For a fixed budget, how much should a fitted digital twin spend on real data and how much on simulation length?

research/budget-twin

Real data or more simulation for a fitted twin: relative variance a(ρ)/n + b(ρ)/m (matches simulation), one real pair ≈ 2 simulated jobs at any load, optimal real-data share 0.57–0.97 by cost ratio, and a simulation-only interval whose real coverage falls 0.79→0.17 as the run lengthens while the input-aware one stays 0.92–0.95.

8 tests

What it found

A twin fitted to n real observations and simulated for m jobs has relative variance a(ρ)/n + b(ρ)/m about the real wait (Whitt’s M/M/1 constant matched to simulation: 30.4 vs 29.0). One real interarrival–service pair carries the information of about two simulated jobs at any load (ratio 2.23 → 2.00), so the optimal real-data share of a budget is interior: 0.97 / 0.81 / 0.57 as a simulated job costs 0.001 / 0.05 / 0.5 of a real observation. In a full pipeline the optimal split has 2.5× lower RMSE than 20% real data. A simulation-only confidence interval is for the twin, not the system: its coverage of the real wait falls from 0.79 to 0.17 as the run grows from 200 to 50 000 jobs, while adding the input variance gives 0.92–0.95 for runs of 1000 or more. Stylised: M/M/1, simulated data, first-order variances.

A figure from its own output

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

Paper, code and results

More in Digital twins & sim-to-real

When should a twin run that counts rare failures stop?When to stop a twin run counting rare failures: sequential Wald stopping halts on zero failures (90% of runs at p=10⁻³, coverage 9.6%), inverse sampling to m failures gives exactly unbiased (m−1)/(N−1) with relative sd ≈1/√(m−2) and an exact interval (95.0–95.5%), while a fixed run planned for the wrong p delivers 63–200% half-width.
What stopping distance can a twin with independent terrain cells certify?Stopping distance certified by a twin with independent per-cell friction: exact incomplete-gamma law (matches braking simulation), 100 twin cells certify 1.17× the mean distance but real terrain with 1–10 patches exceeds it 44%–18% (claimed 0.1%), finer cells are worse, the mean is nearly right, and the measured patch count repairs it.
What approach speed can a lidar twin that returns every beam certify?Approach speed certified by a lidar twin with independent beam dropout vs real whole-scan fades: exact scan-product miss law, real miss ~100× the level at the twin's speed, speed off 10–30% (probabilities off by orders of magnitude), sign reverses when several returns are needed, repaired by a few hundred calibration scans.
How do you estimate a one-in-a-million failure from a twin you can only run a thousand times?Importance sampling of a rare twin failure: exact mean-shift variance, 10⁸→535 runs for 10% error at p=1e-6, a narrow shift target (2× the optimum is 1.7·10⁵× worse, 0% coverage) and effective sample size as the only warning.
Which ego-velocity estimator should a radar twin choose when the real scene has moving targets?Radar ego-velocity from Doppler returns: a static-world twin picks least squares, but with moving targets its variance is exactly 1+ετ² times the claim (95% interval covers 48.7% at ε=0.1, τ=10) and the median wins on a band of ε (0.006–0.97 at τ=10; never at τ=1).
A radar twin with no Doppler folding certifies an ego-velocity estimator at every speed: what does the folding sensor do to it, and when can it be unfolded?A radar twin with no Doppler folding: the twin-tuned ego-speed estimator breaks at v_u−2σ with an exact closed-form bias (saturating at one fold off), and a wrapped-cost search unfolds it iff azimuths are diverse, with a confusion probability Φ(−√E₁/2σ) matching Monte Carlo.

All 164 Digital twins & sim-to-real projects →

Other research topics

Proper scoring & elicitation28 Effort & peer prediction9 Verification games & slashing19 Detection & tolerances14 Markets as routers13 Prediction-market design9 Paying contributors8 Decentralised training systems23 Digital twins & sim-to-real164 LLM chip design loops40 Robot manufacturing loops53 Ambient AI assistant46 Self-replicating manufacturing34 Simulation-first design64 Engineered clothing45 Task-specific AI accelerators40 Algorithmic chip-design loops42 Open-source purpose-built robots44 The software-engineering loop43 Adversarial human imitation41 Open-source residential construction41 Autonomous multi-angle capture34 Sensing, imaging and 3D31 Energy supply and dense energy storage39 Robot societies among people31 Agentic co-design of low-cost robots27 Laundry-hanging robots25 Machine learning on qualitative data23 Robots on the building site27 Civilizations & group psychology1 History & human sciences1

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.