Which rungs of a ladder of digital twins are worth running?

What it found

For twins of decreasing cost and fidelity used as nested control variates the variance is exact, σ²Σ(ρ_i²−ρ_i+1²)/m_i, and a cheaper rung pays below a twin already in use iff ρ₂/ρ₁ > 2√r/(1+r) (0.943 for halved cost, 0.575 for a 10× drop), the single-twin threshold applied to the step correlation. Using every rung is not best (q=0.99, r=0.5, six rungs: 0.284 of real-only variance vs 0.196 for the best two; q=0.9 makes all rungs 1.41× worse than real-only while the best subset gets 0.83), and 10 of 336 paying grid points are infeasible. On a saturated PD mass-spring timestep ladder the best ladder reaches 0.156 of real-only variance (0.204 for the best single twin), collapsing to the cheapest twin at 90%/70% disturbance replay (0.52/0.89 simulated); a coarser rung diverged in 2 of 20,000 contexts. Stylised: one plant, known correlations, step-count costs.

A figure from its own output

Paper, code and results

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

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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.