formulation-bo

Find better material formulations in fewer experiments.

A Bayesian optimization library for lab-scale formulation problems, built by an undergraduate who couldn't afford dozens of trial runs.

When you're optimizing a composite formulation, a grid search means dozens of samples. Each one costs material, equipment time, and money. This library looks at the results you already have and tells you which formulation to run next.

Convergence over 15 BO iterations

I was optimizing a thermal interface material: alumina filler in a PDMS matrix. Two objectives that fight each other — raise the filler fraction and thermal conductivity improves, but viscosity climbs until the paste won't dispense.

Three undergraduates. No budget for a wide sweep.

So instead of testing everything, the library models what it has seen with a Gaussian Process and picks the single most informative next experiment.

1. Optional physics-informed prior. Rather than starting from zero, the surrogate can be anchored to a physical model — McLachlan GEM for effective conductivity, Krieger-Dougherty for suspension viscosity are included as examples. Supply your own, or omit it entirely and fall back to a standard zero-mean GP.
2. Gaussian Process surrogate. Fits the residual between the prior and observed measurements, with an optional mediator layer for hierarchical structure.
3. Multi-objective scalarization. ParEGO collapses any number of competing objectives into a single scalar with a randomized weight vector each round, tracing out the Pareto front over time.
4. Expected Improvement. Chooses the next candidate by balancing exploration of uncertain regions against exploitation of promising ones.

The demo runs against a simulated ground truth built from the physical models, so you can watch it converge without any lab equipment.

git clone https://github.com/mthogeon0731/formulation-bo
cd formulation-bo
pip install -r requirements.txt
python demo.py

It generates a virtual physical system (GEM + Krieger-Dougherty, with measurement noise and fabrication failures), seeds 10 evenly-spaced initial observations, then runs 15 optimization rounds and writes demo_convergence.png.

python tests/test_optimizer.py

No test framework required. Covers the physical domain contract (fail-fast on out-of-range input, never silently clamped), the ask/tell cycle both with and without a mediator variable, minimum-observation validation, and seed reproducibility.

from formulation_bo import FormulationOptimizer, Objective
opt = FormulationOptimizer(
 bounds=(0.30, 0.65),
 objectives={
 "conductivity": Objective(direction="max"),
 "viscosity": Objective(direction="min"),
 },
)
opt.tell(0.35, {"conductivity": 1.40, "viscosity": 60.0})
opt.tell(0.40, {"conductivity": 1.82, "viscosity": 95.0})
opt.tell(0.55, {"conductivity": 3.10, "viscosity": 410.0})
result = opt.ask()
print(result["recommended_x"]) # -> the next formulation worth testing

ask() needs at least 3 observations before it can fit a surrogate. Physical priors are pluggable per objective, and the number of objectives isn't fixed at two.

• Single scalar design variable. The optimizer searches over one continuous variable, such as filler volume fraction. Multi-component simplex blend design is out of scope.
• Built for scarce data. This targets the regime where experiments are expensive and you have roughly 5–30 observations. It's the wrong tool when you can afford thousands of samples.
• Fails loudly at physical boundaries. The Krieger-Dougherty prior is only defined below the maximum packing fraction. Inputs past that boundary are physically impossible, so the library raises PhysicalLimitError rather than silently clamping. A wrong recommendation you can't detect is worse than a crash.
• One suggestion at a time. Batch recommendation isn't implemented yet.

Python, NumPy, scikit-learn, Matplotlib. Written with the help of Codex — I'm a chemical engineering major with no formal ML coursework, and this is the tool I needed for my own research.

MIT