Do I need to install anything?

No. It runs in any modern browser, free, with no account required.

For K-12 Students · Optimize + UQ

Optimize + UQ for a churn cohort

Built for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework. Simulate a churn cohort live below — adjust the inputs and watch it respond, right in your browser.

Optimization + Uncertainty StudioLive

gradient descent · Monte-Carlo UQ

Controls

Objective f(x)

Presets

Start x₀

Input σ (uncertainty)

▶ Run in Python

Data Inspector

Minimum x-1.3008

f(x) at min-3.5139

Output mean-2.308

Output σ2.207

5–95%-3.51 … 1.44

Governing equation

x min f (x), x_{n + 1} = x_{n} - η \nabla f (x_{n}), η = 0.01, x_{0} = 2.5, x^{⋆} \approx - 1.301

Reading this result: Descent from x₀ = 2.5 settled at x ≈ -1.30. With input σ = 0.4, the output spreads to about 2.21 — uncertainty stays tight near a flat minimum but gets amplified where the curve is steep.

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Frequently asked questions

Is this good for k-12 students?: Yes — this version of "Optimize + UQ for a churn cohort" is framed for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.