File size: 9,010 Bytes
814f98a | 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 | """GPyTorch-based Gaussian Process models with physics-informed priors."""
from typing import Callable, Optional, Tuple
import torch
from torch import Tensor
import gpytorch
from gpytorch.models import ExactGP
from gpytorch.means import ConstantMean, ZeroMean
from gpytorch.kernels import ScaleKernel, RBFKernel, MaternKernel
from gpytorch.likelihoods import GaussianLikelihood
from gpytorch.distributions import MultivariateNormal
from gpytorch.mlls import ExactMarginalLogLikelihood
from botorch.models.gpytorch import GPyTorchModel
from botorch.posteriors.gpytorch import GPyTorchPosterior
from botorch.models.transforms.input import Normalize
from botorch.models.transforms.outcome import Standardize
from physics_informed_bo.models.base import SurrogateModel
from physics_informed_bo.models.physics_model import PhysicsMeanFunction
class _ExactGPModel(ExactGP, GPyTorchModel):
"""Core GPyTorch ExactGP model with BoTorch compatibility."""
_num_outputs = 1
def __init__(
self,
train_X: Tensor,
train_y: Tensor,
likelihood: GaussianLikelihood,
mean_module: Optional[gpytorch.means.Mean] = None,
kernel: str = "matern",
ard_num_dims: Optional[int] = None,
):
super().__init__(train_X, train_y.squeeze(-1), likelihood)
self.mean_module = mean_module or ConstantMean()
if kernel == "rbf":
base_kernel = RBFKernel(ard_num_dims=ard_num_dims)
elif kernel == "matern":
base_kernel = MaternKernel(nu=2.5, ard_num_dims=ard_num_dims)
else:
raise ValueError(f"Unknown kernel: {kernel}. Use 'rbf' or 'matern'.")
self.covar_module = ScaleKernel(base_kernel)
def forward(self, X: Tensor) -> MultivariateNormal:
mean = self.mean_module(X)
covar = self.covar_module(X)
return MultivariateNormal(mean, covar)
class StandardGP(SurrogateModel):
"""Standard Gaussian Process model (no physics, pure data-driven).
Uses GPyTorch for the GP and is BoTorch-compatible for optimization.
"""
def __init__(
self,
kernel: str = "matern",
noise_variance: float = 0.01,
learn_noise: bool = True,
normalize_inputs: bool = True,
standardize_outputs: bool = True,
device: str = "cpu",
dtype: torch.dtype = torch.float64,
):
self.kernel = kernel
self.noise_variance = noise_variance
self.learn_noise = learn_noise
self.normalize_inputs = normalize_inputs
self.standardize_outputs = standardize_outputs
self.device = torch.device(device)
self.dtype = dtype
self._model = None
self._likelihood = None
def fit(
self,
X: Tensor,
y: Tensor,
training_iterations: int = 100,
lr: float = 0.1,
) -> None:
"""Fit the GP model by optimizing the marginal log likelihood."""
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._likelihood = GaussianLikelihood()
if not self.learn_noise:
self._likelihood.noise = self.noise_variance
self._likelihood.noise_covar.raw_noise.requires_grad_(False)
self._model = _ExactGPModel(
train_X=X,
train_y=y,
likelihood=self._likelihood,
kernel=self.kernel,
ard_num_dims=X.shape[-1],
).to(device=self.device, dtype=self.dtype)
self._optimize_hyperparameters(X, y, training_iterations, lr)
def _optimize_hyperparameters(
self, X: Tensor, y: Tensor, n_iter: int, lr: float
) -> None:
"""Optimize GP hyperparameters via type-II MLE."""
