Method

What is uncertainty quantification?

Uncertainty quantification puts a range on a prediction, not just a number. The model returns its best estimate and how sure it is, so you can tell a confident answer from a guess and know when to check it first.

Explore STOCHOS How STOCHOS works

A DIM-GP prediction with a mean line and one, two, and three sigma confidence bands that stay tight where data exists and widen where the model extrapolates. — Mean prediction with confidence bands; confidence widens where data is missing.

The black box

A number with no measure of trust

Twelve labeled inputs feed a closed model that returns a single bare prediction of 42.7, with no indication of how far to trust the number. — Twelve inputs, one bare number. Nothing here says whether the model is confident or guessing.

Feed a model twelve settings and it returns one number: 42.7. Two predictions can read the same and mean opposite things. One sits inside the data the model has already seen. One lands far outside it. The bare number hides the difference.

A single value implies a precision that is not there. A forecast that gives a 70 percent chance of rain is more useful than a flat yes. Uncertainty quantification opens the box the same way: every prediction arrives with a measure of how far to trust it.

The same estimate, two ways to report it

Bare number

42.7

One value, no measure of trust. It reads the same whether the model is confident or guessing.

Number with a range

42.7mean

39.142.746.3

The true value lies between 39.1 and 46.3 with 90 percent confidence. The same estimate, plus how far to trust it.

Illustrative numbers, shown to contrast output formats. Not a STOCHOS performance claim.

What goes wrong

Trusting the box blindly

STOCHOS returns confidence bounds on every prediction. Engineers read that confidence map to decide which variants still need a full solve, instead of validating every candidate or trusting them all.

A standard model with no confidence bounds warps toward an outlier and trusts a noisy measurement blindly, with no indication of how much to trust the prediction. — Without uncertainty, a model warps toward outliers and trusts noisy data blindly.

Two kinds of uncertainty

Why a prediction needs a range

Not all uncertainty is the same. Splitting it in two tells you what to do next.

Aleatoric Irreducible

Run the same experiment twice and results still scatter: material batches, sensor error, process drift. This noise lives in the system itself. More data will not remove it, so you plan around it.

Epistemic Reducible

The model is least sure where it has seen little data. Confidence stays tight inside the tested range and widens as the model extrapolates past it. That gap is the line between a safe interpolation and a risky guess, and more data shrinks it.

STOCHOS is probabilistic at its core. The DIM-GP model returns a predicted value together with confidence, separating reliable interpolation from risky extrapolation and flagging where data is sparse. How the DIM-GP algorithm works →

Why it matters in industry

What a range buys you

Quantified uncertainty is not statistical tidiness. It changes the decision in front of you.

Decisions under risk

See whether a design clears its limit comfortably or only under optimistic assumptions. The question moves from what is the value to how likely it is to pass.

Fewer physical tests

Validate where the model is unsure. Where confidence is high, skip the extra bench test or full solve and move on.

When to trust, when not

Act on a confident prediction inside the data. A low-confidence one flags itself for a check before it drives a decision.

Honest safety margins

Separate a real design margin from an unresolved prediction, so a margin guards against physics, not against not knowing.

Uncertainty is also what powers Bayesian optimization, and it turns a surrogate model into a decision you can defend.

Next method

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Bayesian Optimization

Decide: choose the next best experiment or simulation.

Keep reading

Where this applies

Next step

Know when to trust a prediction, and when not.

Bring one dataset. We put a confidence range on predictions with STOCHOS and STOCHOS Flow, on a problem close to yours.

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Local, probabilistic AI. Your data stays on your infrastructure.

Common questions

01What is the difference between aleatoric and epistemic uncertainty?

Aleatoric uncertainty is noise in the system itself, like batch-to-batch variation or sensor error. More data will not remove it, so you plan around it. Epistemic uncertainty is the model's own lack of knowledge, largest where it has seen little data. More data or a better model can reduce it.

02Does a 90 percent range mean a 90 percent chance the truth is inside it?

Only if the range is calibrated. Calibration means that over many predictions, the true value really falls inside the stated range about that often. A range that is never checked can be overconfident, so calibration should be validated on held-out data.

03What is the difference between accuracy and uncertainty?

Accuracy is how close a prediction is to the truth on cases you can check. Uncertainty is the model's own estimate of how far to trust a prediction, including on new cases you have not checked. A useful model reports both, so you know not just the answer but how much to rely on it.

04Does uncertainty quantification slow the model down?

No. With STOCHOS, confidence is part of the probabilistic prediction rather than a separate, costly step. You get the value and its reliability together, in seconds, which is what makes selective validation practical.

05What is uncertainty quantification?

Uncertainty quantification means reporting how reliable each prediction is. A probabilistic model such as STOCHOS returns a value together with a confidence range, so you can see where it interpolates on solid data and where it extrapolates. Low-confidence cases get full validation first, so you know where to spend the checking effort.