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An assessment of multi-layer perceptron networks for streamflow forecasting in large-scale interconnected hydrosystems


This work analyzes the use of artificial neural networks in the short-term streamflow forecasting for large interconnected hydropower systems. The state-of-the-art optimization algorithms, activation functions, and weight initialization techniques are investigated together with classic methods. We present an algorithm to define the neural network inputs in large hydrosystems and apply it to create models for 55 major hydro plants located in the Paraná Basin, which contribute to more than 30% of the total power generated in Brazil. The paper also compares the performance of the neural networks with the hydrological models that are currently used by the independent system operator to define the dispatch of the electric power generators. Our results show that, overall, the neural network models provide more accurate forecasts than the hydrological models used by the Brazilian System Operator. Finally, the paper discusses the contributions of historical rainfall information in the forecasting of streamflow while using neural network models.

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Availability of data and material

The data used in this research are publicly available on the internet.

Code availability

Available upon request.



Adaptive moment estimation


Artificial neural network




Autoregressive moving average


Central processing unit


Gradient descent


Gradient descent with momentum


Graphics processing unit


Independent system operator


Input variable selection


Mean absolute percentage error


Large-scale hydrological model


Multi-layer perceptron


Mean square error


Nash–Sutcliffe efficiency


Optimal weight initialization


Periodic autoregressive


Periodic autoregressive moving average


Rectified linear unit


Root-mean-square propagation


Soil moisture accounting procedure


Support vector machine


Visualizing ecosystem land management assessments


Weight initialization

\({\text{In}}\) :

Set of input candidates

\({\text{In}}_{{\text{S}}}^{*}\) :

Best set of streamflow inputs used in a specific ANN

\({\text{Is}}_{{t_{{\text{I}}} }}\) :

Input streamflow candidate (\(s_{{\text{I}}}\), \(t_{{\text{I}}}\))

\({\text{Ip}}_{{t_{{\text{I}}} }}^{{D_{{{\text{AR}}}} }}\) :

Input rainfall candidate accumulated through \(D_{{{\text{AR}}}}\) days (\(p_{{\text{I}}}\), \(t_{{\text{I}}}\)); \(D_{{{\text{AR}}}} = 1\): nonaccumulated rainfall

\({\text{Os}}_{{t_{{\text{o}}} }}\) :

Output streamflow (\(s_{{\text{O}}}\), \(t_{{\text{O}}}\))

\(p_{{\text{I}}} \in {\text{In}}\_ p\) :

Set of rainfall stations considered for input candidates

\(s_{{\text{I}}} \in {\text{In}}\_s\) :

Set of streamflow stations considered for input candidates

\(s_{{\text{O}}}\) :

Output streamflow station

\(t_{{\text{I}}}\) :

Number of days preceding the first day of forecast

\(t_{{\text{O}}}\) :

Day of forecast

\(C\) :

Component of the cost function that penalizes the difference between \(y^{\left( i \right)}\) and \(\hat{y}^{\left( i \right)}\)

\({\text{Cr}}\left( {A,B} \right)\) :

Function that computes the correlation coefficient between the variables \(A\) and \(B\)

\(E_{{{\text{dev}}}} \left( k \right)\) :

Error in the development set until the \(k{\text{th}}\) epoch simulation

\(J\) :

Cost function with \(\ell_{2}\) regularization

\(M2\) :

Cost function (28)

\(R2\) :

Cost function (29)

\(U\left( {a_{1} ,a_{2} } \right)\) :

Continuous uniform distribution in the interval [\(a_{1}\), \(a_{2}\)]

\(U_{{\text{D}}} \left( {a_{1} ,a_{2} } \right)\) :

Discrete uniform distribution in the interval [\(a_{1}\), \(a_{2}\)]

\({\text{Var}}\left[ {w^{\ell } } \right]\) :

Variance of the weights in the \(\ell {\text{th}}\) layer

\(w_{2}^{2}\) :

Square of the \(\ell_{2}\) norm of the weight matrixes

\(\sigma \left( x \right)\) :

Logistic sigmoid activation function

\(b\) :

Bias vector

\(C_{{\text{IS/OS}}}\) :

Lowest correlation coefficient between the streamflow input candidates and output streamflow

\(C_{{{\text{IR}}}}\) :

Maximum correlation coefficient for the input rainfall candidates

\(C_{{\text{IR/OS}}}\) :

Lowest correlation coefficient between the rainfall input candidates and output streamflow

\(C_{{{\text{IS}}}}\) :

Maximum correlation coefficient for the input streamflow candidates

\(db\) :

Gradients of the bias vector

\(dw\) :

Gradients of the weights

\(D_{{{\text{AR}}}}\) :

Number of days lag that rainfall is accumulated

\(D_{{{\text{IS}}}}\) :

Number of days lag of input streamflow investigated

\(D_{{{\text{OS}}}}\) :

Number of days of output streamflow

\(D_{{{\text{IR}}}}\) :

Number of days lag of input rainfall investigated

\(\overline{{{\text{Epoch}}}}\) :

Maximum number of epochs

\(k_{{{\text{prob}}}}\) :

Regularization hyperparameter in dropout

\(m\) :

Number of output variables

\(n\) :

Number of output examples

\(n_{\ell }\) :

Number of neurons in the \(\ell {\text{th}}\) layer

\(N_{{{\text{Hyp}}}}\) :

Number of times that different hyperparameters are tested

\(N_{{{\text{RC}}}}\) :

Number of times that different \(C_{{\text{IR/OS}}}\) and \(C_{{{\text{IR}}}}\) correlation coefficients are tested

\(N_{{{\text{SC}}}}\) :

Number of times that different \(C_{{\text{IS/OS}}}\) and \(C_{{{\text{IS}}}}\) correlation coefficients are tested

\(w\) :


\(\overline{{y^{\left( i \right)} }}\) :

Average streamflow for the \(i{\text{th}}\) example

\(y^{{\left( {i, t} \right)}}\) :

Estimate for the \(t{\text{th}}\) output variable (day of forecast) in the \(i{\text{th}}\) example

\(\hat{y}^{{\left( {i,t} \right)}}\) :

Expected value for the \(t{\text{th}}\) output variable (day of forecast) in the \(i{\text{th}}\) example

\(\alpha\) :

Learning rate variable

\(\lambda\) :

\(\ell_{2}\) Regularization hyperparameter

\(\mu_{0}\) :

Mean of the output variables \(\hat{y}\)

\(\sigma_{0}\) :

Standard deviation of the output variables \(\hat{y}\)


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The authors would like to express their gratitude to AES Tietê for the financial support of the ANEEL Strategic R&D Project 0064-1052/2017. The authors also would like to thank Eduardo H.S. Silva, Lívia M.P. Gazzi, Eliude P. Ferro, and Lanai Torres for technical discussions during the course of this project.


This research was funded by AES Tietê Brazil under the ANEEL Strategic R&D Project 0064-1052/2017.

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All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by VF and AdQ. The first draft of the manuscript was written by VF, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to V. A. D. de Faria.

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Editorial responsibility: Maryam Shabani.

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de Faria, V.A.D., de Queiroz, A.R., Lima, L.M. et al. An assessment of multi-layer perceptron networks for streamflow forecasting in large-scale interconnected hydrosystems. Int. J. Environ. Sci. Technol. 19, 5819–5838 (2022).

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