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Example: Multi-Fidelity Bayesian Optimization
Uses the physics model as a cheap low-fidelity source and experimental
measurements as the expensive high-fidelity source. The multi-fidelity GP
learns the correlation between fidelities to transfer knowledge.
"""
import torch
from torch import Tensor
from physics_informed_bo.experiment.parameter_space import ParameterSpace
from physics_informed_bo.models.multi_fidelity import MultiFidelitySurrogate
def physics_model(X: Tensor) -> Tensor:
"""Low-fidelity physics model."""
x1, x2 = X[:, 0], X[:, 1]
return torch.sin(x1) * x2 + x1 * 0.5
def true_function(X: Tensor) -> Tensor:
"""High-fidelity ground truth (simulating experiments)."""
x1, x2 = X[:, 0], X[:, 1]
return torch.sin(x1) * x2 + x1 * 0.5 + 0.3 * torch.cos(3 * x1 * x2)
def main():
torch.manual_seed(42)
# Define space
space = ParameterSpace()
space.add_continuous("x1", 0.0, 6.28)
space.add_continuous("x2", 0.0, 5.0)
# Multi-fidelity surrogate
mf_model = MultiFidelitySurrogate(
physics_fn=physics_model,
device="cpu",
)
# Small set of expensive experiments
X_exp = torch.tensor([
[1.0, 2.0], [3.0, 1.0], [5.0, 4.0], [2.0, 3.0], [4.0, 2.5]
], dtype=torch.float64)
y_exp = true_function(X_exp).unsqueeze(-1) + 0.05 * torch.randn(5, 1, dtype=torch.float64)
# Build multi-fidelity dataset (physics=low, experiments=high)
X_mf, y_mf = mf_model.build_multi_fidelity_data(
X_experiment=X_exp,
y_experiment=y_exp,
n_physics_points=50,
)
print(f"Multi-fidelity dataset: {len(X_mf)} points "
f"({len(X_mf) - len(X_exp)} physics + {len(X_exp)} experimental)")
# Fit the model
mf_model.fit(X_mf, y_mf)
# Predict at new points (always at high fidelity)
X_test = torch.tensor([[2.5, 2.5], [4.0, 3.0]], dtype=torch.float64)
mean, var = mf_model.predict(X_test)
print("\nPredictions (high fidelity):")
for i, (m, v) in enumerate(zip(mean, var)):
true_val = true_function(X_test[i:i+1]).item()
print(f" x={X_test[i].tolist()} -> pred={m.item():.3f} ± {v.sqrt().item():.3f} "
f"(true={true_val:.3f})")
if __name__ == "__main__":
main()
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