210 lines
7.1 KiB
Python
Executable File
210 lines
7.1 KiB
Python
Executable File
import torch
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import torch.nn as nn
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import torch.nn.functional as F
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"""
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完整的 EXP 模型，基于 Greenshields 模型反推密度，并结合 LWR 守恒方程物理引导模块，支持仅流量数据输入。
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"""
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class FlowToDensity(nn.Module):
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"""
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根据 Greenshields 基本图反解密度：
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q = v_f * k * (1 - k / k_j)
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通过求解二次方程获得 k。
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"""
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def __init__(self, v_f=15.0, k_j=1.0):
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super().__init__()
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self.v_f = nn.Parameter(torch.tensor(v_f), requires_grad=False)
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self.k_j = nn.Parameter(torch.tensor(k_j), requires_grad=False)
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def forward(self, q): # q: (B, T, N)
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a = -self.v_f / self.k_j
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b = self.v_f
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c = -q
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delta = b**2 - 4 * a * c
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delta = torch.clamp(delta, min=1e-6)
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sqrt_delta = torch.sqrt(delta)
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k1 = (-b + sqrt_delta) / (2 * a)
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k2 = (-b - sqrt_delta) / (2 * a)
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k = torch.where((k1 > 0) & (k1 < self.k_j), k1, k2)
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return k
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class FundamentalDiagram(nn.Module):
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"""
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Greenshields 基本图：根据密度计算速度与流量。
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"""
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def __init__(self, v_free=30.0, k_jam=200.0):
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super().__init__()
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self.v_free = nn.Parameter(torch.tensor(v_free), requires_grad=True)
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self.k_jam = nn.Parameter(torch.tensor(k_jam), requires_grad=True)
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def forward(self, density):
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speed = self.v_free * (1 - density / self.k_jam)
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flux = density * speed
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return speed, flux
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class ConservationLayer(nn.Module):
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"""
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基于 LWR 方程离散化的守恒层。
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"""
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def __init__(self, dt=1.0, dx=1.0):
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super().__init__()
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self.dt = dt
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self.dx = dx
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def forward(self, density, flux, adj):
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# density, flux: (B, N); adj: (N, N)
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# outflow: 流量从节点流出到邻居
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outflow = flux @ adj
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# inflow: 邻居流量流入该节点
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inflow = flux @ adj.T
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# 更新密度
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delta = (inflow - outflow) * (self.dt / self.dx)
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d_next = density + delta
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return d_next.clamp(min=0.0)
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class DynamicGraphConstructor(nn.Module):
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def __init__(self, node_num, embed_dim):
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super().__init__()
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self.nodevec1 = nn.Parameter(torch.randn(node_num, embed_dim))
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self.nodevec2 = nn.Parameter(torch.randn(node_num, embed_dim))
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def forward(self):
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adj = torch.matmul(self.nodevec1, self.nodevec2.T)
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adj = F.relu(adj)
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adj = F.softmax(adj, dim=-1)
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return adj
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class GraphConvBlock(nn.Module):
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def __init__(self, input_dim, output_dim):
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super().__init__()
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self.theta = nn.Linear(input_dim, output_dim)
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self.residual = (input_dim == output_dim)
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if not self.residual:
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self.res_proj = nn.Linear(input_dim, output_dim)
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def forward(self, x, adj):
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res = x
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x = torch.matmul(adj, x)
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x = self.theta(x)
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x = x + (res if self.residual else self.res_proj(res))
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return F.relu(x)
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class MANBA_Block(nn.Module):
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def __init__(self, input_dim, hidden_dim):
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super().__init__()
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self.attn = nn.MultiheadAttention(embed_dim=input_dim, num_heads=4, batch_first=True)
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self.ffn = nn.Sequential(
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nn.Linear(input_dim, hidden_dim),
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nn.ReLU(),
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nn.Linear(hidden_dim, input_dim)
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)
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self.norm1 = nn.LayerNorm(input_dim)
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self.norm2 = nn.LayerNorm(input_dim)
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def forward(self, x):
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res = x
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x_attn, _ = self.attn(x, x, x)
