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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.08738 |
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| _version_ | 1866911295826034688 |
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| author | Sherkhon, Azimov Lopez-Moreno, Susana Dolores-Cuenca, Eric Lee, Sieun Kim, Sangil |
| author_facet | Sherkhon, Azimov Lopez-Moreno, Susana Dolores-Cuenca, Eric Lee, Sieun Kim, Sangil |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08738 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adaptive Nonlinear Vector Autoregression: Robust Forecasting for Noisy Chaotic Time Series Sherkhon, Azimov Lopez-Moreno, Susana Dolores-Cuenca, Eric Lee, Sieun Kim, Sangil Machine Learning Artificial Intelligence Dynamical Systems 68T07, 37M10, 00A79, 37M22, 65P20 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. |
| title | Adaptive Nonlinear Vector Autoregression: Robust Forecasting for Noisy Chaotic Time Series |
| topic | Machine Learning Artificial Intelligence Dynamical Systems 68T07, 37M10, 00A79, 37M22, 65P20 |
| url | https://arxiv.org/abs/2507.08738 |