ml-bayesian-optimization

Bayesian Optimization

Goal

Efficiently find the optimal input parameters (e.g., alloy composition, simulation hyperparameters, process conditions) that minimize or maximize one or more expensive black-box objectives (e.g., formation energy, bandgap, elastic modulus) using Bayesian Optimization (BO). BO builds a probabilistic surrogate model (Gaussian Process) over the objective landscape and uses an acquisition function to intelligently select the next most informative experiments, minimizing the number of expensive evaluations required.

• Single-objective: Expected Improvement (EI) maximized via multi-start L-BFGS-B.
• Multi-objective: ParEGO — random Chebyshev scalarization with independent GPs, one weight vector per batch element, naturally steering candidates toward different Pareto-front regions.

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Instructions

Step 1: Define the Search Space

Create a search_space.yaml in the research directory. Use the template at resources/search_space_template.yaml as a starting point:

# research_dir/search_space.yaml

parameters:
  # Continuous range parameter
  - name: x_Fe
    type: range
    bounds: [0.0, 1.0]
    value_type: float

  # Integer range parameter
  - name: supercell_size
    type: range
    bounds: [2, 6]
    value_type: int

objectives:
  # Single-objective: minimize formation energy
  - name: formation_energy_eV_atom
    minimize: true

  # Multi-objective: additionally maximize bandgap (uncomment to enable)
  # - name: bandgap_eV
  #   minimize: false

Guidelines:

• Use type: range for continuous or integer parameters with known bounds. Only range parameters are passed to the GP surrogate.
• choice and fixed types are recorded in output CSVs but not optimized. Run separate campaigns per discrete choice.
• Choose bounds informed by domain knowledge; avoid unnecessarily wide ranges.

Step 2: Initialize with Quasi-Random Sobol Samples

Generate an initial space-filling design using Sobol sequences. Use a power-of-2 batch_size (4, 8, 16, …) for optimal Sobol balance: