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1ca0208 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 | """PyTorch implementation of the SEEDS conditional diffusion core."""
from __future__ import annotations
import math
from typing import Optional
import torch
from torch import Tensor, nn
def _fourier_embedding(value: Tensor, dim: int, max_period: float = 10000.0) -> Tensor:
"""Return a deterministic sinusoidal embedding for diffusion time."""
half = dim // 2
frequencies = torch.exp(
-math.log(max_period) * torch.arange(half, device=value.device, dtype=value.dtype) / max(half, 1)
)
angles = value[..., None] * frequencies
embedding = torch.cat((angles.sin(), angles.cos()), dim=-1)
if dim % 2:
embedding = torch.nn.functional.pad(embedding, (0, 1))
return embedding
class _AxialBlock(nn.Module):
def __init__(self, dim: int, heads: int, mlp_ratio: int, dropout: float) -> None:
super().__init__()
self.norm1 = nn.LayerNorm(dim)
self.attention = nn.MultiheadAttention(dim, heads, dropout=dropout, batch_first=True)
self.norm2 = nn.LayerNorm(dim)
hidden = dim * mlp_ratio
self.mlp = nn.Sequential(nn.Linear(dim, hidden), nn.GELU(), nn.Linear(hidden, dim), nn.Dropout(dropout))
def forward(self, sequence: Tensor) -> Tensor:
normalized = self.norm1(sequence)
attended, _ = self.attention(normalized, normalized, normalized, need_weights=False)
sequence = sequence + attended
return sequence + self.mlp(self.norm2(sequence))
class SEEDS(nn.Module):
"""Conditional score network for cubed-sphere atmospheric fields.
Inputs use ``[batch, channels, faces, height, width]`` for one snapshot and
``[batch, seeds, channels, faces, height, width]`` for seed forecasts.
The output is the normalized noise prediction with the target snapshot shape.
"""
def __init__(
self,
channels: int = 8,
faces: int = 6,
height: int = 48,
width: int = 48,
patch_size: int = 12,
embed_dim: int = 768,
spatial_layers: int = 6,
field_layers: int = 4,
sequence_layers: int = 6,
mlp_ratio: int = 4,
dropout: float = 0.0,
seed_count: int = 2,
sigma_min: float = 0.01,
sigma_max: float = 100.0,
) -> None:
super().__init__()
if height % patch_size or width % patch_size:
raise ValueError("height and width must be divisible by patch_size")
if embed_dim % 2:
raise ValueError("embed_dim must be even")
self.channels, self.faces = channels, faces
self.height, self.width = height, width
self.patch_size, self.seed_count = patch_size, seed_count
self.patch_rows, self.patch_cols = height // patch_size, width // patch_size
self.patch_count = faces * self.patch_rows * self.patch_cols
self.sigma_min, self.sigma_max = sigma_min, sigma_max
heads = max(1, min(12, embed_dim // 64))
while embed_dim % heads:
heads -= 1
self.patch_embedding = nn.Conv2d(channels, embed_dim, patch_size, patch_size)
self.output_projection = nn.Linear(embed_dim, patch_size * patch_size)
self.position_embedding = nn.Parameter(torch.zeros(1, 1, 1, self.patch_count, embed_dim))
self.field_embedding = nn.Parameter(torch.zeros(1, 1, channels, 1, embed_dim))
self.snapshot_embedding = nn.Parameter(torch.zeros(1, seed_count + 2, 1, 1, embed_dim))
self.time_projection = nn.Sequential(nn.Linear(embed_dim, embed_dim), nn.SiLU(), nn.Linear(embed_dim, embed_dim))
self.spatial_transformer = nn.ModuleList(
[_AxialBlock(embed_dim, heads, mlp_ratio, dropout) for _ in range(spatial_layers)]
)
self.field_transformer = nn.ModuleList(
[_AxialBlock(embed_dim, heads, mlp_ratio, dropout) for _ in range(field_layers)]
)
self.sequence_transformer = nn.ModuleList(
[_AxialBlock(embed_dim, heads, mlp_ratio, dropout) for _ in range(sequence_layers)]
)
nn.init.normal_(self.position_embedding, std=0.02)
nn.init.normal_(self.field_embedding, std=0.02)
nn.init.normal_(self.snapshot_embedding, std=0.02)
def _check_inputs(self, noisy: Tensor, seeds: Tensor, climate: Optional[Tensor]) -> None:
expected = (self.channels, self.faces, self.height, self.width)
if noisy.ndim != 5 or tuple(noisy.shape[1:]) != expected:
raise ValueError(f"noisy must have shape [B, {expected}], got {tuple(noisy.shape)}")
if seeds.ndim != 6 or tuple(seeds.shape[2:]) != expected or seeds.shape[1] != self.seed_count:
raise ValueError(f"seeds must have shape [B, {self.seed_count}, {expected}], got {tuple(seeds.shape)}")
