Data-driven stochastic model for cross-interacting processes with different time scales

2021 ◽  
Author(s):  
Andrey Gavrilov ◽  
Aleksei Seleznev ◽  
Dmitry Mukhin ◽  
Alexander Feigin
Keyword(s):  
Time Series ◽  
Stochastic Model ◽  
Time Scales ◽  
Time Scale ◽  
Sampling Interval ◽  
Bayesian Optimization ◽  
Data Driven ◽  
Middle Pleistocene ◽  
Model Based ◽  
Different Time Scales

<p>The problem of modeling interaction between processes with different time scales is very important in geoscience. In this report, we propose a new form of empirical evolution operator model based on the analysis of multiple time series representing processes with different time scales. We assume that the time series are given on the same time interval.</p><p>To construct the model, we extend the previously developed general form of nonlinear stochastic model based on artificial neural networks and designed for the case of time series with constant sampling interval [1]. This sampling interval is related to the main time scale of the process under consideration, which is described by the deterministic component of the model, while the faster time scales are modeled by its stochastic component, possibly depending on the system’s state. This model also includes slower processes in the form of weak time-dependence, as well as external forcing. The structure of the model is optimized using Bayesian approach [1]. The model has proven its efficiency in a number of applications [2-4].</p><p>The idea of modeling time series with different time scales is to formulate the above-described model individually for each time scale, and then to include the parameterized influence of the other time scales in it. Particularly, the influence of “slower” time series is included in the form of parameter trends, and the influence of “faster” time series is included by time-averaging their statistics. The algorithm and first results of comparison between the new model and the model without cross-interactions will be discussed.</p><p>The work was supported by the Russian Science Foundation (Grant No. 20-62-46056).</p><p>1. Gavrilov, A., Loskutov, E., & Mukhin, D. (2017). Bayesian optimization of empirical model with state-dependent stochastic forcing. Chaos, Solitons & Fractals, 104, 327–337. http://doi.org/10.1016/j.chaos.2017.08.032</p><p>2. Mukhin, D., Kondrashov, D., Loskutov, E., Gavrilov, A., Feigin, A., & Ghil, M. (2015). Predicting Critical Transitions in ENSO models. Part II: Spatially Dependent Models. Journal of Climate, 28(5), 1962–1976. http://doi.org/10.1175/JCLI-D-14-00240.1</p><p>3. Gavrilov, A., Seleznev, A., Mukhin, D., Loskutov, E., Feigin, A., & Kurths, J. (2019). Linear dynamical modes as new variables for data-driven ENSO forecast. Climate Dynamics, 52(3–4), 2199–2216. http://doi.org/10.1007/s00382-018-4255-7</p><p>4. Mukhin, D., Gavrilov, A., Loskutov, E., Kurths, J., & Feigin, A. (2019). Bayesian Data Analysis for Revealing Causes of the Middle Pleistocene Transition. Scientific Reports, 9(1), 7328. http://doi.org/10.1038/s41598-019-43867-3</p>

scholarly journals Multi-scale event synchronization analysis for unravelling climate processes: A wavelet-based approach

2017 ◽  
Author(s):  
Ankit Agarwal ◽  
Norbert Marwan ◽  
Maheswaran Rathinasamy ◽  
Bruno Merz ◽  
Jürgen Kurths
Keyword(s):  
Time Series ◽  
Time Scales ◽  
Time Scale ◽  
Temporal Dynamics ◽  
Multiple Scales ◽  
Nonlinear Interactions ◽  
Reference Time ◽  
Multi Scale ◽  
Spatio Temporal ◽  
Different Time Scales

Abstract. The temporal dynamics of climate processes are spread across different time scales and, as such, the study of these processes only at one selected time scale might not reveal the complete mechanisms and interactions within and between the (sub-) processes. For capturing the nonlinear interactions between climatic events, the method of event synchronization has found increasing attention recently. The main drawback with the present estimation of event synchronization is its restriction to analyse the time series at one reference time scale only. The study of event synchronization at multiple scales would be of great interest to comprehend the dynamics of the investigated climate processes. In this paper, wavelet based multi-scale event synchronization (MSES) method is proposed by combining the wavelet transform and event synchronization. Wavelets are used extensively to comprehend multi-scale processes and the dynamics of processes across various time scales. The proposed method allows the study of spatio-temporal patterns across different time scales. The method is tested on synthetic and real-world time series in order to check its replicability and applicability. The results indicate that MSES is able to capture relationships that exist between processes at different time scales.

