What does it cost to keep a digital twin in sync with a drifting plant, and is probing worth it?

research/twin-upkeep

Keeping a digital twin in sync with a drifting plant: closed-form Kalman tracking variance and control regret (matched to simulation), a frozen twin loses half its edge in ln 2/(2(1−ρ)) steps, probing never pays for one drifting parameter, and a two-parameter closed-loop blind direction gives a mean-field dither law ν* ∝ q^{1/6} that self-exciting certainty-equivalent control mostly makes unnecessary.

13 tests

What it found

A Kalman twin tracks a drifting actuator gain from the closed-loop data the controller already produces. Its steady-state predictive variance is a closed-form quadratic root (m = q/2 + √(q²/4 + qσ²/v) for a random walk), matching closed-loop simulation to 1–3%, and control regret is ½J_kk(dk*/db)²m (0.00447 predicted vs 0.00466 simulated). A calibrate-and-freeze twin loses half its edge over the population mean after ln 2/(2(1−ρ)) = 34.5 steps. For one drifting parameter a dedicated probing budget never pays (information price 0.70 vs marginal value ≤ 0.04); for two, the closed-loop blind direction makes a fixed-gain twin unobservable and the mean-field optimal dither scales exactly as q^1/6, yet simulation shows the controller’s own gain jitter supplies most of that excitation, so the mean-field law is an upper bound. Stylised.

A figure from its own output

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

Paper, code and results

More in Digital twins & sim-to-real

How often, and how long, should a digital twin be re-identified as the plant drifts?Re-identifying a drifting twin by dedicated experiments: closed-form interval T*∝q_d^{−2/3} with downtime, noise and drift regret exactly equal at the optimum, excess ∝q_d^{1/3}, a 4× drift misjudgement costs ≤26%, but the second-order optimum destabilises 0.7–15% of cycles and a safe schedule is 37–200× worse than an always-on Kalman twin.
What should you pay a digital-twin provider for?What to pay a digital-twin provider for: cost-paid twins differ from Brier-paid ones, certainty-equivalence loss is quartic in spread, payment caps make the elicited twin jump at a closed-form threshold, and Brier mispays probing by 15×.
How long can a digital twin be wrong before you can prove it, and what does waiting cost?Anytime-valid e-process audit of a digital twin in closed loop: peeking-safe (2.4% vs 58% false alarms), delay set by the controller's own excitation, regret before detection nearly independent of the gap, dither pays only for gross errors.
What does a Gaussian-clutter radar simulator do to a CFAR detector's false-alarm rate?What a Gaussian-clutter radar twin does to a CA-CFAR detector: exact false-alarm law under gamma texture (matched to simulation), 9–30× inflation at design 1e-4, 1.9–3.7 dB threshold repair, shared texture is harmless, and a real-cell calibration budget (median 1.1× at 1000 cells).
Does a more robust CFAR detector survive a Gaussian-clutter radar simulator?Does a more robust CFAR survive a Gaussian-clutter twin? CA, OS and log-t all inflate 8–44× at design 1e-4 (no detector escapes), a known-scale oracle inflates as much as CA (the test cell's own texture), and CA detects best at equal real Pfa after repair.
What does a light-tailed simulated human do to a collaborative robot's timeout?When a collaborative robot should give up waiting for a human: J'(τ)=S(τ)(w−c·h(τ)) makes exponential/Weibull simulated humans corner-only (never abort), 3.7% regret in the base case rising to 37–81% for heavy tails and cheap aborts, plug-in lognormal fit regret 1/n (delta method within 11%).

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.