What is a digital twin worth for training a controller?

What it found

In a scalar linear-quadratic plant the twin-trained gain has exact deployment regret, asymmetric with a stability cliff: underestimating actuation to 0.21× is infinitely costly while 2× over costs 0.22. A twin can score perfectly on passive logs (log-score gap exactly 0) yet mistrain the controller, and closed-loop logs are blind along Δa = kΔb, so validation needs designed probing. Used as a ridge prior, a twin with bias δ is worth exactly σ²/(vδ²) real probe steps at every accuracy target (22 steps at δ=0.3), and removes small-sample divergence (3.1% to 0 at n=10). Matched to simulation within 1–4%. Stylised.

A figure from its own output

Paper, code and results

• README and method
• White paper
• Experiments and results
• Code
• Tests

More in Digital twins & sim-to-real

• How wide should domain randomization be, and what does it buy?Domain randomization over a twin, exactly: cliff-limited width, quartic price when the twin was right, cliff pushed out ~15%, but uniform-average training is not minimax and the best width tracks the prior.
• What does it cost to keep a digital twin in sync with a drifting plant, and is probing worth it?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.
• 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).

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

Other research topics

Proper scoring & elicitation28Effort & peer prediction9Verification games & slashing19Detection & tolerances14Markets as routers13Prediction-market design9Paying contributors8Decentralised training systems23Digital twins & sim-to-real164LLM chip design loops40Robot manufacturing loops53Ambient AI assistant46Self-replicating manufacturing34Simulation-first design64Engineered clothing45Task-specific AI accelerators40Algorithmic chip-design loops42Open-source purpose-built robots44The software-engineering loop43Adversarial human imitation41Open-source residential construction41Autonomous multi-angle capture34Sensing, imaging and 3D31Energy supply and dense energy storage39Robot societies among people31Agentic co-design of low-cost robots27Laundry-hanging robots25Machine learning on qualitative data23Robots on the building site27Civilizations & group psychology1History & 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.