A Response Theory Probe for Learned Stochastic AI Simulators, Tested on Lorenz-63
A response-theory probe tests whether learned chaotic simulators react correctly to forcing on Lorenz-63.
The paper turns linear response theory into a mode-resolved pass-fail probe for learned simulators of chaotic and stochastic systems, testing whether surrogates respond correctly to forcing rather than only matching forecasts or long-run statistics. On stochastic Lorenz-63 it evaluates SINDy, an MLP, a reservoir computer, a neural ODE and a neural SDE over up to 80 rollouts each. A sparse-regression model with the correct library passes every check at rates consistent with the true system, while invariant-statistics fidelity and slow-mode response fidelity dissociate for reservoir computers versus neural ODEs and SDEs. For a fixed network, the training formulation determines which properties are recovered.
- The probe checks forced response via a fluctuation-dissipation relation and Ruelle-Pollicott modes.
- SINDy, an MLP, a reservoir computer, a neural ODE and a neural SDE are tested on Lorenz-63.
- A correct-library sparse model passes at rates consistent with the true system.
- Invariant-statistics fidelity and response-mode fidelity can fail independently.
From the original article
1 min read at arxiv.orgMachine-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.
By João Böger · arxiv.org
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