{"ID":2895786,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.08738","arxiv_id":"2507.08738","title":"Adaptive Nonlinear Vector Autoregression: Robust Forecasting for Noisy Chaotic Time Series","abstract":"Nonlinear vector autoregression (NVAR) and reservoir computing (RC) have shown promise in forecasting chaotic dynamical systems, such as the Lorenz-63 model and El Nino-Southern Oscillation. However, their reliance on fixed nonlinear transformations - polynomial expansions in NVAR or random feature maps in RC - limits their adaptability to high noise or complex real-world data. Furthermore, these methods also exhibit poor scalability in high-dimensional settings due to costly matrix inversion during optimization. We propose a data-adaptive NVAR model that combines delay-embedded linear inputs with features generated by a shallow, trainable multilayer perceptron (MLP). Unlike standard NVAR and RC models, the MLP and linear readout are jointly trained using gradient-based optimization, enabling the model to learn data-driven nonlinearities, while preserving a simple readout structure and improving scalability. Initial experiments across multiple chaotic systems, tested under noise-free and synthetically noisy conditions, showed that the adaptive model outperformed in predictive accuracy the standard NVAR, a leaky echo state network (ESN) - the most common RC model - and a hybrid ESN, thereby showing robust forecasting under noisy conditions.","short_abstract":"Nonlinear vector autoregression (NVAR) and reservoir computing (RC) have shown promise in forecasting chaotic dynamical systems, such as the Lorenz-63 model and El Nino-Southern Oscillation. However, their reliance on fixed nonlinear transformations - polynomial expansions in NVAR or random feature maps in RC - limits...","url_abs":"https://arxiv.org/abs/2507.08738","url_pdf":"https://arxiv.org/pdf/2507.08738v2","authors":"[\"Azimov Sherkhon\",\"Susana Lopez-Moreno\",\"Eric Dolores-Cuenca\",\"Sieun Lee\",\"Sangil Kim\"]","published":"2025-07-11T16:40:10Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\",\"math.DS\"]","methods":"[]","has_code":false}