Using machine learning to predict statistical properties of non-stationary dynamical processes: System climate,regime transitions, and the effect of stochasticity

Patel, Dhruvit; Canaday, Daniel; Girvan, Michelle; Pomerance, Andrew; Ott, Edward

doi:10.1063/5.0042598

Cited by 59 publications

(40 citation statements)

References 82 publications

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“…However, due to the complexities in the change of rainfall characteristics [4] which is caused by natural and anthropogenic factors, the physical factors that impact rainfall characteristics are needed in the models as prediction factors in the long term rainfall prediction to reveal this change. In addition, other climatic and meteorological variables utilized as predictors also show non-stationarity and complexity in dynamic climate systems [68]. Identifying major drivers of regional rainfall for mapping relationship construction is also important to enhance the predictive ability.…”

Section: Discussionmentioning

confidence: 99%

A Stacking Ensemble Learning Model for Monthly Rainfall Prediction in the Taihu Basin, China

Zhou

Chalov

et al. 2022

Water

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The prediction of monthly rainfall is greatly beneficial for water resources management and flood control projects. Machine learning (ML) techniques, as an increasingly popular approach, have been applied in diverse climatic regions, showing their respective superiority. On top of that, the ensemble learning model that synthesizes the advantages of different ML models deserves more attention. In this study, an ensemble learning model based on stacking approach was proposed. Four prevalent ML models, namely k-nearest neighbors (KNN), extreme gradient boosting (XGB), support vector regression (SVR), and artificial neural networks (ANN) are taken as base models. To combine the outputs from the base models, the weighting algorithm is used as second-layer learner to generate predictions. Large-scale climate indices, large-scale atmospheric variables, and local meteorological variables were used as predictors. R2, RMSE and MAE, were used as evaluation metrics. The results show that the performance of base models varied among the nine stations in the Taihu Basin, while the stacking approach generally performed better than the four base models. The stacking model showed better performance in spring and winter than in summer and autumn. During wet months, the accuracy of model prediction varied more significantly. On the whole, based on performance evaluation measures, it is concluded that the proposed stacking ensemble multi-ML model can provide a flexible and reasonable prediction framework applicable to other regions.

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Section: Discussionmentioning

confidence: 99%

A Stacking Ensemble Learning Model for Monthly Rainfall Prediction in the Taihu Basin, China

Zhou

Chalov

et al. 2022

Water

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“…This chapter extends the analysis to noisy and time-varying environments representing one of the first works, together with [5,10,11], that tries to bridge the gap between the ideal deterministic case and the practical applications.…”

Section: Evaluating the Effect Of Noisementioning

confidence: 99%

“…An R 2 -score of −1 reveals that the target and predicted sequences are two trajectories with the same statistical properties (they move within the same chaotic attractor) but not correlated [3,4]. In other words, the predictor would be able to reproduce the actual attractor, but the timing of the forecasting is completely wrong (in this case, we would say that we can reproduce the long-term behavior or the climate of the attractor [5,6]).…”

Section: Predictors' Identificationmentioning

confidence: 99%

Deep Learning in Multi-step Forecasting of Chaotic Dynamics

Sangiorgio

2022

SpringerBriefs in Applied Sciences and Technology

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The prediction of chaotic dynamical systems’ future evolution is widely debated and represents a hot topic in the context of nonlinear time series analysis. Recent advances in the field proved that machine learning techniques, and in particular artificial neural networks, are well suited to deal with this problem. The current state-of-the-art primarily focuses on noise-free time series, an ideal situation that never occurs in real-world applications. This chapter provides a comprehensive analysis that aims at bridging the gap between the deterministic dynamics generated by archetypal chaotic systems, and the real-world time series. We also deeply explore the importance of different typologies of noise, namely observation and structural noise. Artificial intelligence techniques turned out to provide robust predictions, and potentially represent an effective and flexible alternative to the traditional physically-based approach for real-world applications. Besides the accuracy of the forecasting, the domain-adaptation analysis attested the high generalization capability of the neural predictors across a relatively heterogeneous spatial domain.

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“…Reservoir computing methods are capable of representing a wide range of dynamical phenomena beyond what can be described by Eq. 1, including noisy dynamics ( [30]), nonautonomous systems ( [31,32]), control systems ( [33,34]), discrete-time maps ( [32]), partial differential equations ( [12]), delay differential equations ( [35]), and more. Generalizations of the version of MARC presented here are straightforward and only involve modifying the form of RC used to represent library members.…”

Section: Definitions and Scopementioning

confidence: 99%

A Meta-learning Approach to Reservoir Computing: Time Series Prediction with Limited Data

Canaday,

Pomerance,

Girvan

2021

Preprint

Self Cite

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Recent research has established the effectiveness of machine learning for data-driven prediction of the future evolution of unknown dynamical systems, including chaotic systems. However, these approaches require large amounts of measured time series data from the process to be predicted. When only limited data is available, forecasters are forced to impose significant model structure that may or may not accurately represent the process of interest. In this work, we present a Meta-learning Approach to Reservoir Computing (MARC), a data-driven approach to automatically extract an appropriate model structure from experimentally observed "related" processes that can be used to vastly reduce the amount of data required to successfully train a predictive model. We demonstrate our approach on a simple benchmark problem, where it beats the state of the art meta-learning techniques, as well as a challenging chaotic problem.

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Using machine learning to predict statistical properties of non-stationary dynamical processes: System climate,regime transitions, and the effect of stochasticity

Cited by 59 publications

References 82 publications

A Stacking Ensemble Learning Model for Monthly Rainfall Prediction in the Taihu Basin, China

A Stacking Ensemble Learning Model for Monthly Rainfall Prediction in the Taihu Basin, China

Deep Learning in Multi-step Forecasting of Chaotic Dynamics

A Meta-learning Approach to Reservoir Computing: Time Series Prediction with Limited Data

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