Find the minimum of a function by gradient descent, then quantify how uncertainty in the input propagates to the output — the two workflows behind real engineering design.
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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How it works
Gradient descent uses a numerical gradient to walk downhill to a local minimum, drawing its path on the curve. Monte-Carlo uncertainty quantification then samples the input from a normal distribution around that optimum and reports the mean, standard deviation, and 5–95% band of the output — exactly how engineers turn a nominal design into a robust one.
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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.