How should a simulation budget be split across twin fidelities?

research/ladder-twin

Splitting a simulation budget across twin fidelities (multilevel Monte Carlo): smooth quantity saves 3.6×–897× (rates α=1, β=2), a failure probability only β=1 so multilevel loses at loose targets (0.4×) and reaches 7.7× at 1e-4; equal samples per level cost 156×/3.9× the optimum.

10 tests

What it found

A twin runs at several fixed-step fidelities (n=2^l+1 Euler steps). Multilevel Monte Carlo telescopes the finest-level answer over coupled pairs sharing scenario draws, with allocation N_l ∝ √(V_l/C_l). For a smooth terminal state (bias rate α=1.000, variance rate β=2.001, cost rate 1) it needs 3.6× fewer steps than one fine twin at RMSE 10⁻² and 897× fewer at 3×10⁻⁵. For a failure probability the variance only halves per level (β=1.000), so multilevel loses at loose targets (0.4× at 3×10⁻²), breaks even near 10⁻³ and reaches 7.7× at 10⁻⁴. Equal samples per level cost 156× (smooth) and 3.9× (failure) the optimum; a coarse twin alone is off by 10–48% however many runs. Stylised: one scalar linear system, exact level moments.

A figure from its own output

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

Paper, code and results

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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.