|
| 1 | +import torch |
| 2 | +import torch_geometric as pyg |
| 3 | +import torch_geometric.utils as pyg_utils |
| 4 | +from ParticleGraph.utils import to_numpy |
| 5 | + |
| 6 | +class PDE_D_DensityDragCIL(pyg.nn.MessagePassing): |
| 7 | + """ |
| 8 | + Density-dependent mobility (CIL) + velocity-dependent fp drag. |
| 9 | +
|
| 10 | + Combines two proven convergence mechanisms that have NEVER been used together: |
| 11 | + 1. Contact Inhibition of Locomotion (Mayor & Carmona-Fontaine 2010): |
| 12 | + Particles reduce mobility when local density is high. |
| 13 | + f(rho) = 1 / (1 + (rho/rho_0)^n) |
| 14 | + 2. Velocity-dependent fp drag (Tranquillo & Lauffenburger 1987): |
| 15 | + Fast-moving particles reduce chemotactic sensitivity. |
| 16 | + drag = 1 / (1 + fp_drag * |v| / v_ref) |
| 17 | +
|
| 18 | + Rationale: CIL provides density-based self-limiting aggregation, but |
| 19 | + clusters can oscillate as particles overshoot the density equilibrium. |
| 20 | + Adding velocity drag penalizes fast oscillatory motion, potentially |
| 21 | + stabilizing the CIL mechanism and improving convergence. |
| 22 | +
|
| 23 | + Physics: |
| 24 | + 1. fp: v = M * f(rho) * nabla_C / (1 + fp_drag * |vel|/v_ref) |
| 25 | + - f(rho) = 1/(1+(rho/rho_0)^n) is Hill function CIL |
| 26 | + - drag attenuates response at high speed |
| 27 | + 2. pf: Standard consumption/production |
| 28 | + 3. pp: Standard attraction-repulsion (density computed from pp graph) |
| 29 | +
|
| 30 | + Literature: |
| 31 | + - Mayor, R. & Carmona-Fontaine, C. (2010) Trends in Cell Biology 20:319-328 |
| 32 | + "Keeping in touch with contact inhibition of locomotion" |
| 33 | + - Cates, M. E. & Tailleur, J. (2015) ARCMP 6:219-244 |
| 34 | + "Motility-induced phase separation" |
| 35 | + - Tranquillo, R. T. & Lauffenburger, D. A. (1987) J Math Biol 25:229-262 |
| 36 | + "Stochastic model of leukocyte chemosensory movement" |
| 37 | +
|
| 38 | + Per-type params layout: [M1, M2, consumption, production, ar_p1, ar_p2, ar_p3, ar_p4] |
| 39 | + """ |
| 40 | + |
| 41 | + PARAMS_DOC = { |
| 42 | + "model_name": "DensityDragCIL", |
| 43 | + "literature": "Mayor & Carmona-Fontaine (2010); Cates & Tailleur (2015); Tranquillo (1987)", |
| 44 | + "description": "Density-dependent CIL + velocity drag: density limits aggregation, speed limits oscillation", |
| 45 | + "equations": { |
| 46 | + "field_to_particle": "v = M * f(rho) * nabla_C / (1 + fp_drag * |vel|/v_ref)", |
| 47 | + "density_function": "f(rho) = 1 / (1 + (rho/rho_0)^n)", |
| 48 | + "particle_to_field": "dC1 = -consumption * w(r), dC2 = production * w(r)", |
| 49 | + "particle_to_particle": "f = (p1*exp(-d^(2p2)/(2sigma^2)) - p3*exp(-d^(2p4)/(2sigma^2))) * dir" |
| 50 | + }, |
| 51 | + "params_mesh": [ |
| 52 | + { |
| 53 | + "row": 0, "description": "C1 field parameters", |
| 54 | + "slots": [ |
| 55 | + {"index": 0, "name": "D1", "description": "Diffusion coeff for C1"}, |
| 56 | + {"index": 1, "name": "Da_c", "description": "Damkohler number"}, |
