Predicting amplitude death with machine learning

Xiao, Rui; Kong, Ling-Wei; Sun, Zhongkui; Lai, Ying Cheng

doi:10.1103/physreve.104.014205

Cited by 33 publications

(10 citation statements)

References 60 publications

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“…We predict correlation matrices for cases that closely match real-world scenarios. A dynamic system with a fixed number of nodes can undergo two types of changes (1) coupling strength between nodes can either increase or decrease. (2) a small structural change with rearrangement of links between nodes.…”

Section: Methods and Resultsmentioning

confidence: 99%

“…Machine learning has been applied in diverse areas of physical sciences ranging from condensed matter to high energy physics to complex systems. In complex systems, neural network-based machine learning techniques have been used in predicting amplitude death [1], anticipation of synchronization [2], phase transitions in complex networks [3], time series prediction [4], etc. In particular, forecasting time series data has attracted interest from the scientific fraternity due to its diverse applications in real-world dynamical systems like stock markets and the brain.…”

Section: Introductionmentioning

confidence: 99%

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Estimation of Correlation Matrices from Limited time series Data using Machine Learning

Easaw¹,

Soek²,

Lohiya³

et al. 2022

Preprint

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Prediction of correlation matrices from given time series data has several applications for a range of problems, such as inferring neuronal connections from spiking data, deducing causal dependencies between genes from expression data, and discovering long spatial range influences in climate variations. Traditional methods of predicting correlation matrices utilize time series data of all the nodes of the underlying networks. Here, we use a supervised machine learning technique to predict the correlation matrix of entire systems from finite time series information of a few randomly selected nodes. The accuracy of the prediction from the model confirms that only a limited time series of a subset of the entire system is enough to make good correlation matrix predictions. Furthermore, using an unsupervised learning algorithm, we provide insights into the success of the predictions from our model. Finally, we apply the machine learning model developed here to real-world data sets.

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Section: Methods and Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Estimation of Correlation Matrices from Limited time series Data using Machine Learning

Easaw¹,

Soek²,

Lohiya³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…While prediction of stationary systems by machine learning (ML) has received much recent attention, less progress has been made in applying ML to the problem of predicting the time evolution of nonstationary dynamical systems, particularly of their climate and of the tipping points they may experience. Refer to [12,[28][29][30] for recent works which apply machine learning to the problem of predicting the short-term state evolution of non-stationary dynamical systems and to [27,[31][32][33][34] for recent works which aim to address the problem of predicting changing statistical properties of non-stationary dynamical systems (including anticipating tipping points). In previous work [27] we demonstrated that ML provides a promising avenue for predicting the climate of a non-stationary dynamical system using the time series of its past states and knowledge of a non-stationarity-inducing system parameter time dependence.…”

Section: Introductionmentioning

confidence: 99%

“…In contrast, in previous work on predicting tipping points and the associated post-tipping-point dynamics [27,33,34] ML prediction was considered for cases in which the training data was obtained from orbits that typically explored large state space regions that included all or most of the state space visited by the predicted future orbits. Thus, in this prior work the ML predictor was directly aware of dynamical system information needed for the prediction of the future behavior, e.g., after a predicted tipping point.…”

Section: Introductionmentioning

confidence: 99%

“…A further contribution of our paper relative to previous related papers using ML for prediction of non-stationary behavior [27,33,34] is that those previous works considered the case where the system non-stationarity was induced by time variation of a parameter of an otherwise unknown system, and this parameter time variation was assumed to be known and was used as an input to the ML prediction system. In this current paper, on the other hand, we consider the case where knowledge of the type described above may not be available.…”

Section: Introductionmentioning

confidence: 99%

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Using Machine Learning to Anticipate Tipping Points and Extrapolate to Post-Tipping Dynamics of Non-Stationary Dynamical Systems

Patel¹,

Ott²

2022

Preprint

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In this paper we consider the machine learning (ML) task of predicting tipping point transitions and long-term post-tipping-point behavior associated with the time evolution of an unknown (or partially unknown), non-stationary, potentially noisy and chaotic, dynamical system. We focus on the particularly challenging situation where the past dynamical state time series that is available for ML training predominantly lies in a restricted region of the state space, while the behavior to be predicted evolves on a larger state space set not fully observed by the ML model during training. In this situation, it is required that the ML prediction system have the ability to extrapolate to different dynamics past that which is observed during training. We investigate the extent to which ML methods are capable of accomplishing useful results for this task, as well as conditions under which they fail. In general, we found that the ML methods were surprisingly effective even in situations that were extremely challenging, but do (as one would expect) fail when "too much" extrapolation is required. For the latter case, we investigate the effectiveness of combining the ML approach with conventional modeling based on scientific knowledge, thus forming a hybrid prediction system which we find can enable useful prediction even when its ML-based and knowledge-based components fail when acting alone. We also found that achieving useful results may require using very carefully selected ML hyperparameters and we propose a hyperparameter optimization strategy to address this problem. The main conclusion of this paper is that ML-based approaches are promising tools for predicting the behavior of non-stationary dynamical systems even in the case where the future evolution (perhaps due to the crossing of a tipping point) includes dynamics on a set outside of that explored by the training data.

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Adjoint Sensitivities of Chaotic Flows Without Adjoint Solvers: A Data-Driven Approach

Ozan,

Magri

2024

Lecture Notes in Computer Science

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Predicting amplitude death with machine learning

Cited by 33 publications

References 60 publications

Estimation of Correlation Matrices from Limited time series Data using Machine Learning

Estimation of Correlation Matrices from Limited time series Data using Machine Learning

Using Machine Learning to Anticipate Tipping Points and Extrapolate to Post-Tipping Dynamics of Non-Stationary Dynamical Systems

Adjoint Sensitivities of Chaotic Flows Without Adjoint Solvers: A Data-Driven Approach

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