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Heidarnejad, et al.

taking into account computational efficiency. It is resilient models, and offering a judicious balance in
plausible to assess diverse transfer functions to identify computational expense. 49
the most appropriate one. An ANN may encompass To simulate and model a problem using the MARS
one or more hidden layers. After finalizing the MLP algorithm, the first step is to define the objective of
structure (including the number of hidden layers and the modeling process, whether it involves predicting
the number of neurons within each hidden layer), the a continuous variable (regression) or classifying data.
determination of weights and biases ensues, a phase Once the problem is clearly understood, a relevant
referred to as model training. 46 dataset is collected and preprocessed by handling
The process of the MLP model design entails a sequence missing values, removing outliers if necessary, and
of strategic stages: normalizing or scaling the features to ensure consistent
(i) Evaluation of hidden layer count: The initial phase input data. After preparing the dataset, it is typically
involves assessing the optimal number of hidden divided into training and testing sets to allow for
layers in the network architecture subsequent performance evaluation. The MARS model
(ii) Determination of neuron quantity in each layer: The is then initialized by selecting key parameters, such as
second step entails deciding on the suitable number the maximum number of basis functions, the degree
of neurons within each hidden layer of interactions allowed between variables, and any
(iii) Specification of transfer functions: The penalties for model complexity to prevent overfitting.
identification of appropriate transfer functions for The training process begins by allowing the model to
neuron activations is pursued construct a set of piecewise linear basis functions, which
(iv) Selection of training algorithm: The selection adaptively split the data at optimal points (called knots).
of an effective training algorithm for network MARS adds these functions in a forward stepwise
optimization concludes the design process. manner to minimize residual error and capture non-
linear relationships and interactions between variables.
To achieve an optimal MLP model configuration, a After building a complex model in the forward phase,
systematic approach is adopted. Initially, a single hidden a backward pruning process is applied to eliminate
layer is proposed, where the neuronal count aligns with redundant or less important basis functions, resulting in
the quantity of input features. Subsequently, various a simpler and more generalizable model. Once training
transfer functions, such as log-sig, tan-sig, and pure- is complete, the model’s performance is evaluated using
line, are systematically assessed. Once an appropriate the testing dataset. Finally, the resulting MARS model
activation function is determined, the augmentation yields an interpretable set of rules or functions that
of predictive precision is pursued. This entails the describe the underlying patterns in the data, rendering it
progressive elevation of the count of hidden layers and useful for both predictions and understanding variable
neurons within these layers, thereby capturing intricacies relationships. 50
within the data and refining model performance through
an iterative refinement process. 47 2.4. Performance assessment criteria of MLMs
Several key metrics were used to assess the effectiveness
2.3.4. MARSs of the employed algorithms in ML prediction and
The inception of MARS, attributed to Friedman, has forecasting models. These metrics encompassed the R ,
48
2
permeated various branches of engineering, particularly the RMSE, the MAE, and the developed discrepancy
hydraulic engineering, demonstrating broad utilization. ratio (DDR), as detailed in Equations XII-XV. 51
MARS is an adaptable tool, facilitating the establishment
of relationships between independent and dependent 2 Σ N (O -O)(P -P)
i
i
variables within a targeted system. By leveraging the R= i=1 (XII)
N
MARS method, latent patterns within complex datasets Σ i=1 (O -O) 2 Σ N (P-P) 2
i
i
i=1
are discerned, unveiling hidden insights in intricate
designs. The pattern recognition process involves the Σ N (O -P ) 2
proposal of a range of coefficients and basis functions, RMSE= i=1 i i (XIII)
validated through regression operations performed on N
the relevant dataset. A key strength of the MARS lies Σ N
in its aptitude for effectively mapping input parameters MAE= i=1 (O -P ) (XIV)
i
i
to desired outputs, constructing uncomplicated yet N

Volume 22 Issue 6 (2025) 80 doi: 10.36922/AJWEP025120081