| 57 | + {"index": 2, "name": "A", "description": "Brusselator A"}, |
| 58 | + {"index": 3, "name": "B", "description": "Brusselator B"}, |
| 59 | + {"index": 4, "name": "mu", "description": "Morphological param"}, |
| 60 | + {"index": 5, "name": "M1", "description": "Mobility for C1 gradients"}, |
| 61 | + {"index": 6, "name": "unused_6", "description": "Unused (pad)"}, |
| 62 | + {"index": 7, "name": "unused_7", "description": "Unused (pad)"} |
| 63 | + ] |
| 64 | + }, |
| 65 | + { |
| 66 | + "row": 1, "description": "C2 field parameters", |
| 67 | + "slots": [ |
| 68 | + {"index": 0, "name": "D2", "description": "Diffusion coeff for C2"}, |
| 69 | + {"index": 1, "name": "M2", "description": "Mobility for C2 gradients"}, |
| 70 | + {"index": 2, "name": "unused_2", "description": "Unused (pad)"}, |
| 71 | + {"index": 3, "name": "unused_3", "description": "Unused (pad)"}, |
| 72 | + {"index": 4, "name": "unused_4", "description": "Unused (pad)"}, |
| 73 | + {"index": 5, "name": "unused_5", "description": "Unused (pad)"}, |
| 74 | + {"index": 6, "name": "unused_6", "description": "Unused (pad)"}, |
| 75 | + {"index": 7, "name": "unused_7", "description": "Unused (pad)"} |
| 76 | + ] |
| 77 | + }, |
| 78 | + { |
| 79 | + "row": 2, "description": "Particle-field coupling + CIL + drag params", |
| 80 | + "slots": [ |
| 81 | + {"index": 0, "name": "Pe", "description": "Peclet number"}, |
| 82 | + {"index": 1, "name": "consumption", "description": "Consumption rate of C1"}, |
| 83 | + {"index": 2, "name": "production", "description": "Production rate of C2"}, |
| 84 | + {"index": 3, "name": "influence_radius", "description": "Gaussian pf influence radius"}, |
| 85 | + {"index": 4, "name": "rho_0", "description": "CIL critical density threshold"}, |
| 86 | + {"index": 5, "name": "hill_n", "description": "CIL Hill coefficient"}, |
| 87 | + {"index": 6, "name": "fp_drag", "description": "Velocity-dependent fp drag (0=off)"}, |
| 88 | + {"index": 7, "name": "unused_7", "description": "Unused (pad)"} |
| 89 | + ] |
| 90 | + } |
| 91 | + ], |
| 92 | + "width_constraint": "ALL rows of params_mesh MUST have same number of columns (8)." |
| 93 | + } |
| 94 | + |
| 95 | + def __init__(self, aggr_type='mean', p=None, particle_params=None, bc_dpos=None, dimension=2, sigma=0.005): |
| 96 | + super(PDE_D_DensityDragCIL, self).__init__(aggr=aggr_type) |
| 97 | + |
| 98 | + self.p = p |
| 99 | + self.particle_params = particle_params |
| 100 | + self.bc_dpos = bc_dpos |
| 101 | + self.dimension = dimension |
| 102 | + self.sigma = sigma |
| 103 | + |
| 104 | + # Global parameters from mesh |
| 105 | + self.M1 = p[0, 5] |
| 106 | + self.M2 = p[1, 1] |
| 107 | + self.consumption_rate = p[2, 1] |
| 108 | + self.production_rate = p[2, 2] |
| 109 | + self.influence_radius = p[2, 3] |
| 110 | + self.Pe = p[2, 0] |
| 111 | + self.repulsion_strength = 50 |
| 112 | + self.repulsion_range = 0.04 |
| 113 | + |
| 114 | + # CIL parameters (Mayor & Carmona-Fontaine 2010) |
| 115 | + self.rho_0 = p[2, 4] if p.shape[1] > 4 and p[2, 4] != 0 else 34.0 |