scholarly journals Locally and Remotely Forced Subtropical AMOC Variability: A Matter of Time Scales

2020 ◽  
Vol 33 (12) ◽  
pp. 5155-5172
Author(s):  
Quentin Jamet ◽  
William K. Dewar ◽  
Nicolas Wienders ◽  
Bruno Deremble ◽  
Sally Close ◽  
...  
Keyword(s):  
Time Series ◽  
Time Scales ◽  
North Atlantic ◽  
Time Scale ◽  
Low Frequency ◽  
Meridional Overturning Circulation ◽  
Open Boundary ◽  
Overturning Circulation ◽  
Decadal Scale ◽  
Meridional Overturning

AbstractMechanisms driving the North Atlantic meridional overturning circulation (AMOC) variability at low frequency are of central interest for accurate climate predictions. Although the subpolar gyre region has been identified as a preferred place for generating climate time-scale signals, their southward propagation remains under consideration, complicating the interpretation of the observed time series provided by the Rapid Climate Change–Meridional Overturning Circulation and Heatflux Array–Western Boundary Time Series (RAPID–MOCHA–WBTS) program. In this study, we aim at disentangling the respective contribution of the local atmospheric forcing from signals of remote origin for the subtropical low-frequency AMOC variability. We analyze for this a set of four ensembles of a regional (20°S–55°N), eddy-resolving (1/12°) North Atlantic oceanic configuration, where surface forcing and open boundary conditions are alternatively permuted from fully varying (realistic) to yearly repeating signals. Their analysis reveals the predominance of local, atmospherically forced signal at interannual time scales (2–10 years), whereas signals imposed by the boundaries are responsible for the decadal (10–30 years) part of the spectrum. Due to this marked time-scale separation, we show that, although the intergyre region exhibits peculiarities, most of the subtropical AMOC variability can be understood as a linear superposition of these two signals. Finally, we find that the decadal-scale, boundary-forced AMOC variability has both northern and southern origins, although the former dominates over the latter, including at the site of the RAPID array (26.5°N).

scholarly journals Methods of Constructing Time Series for Predicting Local Time Scales by Means of a GMDH-Type Neural Network

2021 ◽  
Vol 11 (12) ◽  
pp. 5615
Author(s):  
Łukasz Sobolewski ◽  
Wiesław Miczulski
Keyword(s):  
Neural Network ◽  
Time Series ◽  
Local Time ◽  
Time Scales ◽  
Time Scale ◽  
Prediction Accuracy ◽  
Prediction Horizon

Ensuring the best possible stability of UTC(k) (local time scale) and its compliance with the UTC scale (Universal Coordinated Time) forces predicting the [UTC-UTC(k)] deviations, the article presents the results of work on two methods of constructing time series (TS) for a neural network (NN), increasing the accuracy of UTC(k) prediction. In the first method, two prepared TSs are based on the deviations determined according to the UTC scale with a 5-day interval. In order to improve the accuracy of predicting the deviations, the PCHIP interpolating function is used in subsequent TSs, obtaining TS elements with a 1-day interval. A limitation in the improvement of prediction accuracy for these TS has been a too large prediction horizon. The introduction in 2012 of the additional UTC Rapid scale by BIPM makes it possible to shorten the prediction horizon, and the building of two TSs has been proposed according to the second method. Each of them consists of two subsets. The first subset is based on deviations determined according to the UTC scale, the second on the UTC Rapid scale. The research of the proposed TS in the field of predicting deviations for the Polish Timescale by means of GMDH-type NN shows that the best accuracy of predicting the deviations has been achieved for TS built according to the second method.

scholarly journals Sub-daily runoff simulations with parameters inferred at the daily time scale

2015 ◽  
Vol 12 (8) ◽  
pp. 7437-7467 ◽  
Author(s):  
J. E. Reynolds ◽  
S. Halldin ◽  
C. Y. Xu ◽  
J. Seibert ◽  
A. Kauffeldt
Keyword(s):  
Time Series ◽  
Numerical Method ◽  
Time Scales ◽  
Time Scale ◽  
Input Data ◽  
Flood Forecasting ◽  
Euler Method ◽  
Time Stepping ◽  
Parameter Values ◽  
Daily Time

