_weights()
def _init_weights(self):
"""Initialize weights with Xavier uniform."""
for module in self.modules():
if isinstance(module, nn.Linear):
nn.init.xavier_uniform_(module.weight)
if module.bias is not None:
nn.init.zeros_(module.bias)
def forward(
self,
features: torch.Tensor,
coords: Optional[torch.Tensor] = None,
mask: Optional[torch.Tensor] = None,
) -> torch.Tensor:
"""
Embed station observations.
Args:
features: Weather features of shape (batch, n_stations, seq_len, n_features)
or (batch, n_stations, n_features) for single timestep
coords: Station coordinates (lat, lon, elev) of shape (batch, n_stations, 3)
mask: Valid observation mask of shape (batch, n_stations, seq_len)
Returns:
Embeddings of shape (batch, n_stations, seq_len, output_dim)
or (batch, n_stations, output_dim) for single timestep
"""
# Handle different input shapes
single_timestep = features.dim() == 3
if single_timestep:
features = features.unsqueeze(2) # Add seq_len dimension
batch_size, n_stations, seq_len, n_features = features.shape
# Reshape for MLP processing
x = features.reshape(-1, n_features)
# Apply mask if provided (zero out invalid observations)
if mask is not None:
mask_flat = mask.reshape(-1, 1).float()
x = x * mask_flat
# Normalize input
x = self.input_norm(x)
# Feature embedding
x = self.feature_mlp(x)
# Reshape back
x = x.reshape(batch_size, n_stations, seq_len, self.output_dim)
# Add positional encoding
if self.use_position and coords is not None:
lat = coords[:, :, 0]
lon = coords[:, :, 1]
elev = coords[:, :, 2]
pos_enc = self.pos_encoding(lat, lon, elev) # (batch, n_stations, output_dim)
x = x + pos_enc.unsqueeze(2) # Broadcast over seq_len
# Output normalization
x = self.output_norm(x)
if single_timestep:
x = x.squeeze(2) # Remove seq_len dimension
return x
class TemporalPositionEncoding(nn.Module):
"""
Temporal position encoding using cyclical features.
Encodes day-of-year, month, and other temporal patterns.
"""
def __init__(self, d_model: int):
super().__init__()
self.d_model = d_model
# Projection from temporal features to model dimension
# Features: day_sin, day_cos, month_sin, month_cos, year_normalized
self.proj = nn.Linear(5, d_model)
def forward(
self,
day_of_year: torch.Tensor,
year: Optional[torch.Tensor] = None,
) -> torch.Tensor:
"""
Encode temporal position.
Args:
day_of_year: Day of year (1-366), shape (batch, seq_len)
year: Year, shape (batch, seq_len)
Returns:
Temporal encoding of shape (batch, seq_len, d_model)
"""
# Day of year (cyclical)
day_rad = 2 * math.pi * day_of_year / 365.0
day_sin = torch.sin(day_rad)
day_cos = torch.cos(day_rad)
# Month (cyclical) - approximate from day
month_rad = 2 * math.pi * day_of_year / 30.0
month_sin = torch.sin(month_rad)
month_cos = torch.cos(month_rad)
# Year normalized (for climate trends)
if year is not None:
year_norm = (year - 2000) / 50.0 # Center around 2000, scale by 50 years
else:
year_norm = torch.zeros_like(day_sin)
# Combine features
features = torch.stack([
day_sin, day_cos, month_sin, month_cos, year_norm
], dim=-1)
return self.proj(features)
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