How do surrogate models work in MatCraft?

Surrogate models are lightweight machine learning models that approximate expensive-to-evaluate functions. In MatCraft, they replace costly physics simulations or physical experiments during the optimization loop, enabling the optimizer to evaluate thousands of candidate compositions in seconds.

The Role of Surrogates

In a typical materials optimization pipeline without surrogates, each evaluation might require:

• A DFT calculation (hours to days per composition)
• A molecular dynamics simulation (minutes to hours)
• A physical experiment (days to weeks)

A trained surrogate model can approximate these evaluations in milliseconds, enabling the CMA-ES optimizer to explore the design space efficiently.

MLP Surrogate (Default)

MatCraft's default surrogate is a multi-layer perceptron (MLP) neural network:

from materia.surrogate import MLPSurrogate

surrogate = MLPSurrogate(
    hidden_layers=[64, 64],   # Two hidden layers with 64 neurons each
    activation="relu",         # ReLU activation function
    learning_rate=0.001,       # Adam optimizer learning rate
    epochs=200,                # Training epochs
    validation_split=0.2,      # 20% held out for validation
    early_stopping_patience=20 # Stop if validation loss plateaus
)

The MLP takes component values as input and predicts objective values as output. For multi-objective problems, a separate output head is trained for each objective.

Training Pipeline

1. Normalization: Input features are standardized to zero mean and unit variance. Objectives are min-max scaled.
2. Training: The MLP is trained using the Adam optimizer with mean squared error loss. Early stopping prevents overfitting on small datasets.
3. Uncertainty estimation: MatCraft uses MC Dropout or an ensemble of models to estimate prediction uncertainty. This uncertainty is critical for the active learning acquisition function.
4. Retraining: After each active learning iteration adds new data, the surrogate is retrained from scratch (not fine-tuned) to avoid catastrophic forgetting.

When Surrogates Struggle

• Very small datasets (<10 points): The surrogate may not have enough data to learn meaningful patterns. Consider starting with a space-filling design (Latin Hypercube).
• Highly discontinuous objectives: MLPs assume some smoothness. If your objective has sharp phase transitions, increase network depth or consider a Gaussian Process surrogate.
• Extrapolation: Surrogates are less reliable outside the range of training data. MatCraft's acquisition function accounts for this by penalizing high-uncertainty regions.