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<p>Short-horizon prediction of chaotic dynamics becomes structurally ambiguous when only part of the state is observed: Measured variables may not form a closed autonomous system, and similar observed histories can correspond to different finite-horizon futures. ICA-KS, in-context analog Koopman selection, addresses this ambiguity by placing sparse identification of nonlinear dynamics (SINDy), delay-SINDy, a regularized Koopman predictor obtained from lifted regression, and training-only analog predictors in a finite candidate pool. Each candidate is fitted from training data, evaluated by validation rollouts and branch-specific safety diagnostics, and then one predictor is retained before held-out evaluation. The local future-dispersion statistic <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(U\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>U</mi> </math></EquationSource> </InlineEquation> is a weighted empirical spread of retrieved training futures that supports validation screening. On a 192-case confirmation benchmark with six chaotic systems, four observation masks, four data conditions, and two seeds, ICA-KS obtains median normalized root mean squared error (nRMSE) 0.660, failure rate 0.469, divergence rate 0.057, and average rank 4.747. The corresponding Koopman values are 1.051, 0.620, 0.182, and 6.044. The direct context-matching analog predictor has zero divergence under the chosen indicator but higher failure and worse rank. The analysis characterizes validation-frozen finite-candidate prediction across the specified benchmark.</p>

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Closure-aware Koopman–analog selection for partially observed chaotic dynamics

  • 期刊论文

  • 发表日期：

    2026年7月27日

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  • Changyao Gao

摘要

Short-horizon prediction of chaotic dynamics becomes structurally ambiguous when only part of the state is observed: Measured variables may not form a closed autonomous system, and similar observed histories can correspond to different finite-horizon futures. ICA-KS, in-context analog Koopman selection, addresses this ambiguity by placing sparse identification of nonlinear dynamics (SINDy), delay-SINDy, a regularized Koopman predictor obtained from lifted regression, and training-only analog predictors in a finite candidate pool. Each candidate is fitted from training data, evaluated by validation rollouts and branch-specific safety diagnostics, and then one predictor is retained before held-out evaluation. The local future-dispersion statistic \(U\) U is a weighted empirical spread of retrieved training futures that supports validation screening. On a 192-case confirmation benchmark with six chaotic systems, four observation masks, four data conditions, and two seeds, ICA-KS obtains median normalized root mean squared error (nRMSE) 0.660, failure rate 0.469, divergence rate 0.057, and average rank 4.747. The corresponding Koopman values are 1.051, 0.620, 0.182, and 6.044. The direct context-matching analog predictor has zero divergence under the chosen indicator but higher failure and worse rank. The analysis characterizes validation-frozen finite-candidate prediction across the specified benchmark.