if climate is not None and (climate.ndim != 5 or tuple(climate.shape[1:]) != expected):
raise ValueError(f"climate must have shape [B, {expected}], got {tuple(climate.shape)}")
def _embed_snapshot(self, snapshot: Tensor) -> Tensor:
batch, channels, faces, _, _ = snapshot.shape
embedded = self.patch_embedding(snapshot.permute(0, 2, 1, 3, 4).reshape(batch * faces, channels, self.height, self.width))
embedded = embedded.flatten(2).transpose(1, 2).reshape(batch, faces * self.patch_rows * self.patch_cols, -1)
return embedded
def forward(self, noisy: Tensor, seeds: Tensor, climate: Optional[Tensor] = None, diffusion_time: Optional[Tensor] = None) -> Tensor:
self._check_inputs(noisy, seeds, climate)
batch = noisy.shape[0]
if climate is None:
climate = torch.zeros_like(noisy)
snapshots = torch.cat((noisy[:, None], seeds, climate[:, None]), dim=1)
sequence = torch.stack([self._embed_snapshot(snapshots[:, index]) for index in range(snapshots.shape[1])], dim=1)
sequence = sequence[:, :, None] + self.position_embedding + self.field_embedding
if diffusion_time is None:
diffusion_time = torch.zeros(batch, device=noisy.device, dtype=noisy.dtype)
time = self.time_projection(_fourier_embedding(diffusion_time, sequence.shape[-1])).to(sequence.dtype)
sequence[:, 0] = sequence[:, 0] + time[:, None, None]
sequence = sequence.expand(-1, -1, self.channels, -1, -1) + self.snapshot_embedding[:, : sequence.shape[1]]
shape = sequence.shape
sequence = sequence.reshape(batch * shape[1] * shape[2], shape[3], shape[4])
for block in self.spatial_transformer:
sequence = block(sequence)
sequence = sequence.reshape(batch * shape[1] * shape[3], shape[2], shape[4])
for block in self.field_transformer:
sequence = block(sequence)
sequence = sequence.reshape(batch * shape[2] * shape[3], shape[1], shape[4])
for block in self.sequence_transformer:
sequence = block(sequence)
sequence = sequence.reshape(batch, shape[1], shape[2], shape[3], shape[4])[:, 0]
patches = self.output_projection(sequence).reshape(batch, self.channels, self.faces, self.patch_rows, self.patch_cols, self.patch_size, self.patch_size)
return patches.permute(0, 1, 2, 3, 5, 4, 6).reshape(batch, self.channels, self.faces, self.height, self.width)
def sigma(self, diffusion_time: Tensor) -> Tensor:
return self.sigma_min * (self.sigma_max / self.sigma_min) ** diffusion_time
def denoising_loss(
self,
clean: Tensor,
seeds: Tensor,
climate: Optional[Tensor] = None,
diffusion_time: Optional[Tensor] = None,
noise: Optional[Tensor] = None,
) -> Tensor:
if diffusion_time is None:
diffusion_time = torch.rand(clean.shape[0], device=clean.device, dtype=clean.dtype)
if noise is None:
noise = torch.randn_like(clean)
sigma = self.sigma(diffusion_time).view(-1, 1, 1, 1, 1)
noisy = clean + sigma * noise
model_input = noisy / torch.sqrt(1.0 + sigma.square())
prediction = self(model_input, seeds, climate, diffusion_time)
return ((prediction - noise) ** 2).flatten(1).mean()
@torch.no_grad()
def sample(
self,
seeds: Tensor,
climate: Optional[Tensor] = None,
members: int = 1,
steps: int = 64,
member_batch_size: Optional[int] = None,
) -> Tensor:
if members < 1 or steps < 1:
raise ValueError("members and steps must be positive")
chunk_size = min(member_batch_size or members, members)
generated = []
schedule = torch.linspace(1.0, 0.0, steps + 1, device=seeds.device, dtype=seeds.dtype)
sigma_schedule = self.sigma(schedule)
for start in range(0, members, chunk_size):
current_members = min(chunk_size, members - start)
expanded_seeds = seeds.repeat_interleave(current_members, dim=0)
expanded_climate = None if climate is None else climate.repeat_interleave(current_members, dim=0)
sample = torch.randn_like(expanded_seeds[:, 0]) * sigma_schedule[0]
for index, current in enumerate(schedule[:-1]):
current_time = torch.full((sample.shape[0],), current, device=sample.device, dtype=sample.dtype)
sigma = sigma_schedule[index]
model_input = sample / torch.sqrt(1.0 + sigma.square())
predicted_noise = self(model_input, expanded_seeds, expanded_climate, current_time)
sample = sample + (sigma_schedule[index + 1] - sigma) * predicted_noise
generated.append(
sample.reshape(seeds.shape[0], current_members, self.channels, self.faces, self.height, self.width)
)
return torch.cat(generated, dim=1)
SEEDSModel = SEEDS
|