•  
  •  
 

Article Type

Research Article

Abstract

Modern dynamical systems increasingly operate with evidence that is not merely noisy but incomplete, contradictory, or only partially trustworthy. Conventional Koopman methods represent nonlinear dynamics through linear evolution of observables, while robust and adaptive variants address parameter and model uncertainty. They do not, however, preserve the semantic distinction between support, indeterminacy, and counter-support when those conditions are compressed into a single uncertainty variable. This paper develops NeutroKoopman, a channel-preserving Koopman framework in which the physical state is augmented by a single-valued neutrosophic evidence state νt = ( Tt,It,Ft ). Deterministic and Markovian formulations are given, and finite approximations retain separate truth, indeterminacy, falsity, physical, and coupling blocks. The resulting block structure defines three diagnostics: the Indeterminacy Spectral Radius (ISR), the Indeterminacy Injection Gain (IIG), and a normalized Truth-Falsity Coupling (TFC) index. Five formal results establish the standard Markov-Koopman operator properties, non-identifiability under linear scalar compression of ( T,I,F ), a finite-time indeterminacy bound under an induced-norm contraction condition, the precise relation between ISR and finite-time contraction for non-normal blocks, and invariance of ISR under invertible within-channel basis changes. Two estimators are developed: NeutroKoopman-EDMD and a Gaussian Kolmogorov-Arnold lifting variant. Validation includes an exact scalar-compression counterexample, a direct recovery test for ISR/IIG/TFC, a 50,000-system numerical verification of the dissipation bound with zero violations, and a nonlinear Hénon-evidence benchmark. On the latter, the Gaussian-KAN lift reduced standardized one-step evidence-channel RMSE from 0.1404 for a quadratic EDMD lift to 0.0144, while the physical quadratic map remained represented to numerical precision. NeutroKoopman therefore extends Koopman analysis at the level of state semantics and finite operator structure, allowing indeterminacy and contradiction to remain separately measurable throughout operator learning.

Keywords

Neutrosophic dynamics, Koopman operator, Nonlinear systems, Indeterminacy, Contradiction, Spectral analysis, Extended dynamic mode decomposition, Kolmogorov-Arnold networks, Uncertainty-aware modeling, Scientific machine learning

Download

Share

COinS