Abstract. Concentration times in small and medium-sized watersheds (~ 100–1000 km2) are commonly less than 24 h. Flood-forecasting models then require data at sub-daily time scales, but time-series of input and runoff data with sufficient lengths are often only available at the daily time scale, especially in developing countries. This has led to a search for time-scale relationships to infer parameter values at the time scales where they are needed from the time scales where they are available. In this study, time-scale dependencies in the HBV-light conceptual hydrological model were assessed within the generalized likelihood uncertainty estimation (GLUE) approach. It was hypothesised that the existence of such dependencies is a result of the numerical method or time-stepping scheme used in the models rather than a real time-scale-data dependence. Parameter values inferred showed a clear dependence on time scale when the explicit Euler method was used for modelling at the same time steps as the time scale of the input data (1–24 h). However, the dependence almost fully disappeared when the explicit Euler method was used for modelling in 1 h time steps internally irrespectively of the time scale of the input data. In other words, it was found that when an adequate time-stepping scheme was implemented, parameter sets inferred at one time scale (e.g., daily) could be used directly for runoff simulations at other time scales (e.g., 3 or 6 h) without any time scaling and this approach only resulted in a small (if any) model performance decrease, in terms of Nash–Sutcliffe and volume-error efficiencies. The overall results of this study indicated that as soon as sub-daily driving data can be secured, flood forecasting in watersheds with sub-daily concentration times is possible with model-parameter values inferred from long time series of daily data, as long as an appropriate numerical method is used.

scholarly journals Characterizing ecosystem-atmosphere interactions from short to interannual time scales

2007 ◽  
Vol 4 (3) ◽  
pp. 1405-1435
Author(s):  
M. D. Mahecha ◽  
M. Reichstein ◽  
H. Lange ◽  
N. Carvalhais ◽  
C. Bernhofer ◽  
...  
Keyword(s):  
Time Series ◽  
Time Scales ◽  
System Analysis ◽  
Singular System ◽  
Low Frequency ◽  
Data Adaptive ◽  
Effective Signal ◽  
Observation Space ◽  
Different Time Scales ◽  
Observation Period

Abstract. Characterizing ecosystem-atmosphere interactions in terms of carbon and water exchange on different time scales is considered a major challenge in terrestrial biogeochemical cycle research. The respective time series are now partly comprising an observation period of one decade. In this study, we explored whether the observation period is already sufficient to detect cross relationships of the variables beyond the annual cycle as they are expected from comparable studies in climatology. We explored the potential of Singular System Analysis (SSA) to extract arbitrary kinds of oscillatory patterns. The method is completely data adaptive and performs an effective signal to noise separation. We found that most observations (NEE, GPP, Reco, VPD, LE, H, u, P) were influenced significantly by low frequency components (interannual variability). Furthermore we extracted a set of nonlinear relationships and found clear annual hysteresis effects except for the NEE-Rg relationship which turned out to be the sole linear relationship in the observation space. SSA provides a new tool to investigate these phenomena explicitly on different time scales. Furthermore, we showed that SSA has great potential for eddy covariance data processing since it can be applied as novel gap filling approach relying on the temporal time series structure only.

scholarly journals Stationarity Testing of Accumulated Ethernet Traffic

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Zhiping Lu ◽  
Ming Li ◽  
Wei Zhao
Keyword(s):  
Time Scales ◽  
Unit Root ◽  
Time Scale ◽  
Unit Root Tests ◽  
Quantitative Results ◽  
Different Time Scales

We investigate the stationarity property of the accumulated Ethernet traffic series. We applied several widely used stationarity and unit root tests, such as Dickey-Fuller test and its augmented version, Phillips-Perron test, as well as the Kwiatkowski-Phillips-Schmidt-Shin test and some of its generalizations, to the assessment of the stationarity of the traffic traces at the different time scales. The quantitative results in this research provide evidence that when the time scale increases, the accumulated traffic series are more stationary.

Bayesian recurrent neural network as a tool for reconstructing dynamical systems from multidimensional data

2020 ◽  
Author(s):  
Alexander Feigin ◽  
Aleksei Seleznev ◽  
Dmitry Mukhin ◽  
Andrey Gavrilov ◽  
Evgeny Loskutov
Keyword(s):  
Neural Network ◽  
Time Series ◽  
Cost Function ◽  
Recurrent Neural Network ◽  
Bayesian Optimization ◽  
Data Driven ◽  
High Dimensional ◽  
Model Learning ◽  
Low Dimensional ◽  
The Cost

