Long-term prediction of chaotic time series with multi-step prediction horizons by a neural network with Levenberg–Marquardt learning algorithm

Multistep ahead prediction of a chaotic time series is a difficult task that has attracted increasing interest in the recent years. The interest in this work is the development of nonlinear neural network models for the purpose of building multistep chaotic time series prediction. In the literature there is a wide range of different approaches but their success depends on the predicting performance of the individual methods. Also the most popular neural models are based on the statistical and traditional feed forward neural networks. But it is seen that this kind of neural model may present some disadvantages when long-term prediction is required. In this paper focused time-lagged recurrent neural network (FTLRNN) model with gamma memory is developed for different prediction horizons. It is observed that this predictor performs remarkably well for short-term predictions as well as medium-term predictions. For coupled partial differential equations generated chaotic time series such as Mackey Glass and Duffing, FTLRNN-based predictor performs consistently well for different depths of predictions ranging from short term to long term, with only slight deterioration after k is increased beyond 50. For real-world highly complex and nonstationary time series like Sunspots and Laser, though the proposed predictor does perform reasonably for short term and medium-term predictions, its prediction ability drops for long term ahead prediction. However, still this is the best possible prediction results considering the facts that these are nonstationary time series. As a matter of fact, no other NN configuration can match the performance of FTLRNN model. The authors experimented the performance of this FTLRNN model on predicting the dynamic behavior of typical Chaotic Mackey-Glass time series, Duffing time series, and two real-time chaotic time series such as monthly sunspots and laser. Static multi layer perceptron (MLP) model is also attempted and compared against the proposed model on the performance measures like mean squared error (MSE), Normalized mean squared error (NMSE), and Correlation Coefficient (r). The standard back-propagation algorithm with momentum term has been used for both the models.

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Comparison between Inverse Model and Chaos Time Series Inverse Model for Long-Term Prediction

Sustainability ◽

10.3390/su9060982 ◽

2017 ◽

Vol 9 (6) ◽

pp. 982 ◽

Cited By ~ 1

Author(s):

Young-Jin Kim

Keyword(s):

Time Series ◽

Inverse Model ◽

Term Prediction ◽

Long Term Prediction

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Long-term prediction of karst water recovery process based on two different approaches in a former mining area, Transdanubian Range, Hungary

10.5194/egusphere-egu2020-18969 ◽

2020 ◽

Author(s):

Kamilla Modrovits ◽

András Csepregi ◽

József Kovács

Keyword(s):

Time Series ◽

Water Level ◽

Trend Analysis ◽

Recovery Process ◽

Karst Water ◽

Deterministic Approach ◽

Term Prediction ◽

Transdanubian Range ◽

Long Term Prediction

The Transdanubian Range is located in the mid-western part of Hungary and contains Mesozoic, mainly Triassic formations with the total thickness of 1.5-2 km. From 1950 to 1990 coal and bauxite mining took place with different centres in this area, therefor large amount of karst water was extracted for preventative purpose. Thus, the water levels decreased from ten to more than a hundred of meters. Since the mining was stopped in the beginning of the 1990s, the natural recharge exceeded the amount of extraction and the recovery of the karst water began. Since then the system is on the way to return to its original &#8211; undisturbed &#8211; state. Because of the rising water level, economic and technical engineering problems have occurred, which requires the better understanding of the process.Water level changes are often predicted with a deterministic approach using different modelling software (e.g. MODFLOW, FEFLOW, etc.). However, stochastic approaches (e.g. trend estimation), which have so far been little used in forecast of groundwater, can also be applied for certain hydrogeological problems. The aims of the research were (i) to find the most accurate trend function describing the recovery process (ii) in order to make a long-term prediction, (iii) and compare the results with the results deterministic modelling. For this purpose, decades of time series from 107 monitoring wells were investigated.As a result of the research, it was identified that the karst water time series from the Transdanubian Range can be properly estimated (R2 > 0.9 in the 82.24% of the cases) by growth and logistic curves, especially by the so-called Richards and &#8220;63%&#8221; ones. These curves gave the best fit in 57.95% of the cases based on the R2 value obtained by fitting the 10 examined models. Both the deterministic approach modelling (MODFLOW) and the stochastic approach trend analysis are suitable for estimating and predicting the water level rise in the karst aquifer, but the results are slightly different. Modelling with the MODFLOW software can be affected by the accuracy of input parameters (infiltration, yield of springs, etc.) and the realness of the conceptual model. First and foremost, more and better-quality water level data series are needed for trend analysis, and based on our prior knowledge, it is essential to provide an accurate expected maximum water level (upper limit). The comparison of the two methods unveiled, that growth and logistic curves can also be successfully used in the prediction of groundwater levels. As a conclusion, the number of methods which may be used for such research can be expanded.This research is part of a project that has received funding from the European Union&#8217;s Horizon 2020 research and innovation programme under grant agreement No 810980.

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