A Response Theory Probe for Learned Stochastic AI Simulators, Tested on Lorenz-63
Machine-learning emulators of chaotic and stochastic systems are usually validated on forecast skill and long-run statistics. Neither certifies that an emulator responds correctly to forcing, the property that projection and attribution studies rely on. Linear response theory makes this testable: the forced response follows from unperturbed correlations through a generalized fluctuation-dissipation relation, and decomposes over the stochastic Ruelle-Pollicott resonances of the Koopman generator. Building on the Koopmanism Response framework, we turn this into a calibrated, mode-resolved test for learned surrogates: each surrogate rollout passes or fails each check, and failure rates are c...
| Authors | João Böger, Simon Driscoll, Niccolò Zagli et al. |
|---|---|
| Primary category | math.DS |
| Published | 5 October 2026 |
| Last updated at source | 6 October 2026 |
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