NVAR models exhibit training error scaling laws tied to feature library representation of Lie-series coefficients, with delays reducing one-step error but aiding long-horizon forecasts only under sufficient nonlinearity.
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Transformers fail to predict catastrophic collapse in unseen parameter regimes of nonlinear dynamical systems, while reservoir computing reliably succeeds.
Optimizing reservoir computing by minimizing error in the reconstructed invariant distribution reproduces Lyapunov exponents and chaotic attractors more reliably than maximizing prediction time.
ITF inflates curvature in switching AL-RNNs by conditioning on one regime path while marginal likelihood reduces curvature with a missing-information correction for plausible switches, and evidence fine-tuning can degrade dynamical QoIs despite better held-out evidence.
citing papers explorer
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Flow map learning in nonlinear vector autoregressive models: influence of the feature-library structure on the training error
NVAR models exhibit training error scaling laws tied to feature library representation of Lie-series coefficients, with delays reducing one-step error but aiding long-horizon forecasts only under sufficient nonlinearity.
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Can Transformers predict system collapse in dynamical systems?
Transformers fail to predict catastrophic collapse in unseen parameter regimes of nonlinear dynamical systems, while reservoir computing reliably succeeds.
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Optimizing Reservoir Computing for Reconstructing Ergodic Properties
Optimizing reservoir computing by minimizing error in the reconstructed invariant distribution reproduces Lyapunov exponents and chaotic attractors more reliably than maximizing prediction time.
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Teacher Forcing as Generalized Bayes: Optimization Geometry Mismatch in Switching Surrogates for Chaotic Dynamics
ITF inflates curvature in switching AL-RNNs by conditioning on one regime path while marginal likelihood reduces curvature with a missing-information correction for plausible switches, and evidence fine-tuning can degrade dynamical QoIs despite better held-out evidence.