8 papers
Equation-Free Screening of Mittag-Leffler-Compatible Dynamics from Scalar Time Series via kNN Multi-Horizon Profiles
N'Gbo N'Gbo, Andrei Velichko, Bruno Carpentieri
Fractional models provide a natural description of systems with memory, but a noninteger derivative should not be introduced solely because a time series is curved or slowly relaxi…
Unified Geometry-Guided ML-FTLE for Tracking Transient Chaos from Scalar Time Series
S. V. Manivelan, Andrei Velichko, I. Manimehan
Detecting transient chaos from scalar observations without governing equations represents a fundamental challenge in nonlinear dynamics. We propose a geometry-guided machine learni…
FEG-Pro: Forecast-Error Growth Profiling for Finite-Horizon Instability Analysis of Nonlinear Time Series
Andrei Velichko, N'Gbo N'Gbo, Bruno Carpentieri +1
Estimating the largest Lyapunov exponent from a scalar time series is difficult when the governing equations, tangent dynamics, and full state vector are unavailable. We propose FE…
Interpretable AI-Assisted Early Reliability Prediction for a Two-Parameter Parallel Root-Finding Scheme
Bruno Carpentieri, Andrei Velichko, Mudassir Shams +1
We propose an interpretable AI-assisted reliability diagnostic framework for parameterized root-finding schemes based on kNN-LLE proxy stability profiling and multi-horizon early p…
Direct Finite-Time Contraction (Step-Log) Profiling--Driven Optimization of Parallel Schemes for Nonlinear Problems on Multicore Architectures
Mudassir Shams, Andrei Velichko, Bruno Carpentieri
Efficient computation of all distinct solutions of nonlinear problems is essential in many scientific and engineering applications. Although high-order parallel iterative schemes o…
Optimizing Parallel Schemes with Lyapunov Exponents and kNN-LLE Estimation
Mudassir Shams, Andrei Velichko, Bruno Carpentieri
Inverse parallel schemes remain indispensable tools for computing the roots of nonlinear systems, yet their dynamical behavior can be unexpectedly rich, ranging from strong contrac…
Local Lyapunov analysis via micro-ensembles: finite-time Lyapunov exponent estimation and KNN-based predictive comparison in complex-valued BAM neural networks
Yazhini Muruganantham, Andrei Velichko, Samidurai Rajendran
Complex-valued bidirectional associative memory (BAM) neural networks with fractional-order dynamics and delays can exhibit transient instabilities that degrade synchronization and…
Evaluating COVID 19 Feature Contributions to Bitcoin Return Forecasting: Methodology Based on LightGBM and Genetic Optimization
Imen Mahmoud, Andrei Velichko
This study proposes a novel methodological framework integrating a LightGBM regression model and genetic algorithm (GA) optimization to systematically evaluate the contribution of…