| 116 | + self.hill_n = p[2, 5] if p.shape[1] > 5 and p[2, 5] != 0 else 2.0 |
| 117 | + self.sensing_radius = 0.05 |
| 118 | + |
| 119 | + # Velocity-dependent fp drag (Tranquillo & Lauffenburger 1987) |
| 120 | + self.fp_drag = p[2, 6] if p.shape[1] > 6 and p[2, 6] != 0 else 0.0 |
| 121 | + self.v_ref = 0.01 |
| 122 | + |
| 123 | + # Convert to proper tensors if needed |
| 124 | + if not isinstance(self.rho_0, torch.Tensor): |
| 125 | + self.rho_0 = torch.tensor(float(self.rho_0), device=p.device) |
| 126 | + if not isinstance(self.hill_n, torch.Tensor): |
| 127 | + self.hill_n = torch.tensor(float(self.hill_n), device=p.device) |
| 128 | + if not isinstance(self.fp_drag, torch.Tensor): |
| 129 | + self.fp_drag = torch.tensor(float(self.fp_drag), device=p.device) |
| 130 | + |
| 131 | + # Storage for local density (computed in pp pass, used in fp pass) |
| 132 | + self.local_density = None |
| 133 | + |
| 134 | + # Report configuration |
| 135 | + rho0_val = self.rho_0.item() if hasattr(self.rho_0, 'item') else self.rho_0 |
| 136 | + hill_val = self.hill_n.item() if hasattr(self.hill_n, 'item') else self.hill_n |
| 137 | + drag_val = self.fp_drag.item() if hasattr(self.fp_drag, 'item') else self.fp_drag |
| 138 | + print(f"initialized PDE_D_DensityDragCIL with parameters:") |
| 139 | + print(f" mobility: M1={self.M1.item()}, M2={self.M2.item()}") |
| 140 | + print(f" CIL: rho_0={rho0_val}, hill_n={hill_val}, sensing_radius={self.sensing_radius} (Mayor 2010)") |
| 141 | + print(f" fp_drag={drag_val:.3f}, v_ref={self.v_ref:.4f} (Tranquillo 1987)") |
| 142 | + print(f" Pe={self.Pe.item():.3f}, sigma={self.sigma}") |
| 143 | + print(f" particle->field: consumption={self.consumption_rate.item()}, production={self.production_rate.item()}, influence_radius={self.influence_radius.item():.3f}") |
| 144 | + if particle_params is not None: |
| 145 | + print(f" multi-type support: {particle_params.shape[0]} particle types") |
| 146 | + |
| 147 | + def forward(self, data, direction='fp'): |
| 148 | + x, edge_index = data.x, data.edge_index |
| 149 | + edge_index, _ = pyg_utils.remove_self_loops(edge_index) |
| 150 | + |
| 151 | + if self.particle_params is not None: |
| 152 | + particle_type = x[:, 1 + 2*self.dimension].long() |
| 153 | + max_type = particle_type.max().item() |
| 154 | + n_param_rows = self.particle_params.shape[0] |
| 155 | + if max_type >= n_param_rows: |
| 156 | + raise ValueError( |
| 157 | + f"PDE_D_DensityDragCIL: particle_params has {n_param_rows} rows but found " |
| 158 | + f"particle type {max_type}. Need {max_type + 1} rows in simulation.params." |
| 159 | + ) |
| 160 | + parameters = self.particle_params[to_numpy(particle_type), :] |
| 161 | + else: |
| 162 | + parameters = None |
| 163 | + |
| 164 | + if direction == 'interpolate': |
| 165 | + result = self.propagate(edge_index, x=x, mode='interpolate', parameters=parameters) |
| 166 | + pos = x[:, 1:self.dimension+1] |
| 167 | + in_box = ((pos >= 0) & (pos <= 1)).all(dim=1, keepdim=True) |
