Publishing type：Research paper (scientific journal)   Publisher：AIP Publishing  

Recent theoretical studies on reservoir computing have shown that when the spectral radius of the adjacency matrix is sufficiently small, the dynamics of a reference system can be embedded in the reservoir space, enabling the reconstruction of dynamical invariants. However, reservoir models often reproduce time series accurately even when the spectral radius is relatively large, where the underlying mechanism is not well understood. In this study, we investigate the reconstruction of dynamical structures from the perspective of Lyapunov analysis using reservoir computing applied to the Hénon map. By comparing the Lyapunov spectrum of the reservoir dynamics with that of the reference system, we show that the reference dynamics are embedded in a low-dimensional inertial manifold in the reservoir space. We further demonstrate that the full Lyapunov spectrum of the reference system can be recovered by restricting the analysis to the tangent space of this manifold, even when the spectral radius is relatively large. These results clarify the geometric mechanism underlying the successful reconstruction of chaotic dynamics by reservoir computing beyond the regime where theoretical guarantees currently exist.

DOI： 10.1063/5.0315384

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Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

Abstract

The prediction of the Madden–Julian Oscillation (MJO), a massive tropical weather event with global socio-economic impacts, has been infamously difficult with physics-based weather prediction models. We employ the reservoir computing, a brain-inspired machine-learning technique, to construct a machine learning model that forecasts the real-time multivariate MJO index (RMM), a macroscopic variable that represents the state of the MJO. The training data was refined by development of a novel real-time band-pass filter that extracts the recurrency of MJO signals only from the past raw atmospheric data, and by selection of a suitable time-delay coordinate of the RMM that enhances the recurrency of the input data. The constructed model demonstrated the skill to forecast the time sequence of the RMM for a month from pre-developmental stages of the MJO. Examination of best-performing cases suggested that RMM sequences may be predicted for over two months in some cases. These results imply that inherent predictability limit of the MJO is longer than that has been estimated from physics-based weather prediction models.

DOI： 10.1007/s13160-026-00770-5

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Other Link： https://link.springer.com/article/10.1007/s13160-026-00770-5

Publishing type：Research paper (scientific journal)   Publisher：AIP Publishing  

In recent years, the application of machine learning approaches to time-series forecasting of climate dynamical phenomena has become increasingly active. It is known that applying a bandpass filter to a time-series data is a key to obtaining a high-quality data-driven model. Here, to obtain longer-term predictability of machine learning models, we introduce a new type of bandpass filter. It can be applied to realtime operational prediction workflows since it relies solely on past time series. We combine the filter with reservoir computing, which is a machine-learning technique that employs a data-driven dynamical system. As an application, we predict the multi-year dynamics of the El Niño-Southern Oscillation with the prediction horizon of 24 months using only past time series.

DOI： 10.1063/5.0261124

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：American Physical Society (APS)  

DOI： 10.1103/physreve.111.014212

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Other Link： http://harvest.aps.org/v2/journals/articles/10.1103/PhysRevE.111.014212/fulltext

Publishing type：Research paper (scientific journal)   Publisher：IOP Publishing  

Abstract

We computed the Lyapunov spectrum and finite-time Lyapunov exponents of a data-driven model
constructed using reservoir computing. This analysis was performed for two dynamics that exhibit a
highly dimensionally unstable structure. We focused on the reconstruction of heterochaotic dynam-
ics, which are characterized by the coexistence of different numbers of unstable dimensions. This
was achieved by computing fluctuations in the number of positive finite-time Lyapunov exponents.

DOI： 10.1088/2632-072x/ad5264

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Other Link： https://iopscience.iop.org/article/10.1088/2632-072X/ad5264/pdf

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