Method

What is Bayesian optimization?

Bayesian optimization finds the best recipe, design, or setting in the fewest expensive tries. After each result it updates what it knows and picks the one experiment worth running next. STOCHOS applies it as PI-BO and extends it to geometry as GEN-BO.

Explore STOCHOS How STOCHOS works

The Bayesian optimization loop: a task feeds a model, the acquisition step chooses an experiment, the observation updates the model, and the cycle repeats, carrying uncertainty and cost back each time. — Each result updates the model, which chooses the next experiment.

The loop

Decide, test, learn, repeat

Trying every option is slow. Bayesian optimization runs a short loop: after each result it picks the one experiment worth doing next, reaching a good answer in far fewer tries.

Decide

The model scores every untried option and proposes the one most worth running: high predicted value, high uncertainty, or both.

Test

You run only that one: a lab trial, a full solve, a build. The costly step, spent once per turn.

Learn

The result updates the model and its confidence. What it now understands narrows; what it still guesses about stays wide.

Repeat

Back to decide, better informed. Good designs surface in far fewer runs than a grid or trial and error.

Back to decide Repeat until you hit the target or spend the budget.

Watch one turn

What the model sees each cycle

Animated Bayesian optimization: the model's mean line and its shaded confidence band update as new results are added, while the expected-improvement curve below rises where a new test would help most and a star marks the current best.

Orange line

The model's current best estimate.

Shaded band

Its uncertainty. Wide where it has no data yet.

Blue curve

Expected improvement: where a new test helps most.

In STOCHOS

The model picks your next experiment

STOCHOS runs this loop with DIM-GP, a probabilistic surrogate for small, noisy data. Its acquisition step balances exploration and exploitation, handles constraints and competing targets, and reports confidence at every turn. PI-BO drives parameters; GEN-BO searches geometry.

Use it where each try is expensive: formulation, process tuning, design, and simulation. It runs on asurrogate model and its uncertainty; for new shapes, see generative design.

A DIM-GP fit of impact strength versus additive concentration: an orange mean curve inside a shaded uncertainty band, white dots for measured results, a down-weighted red outlier, and a green star marking the recommended next experiment where predicted value and uncertainty are both high. — A DIM-GP fit and its uncertainty band. The star marks the next experiment: high predicted value and high uncertainty.

Next method

04 / 06

Multi-Fidelity Modeling

Cut the cost: combine cheap screening data with expensive high-quality results.

Keep reading

Where this applies

Lock in your best settings over a few tries, then let the optimizer work the same problem. Try it against yourself

Proof

ZF Friedrichshafen benchmarked PI-BO against adaptive sampling and Latin hypercube designs, presented at a NAFEMS seminar on AI and machine learning in CAE-based simulation. Read the benchmark

Next step

Let the model pick your next experiment

Bring your variables, constraints, and targets. STOCHOS returns the next run worth doing, and the best design so far.

Request a Demo How STOCHOS works

Local-first. Your data stays on your infrastructure.

Common questions

01When is Bayesian optimization better than design of experiments?

When evaluations are expensive and you can run them in sequence. Classical design of experiments commits to a plan upfront, while Bayesian optimization updates after each result and chooses the next run adaptively. For large spaces and costly trials, the adaptive approach usually reaches the target with fewer experiments.

02Can Bayesian optimization handle several objectives at once?

Yes. STOCHOS supports multi-objective Bayesian optimization, which balances competing targets such as performance, cost, and quality and shows the trade-off between them, rather than optimizing one target while ignoring the others.

03What is Bayesian optimization?

Bayesian optimization finds good designs or settings in as few evaluations as possible. It uses a probabilistic surrogate to decide which point to try next, balancing promising regions against uncertain ones. It suits expensive experiments and simulations where every run costs time or money.