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examples/polymer_optimization.py

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+"""
+Example: Physics-Informed Bayesian Optimization for Polymer Design
+
+This example demonstrates optimizing a polymer formulation where:
+- A physics model (simplified Flory-Huggins + Arrhenius kinetics) provides
+  prior knowledge about how composition and temperature affect properties.
+- Initial experimental data provides a warm start.
+- The BO loop efficiently explores the design space, leveraging both
+  physics and data to minimize the number of experiments needed.
+
+Objective: Maximize polymer recyclability metric (higher is better).
+Parameters:
+  - monomer_ratio: Ratio of monomer A to B (0.1 to 0.9)
+  - temperature: Reaction temperature in Kelvin (350 to 500)
+  - catalyst_loading: Catalyst weight percent (0.5 to 5.0)
+"""
+
+import torch
+from torch import Tensor
+
+from physics_informed_bo.experiment.parameter_space import ParameterSpace
+from physics_informed_bo.experiment.campaign import OptimizationCampaign
+from physics_informed_bo.config import OptimizationConfig, AcquisitionType
+
+
+# ============================================================================
+# 1. Define the physics model (simplified polymer recyclability model)
+# ============================================================================
+
+def polymer_physics_model(X: Tensor) -> Tensor:
+    """Simplified physics model for polymer recyclability.
+
+    Based on:
+    - Flory-Huggins mixing thermodynamics
+    - Arrhenius reaction kinetics
+    - Empirical catalyst efficiency model
+
+    Args:
+        X: Tensor of shape (n, 3) with columns:
+           [monomer_ratio, temperature, catalyst_loading]
+
+    Returns:
+        Predicted recyclability metric (higher = better).
+    """
+    ratio = X[:, 0]       # monomer ratio
+    temp = X[:, 1]         # temperature (K)
+    catalyst = X[:, 2]     # catalyst loading (wt%)
+
+    # Flory-Huggins: optimal mixing near 50:50 ratio
+    chi = 0.5 - 0.3 * (ratio - 0.5) ** 2  # chi parameter
+    mixing_term = -ratio * torch.log(ratio + 1e-8) - (1 - ratio) * torch.log(1 - ratio + 1e-8)
+    mixing_free_energy = mixing_term - chi * ratio * (1 - ratio)
+
+    # Arrhenius: reaction rate dependence on temperature
+    Ea = 50.0  # kJ/mol activation energy
+    R = 8.314e-3  # kJ/(mol·K)
+    rate = torch.exp(-Ea / (R * temp))
+
+    # Catalyst efficiency (diminishing returns)
+    catalyst_eff = 1 - torch.exp(-0.8 * catalyst)
+
+    # Combined recyclability metric
+    recyclability = 5.0 * mixing_free_energy * rate * catalyst_eff + 2.0
+
+    return recyclability
+
+
+# ============================================================================
+# 2. Define the "true" function (simulates real experiments with noise)
+# ============================================================================
+
+def true_recyclability(params: dict) -> float:
+    """Simulate running an actual experiment (physics + discrepancy + noise)."""
+    X = torch.tensor(
+        [[params["monomer_ratio"], params["temperature"], params["catalyst_loading"]]],
+        dtype=torch.float64,
+    )
+
+    # Physics prediction
+    physics = polymer_physics_model(X).item()
+
+    # Add model discrepancy (physics doesn't capture everything)
+    ratio = params["monomer_ratio"]
+    temp = params["temperature"]
+    discrepancy = 0.3 * torch.sin(torch.tensor(10.0 * ratio)).item() \
+                  + 0.1 * (temp - 400) / 100
+
+    # Add measurement noise
+    noise = 0.05 * torch.randn(1).item()
+
+    return physics + discrepancy + noise
+
+
+# ============================================================================
+# 3. Set up the optimization campaign
+# ============================================================================
+
+def main():
+    # Define parameter space
+    space = ParameterSpace()
+    space.add_continuous("monomer_ratio", 0.1, 0.9, units="ratio")
+    space.add_continuous("temperature", 350.0, 500.0, units="K")
+    space.add_continuous("catalyst_loading", 0.5, 5.0, units="wt%")
+
+    # Generate some initial experimental data
+    torch.manual_seed(42)
+    X_init = space.sample_latin_hypercube(5)
+    y_init = torch.tensor(
+        [true_recyclability(space.to_dict(X_init)[i]) for i in range(5)],
+        dtype=torch.float64,
+    ).unsqueeze(-1)
+
+    print("=== Initial Data ===")
+    for i, (params, y_val) in enumerate(zip(space.to_dict(X_init), y_init)):
+        print(f"  Exp {i+1}: {params} -> {y_val.item():.4f}")
+
+    # Configure optimization
+    config = OptimizationConfig(
+        acquisition_type=AcquisitionType.PHYSICS_INFORMED_EI,
+        n_initial_samples=5,
+        max_iterations=20,
+        use_physics_mean=True,
+        noise_variance=0.01,
+    )
+
+    # Create campaign
+    campaign = OptimizationCampaign(
+        name="polymer_recyclability",
+        parameter_space=space,
+        physics_fn=polymer_physics_model,
+        initial_data=(X_init, y_init),
+        config=config,
+        maximize=True,
+    )
+
+    print("\n=== Running Optimization ===")
+
+    def callback(iteration, best):
+        print(f"  Iteration {iteration}: best = {best['objective']:.4f}")
+
+    # Run automated optimization
+    results_df = campaign.run_automated(
+        objective_fn=true_recyclability,
+        max_iterations=15,
+        callback=callback,
+    )
+
+    # Report results
+    best = campaign.get_best()
+    print(f"\n=== Best Result ===")
+    print(f"  Parameters: {best['parameters']}")
+    print(f"  Objective:  {best['objective']:.4f}")
+
+    print(f"\n=== Campaign Summary ===")
+    summary = campaign.summary()
+    print(f"  Total experiments: {summary['n_experiments']}")
+    print(f"  Physics model R²: {summary['model_summary'].get('model_quality', {}).get('r2', 'N/A')}")
+
+    # Save results
+    campaign.save("polymer_campaign.json")
+    results_df.to_csv("polymer_results.csv", index=False)
+    print("\nResults saved to polymer_campaign.json and polymer_results.csv")
+
+
+if __name__ == "__main__":
+    main()