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f7040fb | 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 | """Hybrid surrogate model combining physics models with data-driven GP."""
from typing import Callable, Dict, List, Optional, Tuple
import torch
from torch import Tensor
from physics_informed_bo.models.base import SurrogateModel
from physics_informed_bo.models.gp_model import PhysicsInformedGP, StandardGP
from physics_informed_bo.models.physics_model import PhysicsModel
class HybridSurrogate(SurrogateModel):
"""Hybrid model that combines a physics model with a GP.
Provides multiple operating modes:
1. **Physics-as-mean** (default): Physics function is the GP mean,
GP learns the residual/discrepancy.
2. **Weighted ensemble**: Weighted combination of physics prediction
and GP prediction, with weight adapting based on data.
3. **Physics-only**: Pure physics model when no data is available.
4. **GP-only**: Pure GP when physics model is unreliable.
The model automatically transitions from physics-only → hybrid → GP-dominant
as more experimental data becomes available.
"""
def __init__(
self,
physics_fn: Callable[[Tensor], Tensor],
mode: str = "physics_as_mean",
kernel: str = "matern",
noise_variance: float = 0.01,
learn_noise: bool = True,
initial_physics_weight: float = 1.0,
adapt_weight: bool = True,
device: str = "cpu",
dtype: torch.dtype = torch.float64,
):
"""
Args:
physics_fn: Physics model callable. Takes (n, d) tensor, returns (n,) tensor.
mode: One of 'physics_as_mean', 'weighted_ensemble', 'physics_only', 'gp_only'.
kernel: GP kernel type ('rbf' or 'matern').
noise_variance: Initial observation noise variance.
learn_noise: Whether to learn noise variance from data.
initial_physics_weight: Starting weight for physics model (0 to 1).
adapt_weight: Auto-adapt physics weight based on residual analysis.
device: Torch device.
dtype: Torch dtype.
"""
self.physics_fn = physics_fn
self.mode = mode
self.kernel = kernel
self.noise_variance = noise_variance
self.learn_noise = learn_noise
self.physics_weight = initial_physics_weight
self.adapt_weight = adapt_weight
self.device = torch.device(device)
self.dtype = dtype
# Internal models
self._physics_model = PhysicsModel(physics_fn, noise_std=noise_variance**0.5)
self._gp_model: Optional[PhysicsInformedGP] = None
self._standard_gp: Optional[StandardGP] = None
self._is_fitted = False
self._train_X = None
self._train_y = None
def fit(
self,
X: Tensor,
y: Tensor,
training_iterations: int = 200,
lr: float = 0.05,
) -> None:
"""Fit the hybrid model.
If mode is 'physics_as_mean', fits a PhysicsInformedGP.
If mode is 'weighted_ensemble', fits both physics and standard GP,
then determines optimal weighting.
"""
X = X.to(device=self.device, dtype=self.dtype)
y = y.to(device=self.device, dtype=self.dtype)
if y.dim() == 1:
y = y.unsqueeze(-1)
self._train_X = X
self._train_y = y
if self.mode == "physics_only":
self._physics_model.fit(X, y)
elif self.mode == "physics_as_mean":
self._gp_model = PhysicsInformedGP(
physics_fn=self.physics_fn,
kernel=self.kernel,
noise_variance=self.noise_variance,
learn_noise=self.learn_noise,
device=str(self.device),
dtype=self.dtype,
)
self._gp_model.fit(X, y, training_iterations, lr)
elif self.mode == "weighted_ensemble":
# Fit physics-informed GP
self._gp_model = PhysicsInformedGP(
physics_fn=self.physics_fn,
kernel=self.kernel,
noise_variance=self.noise_variance,
learn_noise=self.learn_noise,
device=str(self.device),
dtype=self.dtype,
)
self._gp_model.fit(X, y, training_iterations, lr)
# Fit standard GP
self._standard_gp = StandardGP(
kernel=self.kernel,
noise_variance=self.noise_variance,
learn_noise=self.learn_noise,
device=str(self.device),
dtype=self.dtype,
)
self._standard_gp.fit(X, y, training_iterations, lr)
if self.adapt_weight:
self._adapt_physics_weight(X, y)
elif self.mode == "gp_only":
self._standard_gp = StandardGP(
kernel=self.kernel,
noise_variance=self.noise_variance,
learn_noise=self.learn_noise,
device=str(self.device),
dtype=self.dtype,
)
self._standard_gp.fit(X, y, training_iterations, lr)
self._is_fitted = True
def _adapt_physics_weight(self, X: Tensor, y: Tensor) -> None:
"""Adapt physics weight based on LOO cross-validation of residuals.
If physics model is accurate (small residuals), keep high weight.
If physics model is inaccurate, reduce weight toward pure GP.
"""
with torch.no_grad():
physics_pred = self.physics_fn(X)
residuals = y.squeeze() - physics_pred
relative_error = (residuals.abs() / (y.squeeze().abs() + 1e-8)).mean()
# Sigmoid mapping: high error → low physics weight
self.physics_weight = float(torch.sigmoid(-5.0 * (relative_error - 0.5)))
def predict(self, X: Tensor) -> Tuple[Tensor, Tensor]:
X = X.to(device=self.device, dtype=self.dtype)
if self.mode == "physics_only" or not self._is_fitted:
return self._physics_model.predict(X)
elif self.mode == "physics_as_mean":
return self._gp_model.predict(X)
elif self.mode == "weighted_ensemble":
gp_mean, gp_var = self._gp_model.predict(X)
std_mean, std_var = self._standard_gp.predict(X)
w = self.physics_weight
mean = w * gp_mean + (1 - w) * std_mean
variance = w**2 * gp_var + (1 - w) ** 2 * std_var
return mean, variance
elif self.mode == "gp_only":
return self._standard_gp.predict(X)
def posterior(self, X: Tensor):
if self.mode in ("physics_as_mean", "weighted_ensemble") and self._gp_model:
return self._gp_model.posterior(X)
elif self.mode == "gp_only" and self._standard_gp:
return self._standard_gp.posterior(X)
else:
return self._physics_model.posterior(X)
@property
def model(self):
"""Return the primary BoTorch-compatible model for optimization."""
if self._gp_model is not None:
return self._gp_model.model
elif self._standard_gp is not None:
return self._standard_gp.model
return None
def get_physics_residuals(self) -> Optional[Tensor]:
"""Return residuals between physics predictions and training data."""
if self._train_X is None or self._train_y is None:
return None
with torch.no_grad():
physics_pred = self.physics_fn(self._train_X)
return self._train_y.squeeze() - physics_pred
def physics_model_quality(self) -> Dict:
"""Assess how well the physics model matches the data."""
if self._train_X is None:
return {"status": "no_data"}
residuals = self.get_physics_residuals()
rmse = float((residuals**2).mean().sqrt())
mae = float(residuals.abs().mean())
r2 = float(
1 - (residuals**2).sum() / ((self._train_y.squeeze() - self._train_y.mean()) ** 2).sum()
)
return {
"rmse": rmse,
"mae": mae,
"r2": r2,
"physics_weight": self.physics_weight,
"n_observations": len(self._train_X),
}
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