## 1 Introduction
That study concluded that the developed probabilistic framework can be applied to the hydraulic conductivity of seepage analysis. [PERSON] et al. [25] conducted the stochastic analysis of unsaturated seepage in embankment. They used the advantages of both FEM and Monte Carlo simulation techniques to solve the seepage-related problem through a flood defense embankment with random heterogeneous material properties. In another similar study, [PERSON] et al. [26] presented the probabilistic evaluation of the effects of uncertainty on transient seepage. Considering the actual physical characteristics of the phenomenon, physics-based and conceptual models are reliable tools, although they have some practical restrictions. Remember that the black box models can be more appreciated when perfect estimates are more significant than physical considerations. Auto Regressive Integrated Moving Average (ARIMA) is a standard black box model that can be used to make an aqua-related time series [27]. These models are linear, hence losing their effectiveness in modeling hydraulic processes that are implanted with high levels of complexity, vitality, and nonlinearity in both spatial and temporal scales. Recently, artificial intelligence (AI)methods have been commonly applied to hydraulic procedures as well as other applications in civil engineering [28; 29; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62; 63]. AI models such as Feed Forward Neural Network (FFNN), Support Vector Regression (SVR), and Adaptive Neural Fuzzy Inference System (ANFIS) are reasonably new black box approaches which are applicable to different features of hydraulic engineering [64; 65; 66; 67]). To construct a model of dam seepage, [PERSON] [68] implemented artificial neural networks (ANNs). They used this method in Poland to predict the piezometric heads on an earth fill dam. Their input data was related to the upstream head and downstream water surface levels to predict the obtained results of FEM. In the case of spatial-temporal modeling of the water level in embankments, an ANN model was proposed by [PERSON] and [PERSON] [69]. They performed ANN modeling to simulate the piezometric water level of an earthen dam. In sole ANN modeling, a single ANN was carried out for each piezometer, whereas in the integrated ANN modeling, a unique ANN was applied to all piezometers at different dam sections. The authors in [70] applied and discussed the Neuro-fuzzy and SVR (based on the Support Vector Machine (SVM)) models as other forms of artificial intelligence approaches. In [71], ANN and fuzzy theories were used in designing an exclusive framework to calculate the water head in piezometers of the Iron Gate 2 dam regarding the tail water levels as input data and the water levels in the piezometers. Lastly, the researchers in [72] employed an SVR model to analyze seepage and dam piping. The use of such black box models (e.g., ARIMA, ANN, ANFIS, and SVR) resulted in reasonable outcomes, although it was also revealed that using different models to solve one definite problem may lead to slightly different consequences. For instance, in a time series prediction, one model may relevantly simulate the maximum assessments, whereas the other may denote well the minimum values. Therefore, as a post-processing method, by linking different models through a collective modeling framework, different aspects of the underlying arrangements may be captured more perfectly. The theory of such a model combination has been already argued and applied to various engineering contexts [73; 74; 75]. Furthermore, a number of significant studies have been carried out with objectives similar to those of the present paper. ANN-based techniques have been found capable of solving engineering problems; however, they suffer from certain limitations, including low learning speed and incapability of escaping from local minima [76; 77].