How much of a digital twin's error is that it was fitted to finite real data, however long it is simulated?

research/input-twin

A twin fitted to finite real data: exact delta-method error √(1+(2−ρ)²)/((1−ρ)√n) of its steady-state wait, data needed grows as (1−ρ)⁻² (22 100 per stream for 10% at ρ=0.9), exact instability probability, false SLA certification 36–46% fixed by bootstrap/posterior bounds (delta bound under-covers).

7 tests

What it found

A twin fitted to n real interarrival and service times has a steady-state wait that is one fixed number, so its error is input error that more simulation cannot remove. The relative sd is √(1+(2−ρ)²)/((1−ρ)√n) (0.255 vs 0.257 simulated), so a 10% sd needs 1300 / 22 100 observations per stream at ρ=0.5 / 0.9. The fitted twin is unstable with exact probability P[F(2n,2n) ≥ 1/ρ] (0.370 at ρ=0.9, n=20). Used as truth, the point twin certifies a 10%-violated SLA in 36–46% of fits; the delta-method bound under-covers at high load (0.87–0.89), while bootstrap and posterior bounds reach 0.94 and cut false certification to 2–5% at a large power cost. Stylised: M/M/1, simulated data.

A figure from its own output

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

Paper, code and results

More in Digital twins & sim-to-real

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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.