| 168 | + result = result * in_box.float() |
| 169 | + return result |
| 170 | + elif direction == 'fp': |
| 171 | + result = self.propagate(edge_index, x=x, mode='fp', parameters=parameters) |
| 172 | + |
| 173 | + # Apply density-dependent + velocity drag modulation |
| 174 | + if self.local_density is not None: |
| 175 | + n_total = x.size(0) |
| 176 | + n_particles = self.local_density.size(0) |
| 177 | + n_nodes = n_total - n_particles |
| 178 | + |
| 179 | + # CIL Hill function modulation |
| 180 | + ratio = self.local_density / self.rho_0 |
| 181 | + cil_modulation = 1.0 / (1.0 + ratio ** self.hill_n) |
| 182 | + |
| 183 | + # Apply to particle portion only |
| 184 | + mod_full = torch.ones(n_total, 1, device=x.device) |
| 185 | + mod_full[n_nodes:, 0] = cil_modulation |
| 186 | + result = result * mod_full |
| 187 | + |
| 188 | + # Apply velocity-dependent drag at the aggregate level |
| 189 | + if self.fp_drag > 0: |
| 190 | + n_total = x.size(0) |
| 191 | + vel = x[:, 1+self.dimension:1+2*self.dimension] |
| 192 | + speed = torch.sqrt(torch.sum(vel**2, dim=1, keepdim=True)) |
| 193 | + drag_factor = 1.0 / (1.0 + self.fp_drag * speed / self.v_ref) |
| 194 | + result = result * drag_factor |
| 195 | + |
| 196 | + pos = x[:, 1:self.dimension+1] |
| 197 | + in_box = ((pos >= 0) & (pos <= 1)).all(dim=1, keepdim=True) |
| 198 | + result = result * in_box.float() |
| 199 | + return result |
| 200 | + elif direction == 'pf': |
| 201 | + result = self.propagate(edge_index, x=x, mode='pf', parameters=parameters) |
| 202 | + return result |
| 203 | + else: # direction == 'pp' |
| 204 | + self._compute_local_density(x, edge_index) |
| 205 | + result = self.propagate(edge_index, x=x, mode='pp', parameters=parameters) |
| 206 | + return result |
| 207 | + |
| 208 | + def _compute_local_density(self, x, edge_index): |
| 209 | + """Count particle neighbors within sensing_radius for CIL.""" |
| 210 | + n_particles = x.size(0) |
| 211 | + target_nodes = edge_index[1] |
| 212 | + |
| 213 | + pos_i = x[edge_index[1], 1:self.dimension+1] |
| 214 | + pos_j = x[edge_index[0], 1:self.dimension+1] |
| 215 | + d_pos = self.bc_dpos(pos_j - pos_i) |
| 216 | + dist = torch.sqrt(torch.sum(d_pos**2, dim=1)) |
| 217 | + |
| 218 | + within_radius = dist < self.sensing_radius |
| 219 | + counts = torch.zeros(n_particles, device=x.device) |
| 220 | + counts.scatter_add_(0, target_nodes[within_radius], |
| 221 | + torch.ones(within_radius.sum(), device=x.device)) |
| 222 | + |
| 223 | + self.local_density = counts |
| 224 | + |
| 225 | + def message(self, edge_index_i, edge_index_j, x_i, x_j, mode=None, parameters_i=None): |
| 226 | + pos_i = x_i[:, 1:self.dimension+1] |
| 227 | + pos_j = x_j[:, 1:self.dimension+1] |
| 228 | + |
| 229 | + d_pos = self.bc_dpos(pos_j - pos_i) |
| 230 | + dist = torch.sqrt(torch.sum(d_pos**2, dim=1)) |
| 231 | + dist_safe = torch.clamp(dist, min=1e-6) |
| 232 | + |
| 233 | + if mode == 'interpolate': |
| 234 | + C1_mesh = x_j[:, 6:7] |
| 235 | + C2_mesh = x_j[:, 7:8] |