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x = self.norm1(res + x_attn)
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res2 = x
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x_ffn = self.ffn(x)
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x = self.norm2(res2 + x_ffn)
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return x
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class SandwichBlock(nn.Module):
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def __init__(self, num_nodes, embed_dim, hidden_dim):
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super().__init__()
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self.manba1 = MANBA_Block(hidden_dim, hidden_dim * 2)
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self.graph_constructor = DynamicGraphConstructor(num_nodes, embed_dim)
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self.gc = GraphConvBlock(hidden_dim, hidden_dim)
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self.manba2 = MANBA_Block(hidden_dim, hidden_dim * 2)
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self.fundamental = FundamentalDiagram()
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self.conserve = ConservationLayer()
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def forward(self, h, density):
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# h: (B, N, D)，density: (B, N)
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h1 = self.manba1(h)
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adj = self.graph_constructor()
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_, flux = self.fundamental(density)
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density_next = self.conserve(density, flux, adj)
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h1_updated = h1 + density_next.unsqueeze(-1)
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h2 = self.gc(h1_updated, adj)
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h3 = self.manba2(h2)
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return h3, density_next
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class MLP(nn.Module):
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def __init__(self, in_dim, hidden_dims, out_dim, activation=nn.ReLU):
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super().__init__()
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dims = [in_dim] + hidden_dims + [out_dim]
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layers = []
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for i in range(len(dims) - 2):
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layers += [nn.Linear(dims[i], dims[i+1]), activation()]
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layers += [nn.Linear(dims[-2], dims[-1])]
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self.net = nn.Sequential(*layers)
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def forward(self, x):
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return self.net(x)
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class EXP(nn.Module):
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def __init__(self, args):
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super().__init__()
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self.horizon = args['horizon']
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self.output_dim = args['output_dim']
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self.seq_len = args.get('in_len', 12)
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self.hidden_dim = args.get('hidden_dim', 64)
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self.num_nodes = args['num_nodes']
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self.embed_dim = args.get('embed_dim', 16)
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self.time_slots = args.get('time_slots', 24 * 60 // args.get('time_slot', 5))
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self.flow_to_density = FlowToDensity(
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v_f=args.get('v_f', 15.0),
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k_j=args.get('k_j', 1.0)
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)
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self.time_embedding = nn.Embedding(self.time_slots, self.hidden_dim)
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self.day_embedding = nn.Embedding(7, self.hidden_dim)
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self.input_proj = MLP(
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in_dim=self.seq_len,
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hidden_dims=[self.hidden_dim],
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out_dim=self.hidden_dim
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)
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self.sandwich1 = SandwichBlock(self.num_nodes, self.embed_dim, self.hidden_dim)
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self.sandwich2 = SandwichBlock(self.num_nodes, self.embed_dim, self.hidden_dim)
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self.out_proj = MLP(
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in_dim=self.hidden_dim,
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hidden_dims=[2 * self.hidden_dim],
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out_dim=self.horizon * self.output_dim
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)
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def forward(self, x):
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"""
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x: (B, T, N, 3)
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x[...,0]=flow, x[...,1]=time_in_day, x[...,2]=day_in_week
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"""
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x_flow = x[..., 0]
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x_time = x[..., 1]
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x_day = x[..., 2]
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B, T, N = x_flow.shape
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assert T == self.seq_len
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x_density = self.flow_to_density(x_flow) # (B, T, N)
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dens0 = x_density[:, -1, :] # (B, N)
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x_flat = x_flow.permute(0, 2, 1).reshape(B * N, T)
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h0 = self.input_proj(x_flat).view(B, N, self.hidden_dim)
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t_idx = (x_time[:, -1] * (self.time_slots - 1)).long()
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d_idx = x_day[:, -1].long()
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time_emb = self.time_embedding(t_idx)
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day_emb = self.day_embedding(d_idx)
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h0 = h0 + time_emb + day_emb
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h1, dens1 = self.sandwich1(h0, dens0)
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h1 = h1 + h0
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h2, dens2 = self.sandwich2(h1, dens1)
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out = self.out_proj(h2)
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out = out.view(B, N, self.horizon, self.output_dim)
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out = out.permute(0, 2, 1, 3)
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return out
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