PPolySim OS

Gaussian Process

Regression that knows what it doesn't know. Fit a distribution over functions to your data and watch the uncertainty band widen wherever evidence runs out.

Gaussian Process StudioLive

Controls

A Gaussian process fits a whole distribution over functions to your data. Click the canvas to add training points, or drag them around, and watch the posterior mean, 95% band, and sample functions update live.

Presets

▶ Run in Python

Data Inspector

Training points9
Length-scale ℓ1.00
Signal var σ²1.00
Noise σ_n0.12
Log marginal lik.-9.6

Governing equation

Reading this result: The posterior mean interpolates the 9 points and the 95% band collapses at each observation (up to the noise σ_n=0.12) and widens in the gaps between them — that widening is the model honestly reporting where it has no evidence.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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How it works

Gaussian process regression (also called kriging) places a prior over functions defined by an RBF kernel k(x,x')=σ²exp(−(x−x')²/2ℓ²), then conditions on your observations to get a posterior. The posterior mean interpolates the data while the 95% confidence band collapses at each point and widens in the gaps — an honest map of where the model has evidence and where it is guessing. The length-scale ℓ controls how far each point's influence reaches: short ℓ gives a wiggly fit, long ℓ a smooth one. Everything runs client-side with a from-scratch Cholesky solve of the kernel system — no libraries.

Ask the AI about this model

The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.

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Frequently asked questions

Is this Gaussian process regression kriging tool really free?
Yes. Gaussian Process runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
Can I save or share my simulation?
Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.
How accurate are the results?
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.