| 236 | + weight = torch.exp(-dist / 0.01).unsqueeze(1) |
| 237 | + return torch.cat([C1_mesh * weight, C2_mesh * weight, weight], dim=1) |
| 238 | + |
| 239 | + elif mode == 'fp': |
| 240 | + fields_i = x_i[:, 6:8] |
| 241 | + fields_j = x_j[:, 6:8] |
| 242 | + |
| 243 | + dC1 = fields_j[:, 0:1] - fields_i[:, 0:1] |
| 244 | + dC2 = fields_j[:, 1:2] - fields_i[:, 1:2] |
| 245 | + |
| 246 | + kernel = torch.exp(-dist / 0.05) |
| 247 | + dir_norm = d_pos / dist_safe.unsqueeze(1) |
| 248 | + domain_scale = 32.0 |
| 249 | + grad_C1 = (dC1 * kernel.unsqueeze(1)) / (dist_safe.unsqueeze(1) * domain_scale) |
| 250 | + grad_C2 = (dC2 * kernel.unsqueeze(1)) / (dist_safe.unsqueeze(1) * domain_scale) |
| 251 | + |
| 252 | + if parameters_i is not None: |
| 253 | + M1 = parameters_i[:, 0:1] |
| 254 | + M2 = parameters_i[:, 1:2] |
| 255 | + else: |
| 256 | + M1 = self.M1 |
| 257 | + M2 = self.M2 |
| 258 | + |
| 259 | + velocities = (M1 * grad_C1 + M2 * grad_C2) * dir_norm |
| 260 | + return velocities |
| 261 | + |
| 262 | + elif mode == 'pf': |
| 263 | + weights = torch.exp(-dist**2 / (2 * (self.influence_radius/3)**2)) |
| 264 | + |
| 265 | + if parameters_i is not None: |
| 266 | + consumption = parameters_i[:, 2] |
| 267 | + production = parameters_i[:, 3] |
| 268 | + else: |
| 269 | + consumption = self.consumption_rate |
| 270 | + production = self.production_rate |
| 271 | + |
| 272 | + field_updates = torch.zeros((pos_i.size(0), 2), device=pos_i.device) |
| 273 | + field_updates[:, 0] = -consumption * weights |
| 274 | + field_updates[:, 1] = production * weights |
| 275 | + return field_updates |
| 276 | + |
| 277 | + else: # mode == 'pp' |
| 278 | + if parameters_i is not None: |
| 279 | + p1 = parameters_i[:, 4] |
| 280 | + p2 = parameters_i[:, 5] |
| 281 | + p3 = parameters_i[:, 6] |
| 282 | + p4 = parameters_i[:, 7] |
| 283 | + |
| 284 | + f = (p1 * torch.exp(-dist ** (2 * p2) / (2 * self.sigma ** 2)) |
| 285 | + - p3 * torch.exp(-dist ** (2 * p4) / (2 * self.sigma ** 2))) |
| 286 | + |
| 287 | + forces = f[:, None] * d_pos / dist_safe.unsqueeze(1) |
| 288 | + else: |
| 289 | + forces = torch.zeros_like(pos_i) |
| 290 | + in_range = dist < self.repulsion_range |
| 291 | + if in_range.any(): |
| 292 | + dir_norm = d_pos / dist_safe.unsqueeze(1) |
| 293 | + repulsion_mag = self.repulsion_strength * torch.exp( |
| 294 | + -5.0 * dist[in_range] / self.repulsion_range |
| 295 | + ) |
| 296 | + forces[in_range] = -dir_norm[in_range] * repulsion_mag.unsqueeze(1) |
| 297 | + |
| 298 | + return forces |
| 299 | + |
| 300 | + def update(self, aggr_out, mode=None): |
| 301 | + if mode == 'interpolate': |
| 302 | + C1_weighted = aggr_out[:, 0:1] |
| 303 | + C2_weighted = aggr_out[:, 1:2] |
| 304 | + weight_sum = aggr_out[:, 2:3] |
| 305 | + weight_sum = torch.clamp(weight_sum, min=1e-10) |
| 306 | + return torch.cat([C1_weighted / weight_sum, C2_weighted / weight_sum], dim=1) |
| 307 | + else: |
| 308 | + return aggr_out |
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