Bayesian Forge: Active Learning for Material Discovery

Bayesian Optimization framework for simulated material discovery. Implements the Active Learning Loop used in computational materials science: a probabilistic surrogate model guides experimental design, selecting the most informative composition to test next rather than relying on exhaustive grid search.

This approach is widely used in alloy design, where each experiment (melting, casting, testing) is expensive. By using Gaussian Process regression as a surrogate and acquisition functions to balance exploration vs. exploitation, the optimizer finds optimal compositions in far fewer experiments than random search.

Architecture

                    +-------------------+
                    |  Objective Func   |    Synthetic material property
                    |  (ground truth)   |    landscape (Branin, Hartmann,
                    +--------+----------+    SteelHardness)
                             |
                             | evaluate
                             v
+-------------+    +-------------------+    +-------------------+
| Acquisition | -> | Bayesian Optimizer| -> |   GP Surrogate    |
|  Function   |    | (Active Learning  |    | (Matern 5/2 kern) |
| EI/UCB/PI   |    |     Loop)         |    |   scikit-learn    |
+-------------+    +-------------------+    +-------------------+
                             |
                             v
                    +-------------------+
                    |  Visualization    |    Convergence, acquisition
                    |  (matplotlib)     |    landscape, regret plots
                    +-------------------+

Active Learning Loop:

1. GP surrogate predicts material properties + uncertainty from observed data
2. Acquisition function selects the most informative next experiment
3. Ground truth function evaluates the selected composition
4. Model updates with the new observation
5. Repeat until budget exhausted

Synthetic Material Functions

Function	Dimensions	Simulates	Key Feature
Branin	2	2-component alloy	3 global optima, tests exploration
Hartmann-3	3	3-component alloy	Complex landscape, 1 global optimum
SteelHardness	3	C-Mn-Temperature	Physically motivated hardness model

Quick Start

# Clone and install
git clone https://github.com/gilito11/bayesian-forge.git
cd bayesian-forge
pip install -r requirements.txt

# Run full comparison (all functions, EI vs UCB vs Random)
python demo.py

# Run specific function with specific acquisition
python demo.py --function branin --acquisition ucb --iterations 40

# Run steel hardness with Expected Improvement
python demo.py -f steel -a ei -n 50

Example Output

======================================================================
  SUMMARY TABLE
======================================================================
Function                     Method       Best    Optimum      Gap
----------------------------------------------------------------------
Branin (2-component alloy)   EI         -0.3979    -0.3979   0.0000
Branin (2-component alloy)   UCB        -0.3980    -0.3979   0.0001
Branin (2-component alloy)   Random     -0.5134    -0.3979   0.1155

Hartmann-3 (3-component alloy) EI        3.8560     3.8628   0.0068
Hartmann-3 (3-component alloy) UCB       3.8491     3.8628   0.0137
Hartmann-3 (3-component alloy) Random    3.2104     3.8628   0.6524

Steel Hardness (C-Mn-T)     EI          66.89      67.50     0.61
Steel Hardness (C-Mn-T)     UCB         66.45      67.50     1.05
Steel Hardness (C-Mn-T)     Random      58.32      67.50     9.18

Plots are saved to output/:

• *_convergence.png - Best value vs evaluation number
• *_regret.png - Cumulative regret over time
• *_exploration.png - Sampling pattern (first 2 dims)
• *_landscape.png - 4-panel acquisition landscape (2D functions only)

Project Structure

bayesian-forge/
  forge/
    materials.py      # Synthetic objective functions (ground truth)
    surrogate.py      # Gaussian Process surrogate (scikit-learn)
    acquisition.py    # EI, UCB, PI acquisition functions
    optimizer.py      # Main Bayesian Optimization loop
    plots.py          # Publication-quality visualizations
  demo.py             # Entry point with CLI
  requirements.txt

Author

Eric Gil -- BSc Computer Science, Universitat de Lleida

License

MIT License. See LICENSE.