<p>We suggest a new method for construction of data-driven dynamical models from observed multidimensional time series. The method is based on a recurrent neural network (RNN) with specific structure, which allows for the joint reconstruction of both a low-dimensional embedding for dynamical components in the data and an operator describing the low-dimensional evolution of the system. The key link of the method is a Bayesian optimization of both model structure and the hypothesis about the data generating law, which is needed for constructing the cost function for model learning.  The form of the model we propose allows us to construct a stochastic dynamical system of moderate dimension that copies dynamical properties of the original high-dimensional system. An advantage of the proposed method is the data-adaptive properties of the RNN model: it is based on the adjustable nonlinear elements and has easily scalable structure. The combination of the RNN with the Bayesian optimization procedure efficiently provides the model with statistically significant nonlinearity and dimension.<br>The method developed for the model optimization aims to detect the long-term connections between system’s states – the memory of the system: the cost-function used for model learning is constructed taking into account this factor. In particular, in the case of absence of interaction between the dynamical component and noise, the method provides unbiased reconstruction of the hidden deterministic system. In the opposite case when the noise has strong impact on the dynamics, the method yield a model in the form of a nonlinear stochastic map determining the Markovian process with memory. Bayesian approach used for selecting both the optimal model’s structure and the appropriate cost function allows to obtain the statistically significant inferences about the dynamical signal in data as well as its interaction with the noise components.<br>Data driven model derived from the relatively short time series of the QG3 model – the high dimensional nonlinear system producing chaotic behavior – is shown be able to serve as a good simulator for the QG3 LFV components. The statistically significant recurrent states of the QG3 model, i.e. the well-known teleconnections in NH, are all reproduced by the model obtained. Moreover, statistics of the residence times of the model near these states is very close to the corresponding statistics of the original QG3 model. These results demonstrate that the method can be useful in modeling the variability of the real atmosphere.</p><p>The work was supported by the Russian Science Foundation (Grant No. 19-42-04121).</p>

EMERGING PROPERTIES IN POPULATION DYNAMICS WITH DIFFERENT TIME SCALES

1995 ◽  
Vol 03 (02) ◽  
pp. 591-602 ◽  
Author(s):  
PIERRE AUGER ◽  
JEAN-CHRISTOPHE POGGIALE
Keyword(s):  
Differential Equations ◽  
Time Scales ◽  
Time Scale ◽  
Population Level ◽  
Nonlinear Process ◽  
Linear Process ◽  
Fast Time ◽  
Slow Part ◽  
Spatial Patches ◽  
Different Time Scales

The aim of this work is to show that at the population level, emerging properties may occur as a result of the coupling between the fast micro-dynamics and the slow macrodynamics. We studied a prey-predator system with different time scales in a heterogeneous environment. A fast time scale is associated to the migration process on spatial patches and a slow time scale is associated to the growth and the interactions between the species. Preys go on the spatial patches on which some resources are located and can be caught by the predators on them. The efficiency of the predators to catch preys is patch-dependent. Preys can be more easily caught on some spatial patches than others. Perturbation theory is used in order to aggregate the initial system of ordinary differential equations for the patch sub-populations into a macro-system of two differential equations governing the total populations. Firstly, we study the case of a linear process of migration for which the aggregated system is formally identical to the slow part of the full system. Then, we study an example of a nonlinear process of migration. We show that under these conditions emerging properties appear at the population level.

scholarly journals Multi-Time Scale Economic Optimization Dispatch of the Park Integrated Energy System

2021 ◽  
Vol 9 ◽  
Author(s):  
Peng Li ◽  
Fan Zhang ◽  
Xiyuan Ma ◽  
Senjing Yao ◽  
Zhuolin Zhong ◽  
...  
Keyword(s):  
Renewable Energy ◽  
Time Scales ◽  
Time Scale ◽  
Energy Systems ◽  
Energy System ◽  
Optimal Operation ◽  
Utilization Efficiency ◽  
Integrated Energy System ◽  
Operation Cost ◽  
Different Time Scales

The park integrated energy system (PIES) plays an important role in realizing sustainable energy development and carbon neutral. Furthermore, its optimization dispatch can improve the energy utilization efficiency and reduce energy systems operation cost. However, the randomness and volatility of renewable energy and the instability of load all bring challenges to its optimal operation. An optimal dispatch framework of PIES is proposed, which constructs the operation models under three different time scales, including day-ahead, intra-day and real-time. Demand response is also divided into three levels considering its response characteristics and cost composition under different time scales. The example analysis shows that the multi-time scale optimization dispatch model can not only meet the supply and demand balance of PIES, diminish the fluctuation of renewable energy and flatten load curves, but also reduce the operation cost and improve the reliability of energy systems.

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