File size: 9,773 Bytes
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