self._model.train()
self._likelihood.train()
optimizer = torch.optim.Adam(self._model.parameters(), lr=lr)
mll = ExactMarginalLogLikelihood(self._likelihood, self._model)
for _ in range(n_iter):
optimizer.zero_grad()
output = self._model(X)
loss = -mll(output, y.squeeze(-1))
loss.backward()
optimizer.step()
self._model.eval()
self._likelihood.eval()
def predict(self, X: Tensor) -> Tuple[Tensor, Tensor]:
X = X.to(device=self.device, dtype=self.dtype)
self._model.eval()
self._likelihood.eval()
with torch.no_grad(), gpytorch.settings.fast_pred_var():
posterior = self._likelihood(self._model(X))
mean = posterior.mean.unsqueeze(-1)
variance = posterior.variance.unsqueeze(-1)
return mean, variance
def posterior(self, X: Tensor):
self._model.eval()
self._likelihood.eval()
return self._model.posterior(X)
@property
def model(self):
"""Access the underlying BoTorch-compatible GP model."""
return self._model
class PhysicsInformedGP(SurrogateModel):
"""GP with a physics model as the mean function.
The GP prior mean is set to the physics model predictions, so the GP
learns the residual (discrepancy) between the physics model and reality.
This is the core model of the platform.
Architecture:
f(x) = physics(x) + GP_residual(x)
where GP_residual ~ GP(0, k(x, x'))
"""
def __init__(
self,
physics_fn: Callable[[Tensor], Tensor],
kernel: str = "matern",
physics_output_scale: float = 1.0,
learnable_physics_scale: bool = True,
noise_variance: float = 0.01,
learn_noise: bool = True,
device: str = "cpu",
dtype: torch.dtype = torch.float64,
):
self.physics_fn = physics_fn
self.kernel = kernel
self.physics_output_scale = physics_output_scale
self.learnable_physics_scale = learnable_physics_scale
self.noise_variance = noise_variance
self.learn_noise = learn_noise
self.device = torch.device(device)
self.dtype = dtype
self._model = None
self._likelihood = None
def fit(
self,
X: Tensor,
y: Tensor,
training_iterations: int = 200,
lr: float = 0.05,
) -> None:
"""Fit the physics-informed GP model."""
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._likelihood = GaussianLikelihood()
if not self.learn_noise:
self._likelihood.noise = self.noise_variance
self._likelihood.noise_covar.raw_noise.requires_grad_(False)
physics_mean = PhysicsMeanFunction(
physics_fn=self.physics_fn,
output_scale=self.physics_output_scale,
learnable_scale=self.learnable_physics_scale,
)
self._model = _ExactGPModel(
train_X=X,
train_y=y,
likelihood=self._likelihood,
mean_module=physics_mean,
kernel=self.kernel,
ard_num_dims=X.shape[-1],
).to(device=self.device, dtype=self.dtype)
self._optimize_hyperparameters(X, y, training_iterations, lr)
def _optimize_hyperparameters(
self, X: Tensor, y: Tensor, n_iter: int, lr: float
) -> None:
self._model.train()
self._likelihood.train()
optimizer = torch.optim.Adam(self._model.parameters(), lr=lr)
mll = ExactMarginalLogLikelihood(self._likelihood, self._model)
for _ in range(n_iter):
optimizer.zero_grad()
output = self._model(X)
loss = -mll(output, y.squeeze(-1))
loss.backward()
optimizer.step()
self._model.eval()
self._likelihood.eval()
def predict(self, X: Tensor) -> Tuple[Tensor, Tensor]:
X = X.to(device=self.device, dtype=self.dtype)
self._model.eval()
self._likelihood.eval()
with torch.no_grad(), gpytorch.settings.fast_pred_var():
posterior = self._likelihood(self._model(X))
mean = posterior.mean.unsqueeze(-1)
variance = posterior.variance.unsqueeze(-1)
return mean, variance
def posterior(self, X: Tensor):
self._model.eval()
self._likelihood.eval()
return self._model.posterior(X)
@property
def model(self):
return self._model
def get_residuals(self, X: Tensor, y: Tensor) -> Tensor:
"""Compute residuals between physics predictions and observations."""
with torch.no_grad():
physics_pred = self.physics_fn(X)
return y.squeeze() - physics_pred
|