How far should a real-plant estimate be pulled toward its digital twin?

research/twin-shrinkage

Pulling a real-plant parameter estimate toward its twin (James–Stein): exact risk d−(d−2)²E[1/(d−2+2K)], never worse in total for d≥3, perfect twin risk 2 at any d, worth n+σ²/τ² real samples at large d, but one mismatched parameter takes ≈d/4 noise variances (25.5 at d=100) unless shrinkage is blockwise (1.65 at blocks of 5, d=30).

7 tests

What it found

Shrinking a real estimate of d plant parameters toward the twin's prediction (James–Stein) has an exact risk d−(d−2)²E[1/(d−2+2K)], K~Poisson(λ/2): it never raises total error for d≥3, a perfect twin gives risk 2 at any d (saving 33% at d=3, 80% at d=10), and a twin as noisy as the data (λ/d=1) still saves 14–49% while using it alone saves nothing. At large d the twin is worth n+σ²/τ² real samples (exact values 0.72–0.998 of that at d=5–100). The guarantee is aggregate only: one badly mismatched parameter among d takes about d/4 noise variances of damage (measured 2.9 at d=10, 25.5 at d=100 against 1), and blocks of 5 cap that at 1.65 (d=30) while keeping 72% of the perfect-twin saving. Stylised: Gaussian noise, orthogonal design, no robot data.

A figure from its own output

Figure produced by research/twin-shrinkage: saving_vs_dimension — twin-shrinkage/experiments/saving_vs_dimension.svg, written by the project's own experiment code.

Paper, code and results

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Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.