## 1 Introduction  
Networks have many applications like detection [1; 2], recognition [3; 4], classification [5; 6], and prediction [7; 8]. Steepest descent is a supervised algorithm that is frequently used for neural network tuning, wherein the value of the scale parameters is adjusted according to the cost map. Steepest descent evaluates the first-order partial derivatives of the cost map with respect to the scale parameters in the neural network.  
Mini-batches are commonly used to get better tuning of the steepest descent in a neural network; the training data are divided in mini-batches, and the training of the steepest descent is applied to all the mini-batches taking into account one tuning of the scale parameters for each mini-batch. One tuning of all the mini-batches is one epoch.  
There are several applications for mini-batches. In [9; 10; 11; 12], mini-batches were employed for tuning. In [13; 14], mini-batches were used for clustering. In [15; 16], mini-batches were utilized for optimization. Since mini-batches have been used in several applications, they could be a good alternative to get better tuning using steepest descent.  
Steepest descent with mini-batches is used during tuning with a search for each mini-batch. Nevertheless, steepest descent with mini-batches could be delayed in reaching a minimum. The Hessian has been used as an alternative for neural network tuning, wherein the Hessian evaluates the second-order partial derivatives of the cost map with respect to the scale parameters.  
The Hessian has the same form as the steepest descent. However, steepest descent takes into account constant values in its tuning rate and momentum, while the Hessian takes into account the second-order partial derivatives of the cost map with respect to the scale parameters in its tuning rate and momentum. This is the main reason why the steepest descent method may be delayed in reaching a minimum, while the Hessian could be quicker in reaching a minimum, and it is easier to reach this minimum by using the Hessian with mini-batches.  
There have been several applications of the Hessian. In [17; 18; 19; 20], the Hessian was used for tuning. In [21; 22; 23; 24], the Hessian was employed for segmentation. In [25; 26; 27; 28], the Hessian was utilized for optimization. In [29; 30; 31; 32], the Hessian was used for pattern recognition. In [33; 34], the Hessian was utilized for modeling. In [35; 36], the Hessian was employed for identification. In [37; 38], the Hessian was used for control. Since the Hessian has been used in several applications, it could be a good alternative for neural network tuning.  
In this article, the Hessian is combined with mini-batches for neural network tuning. The full training data are divided in mini-batches, and we take into account each mini-batch to get better tuning of the Hessian in a neural network. One tuning of the mini-batches is known as one epoch.  
Finally, we compare the tuning of the neural network using steepest descent, steepest descent with mini-batches, the Hessian, and the Hessian with mini-batches for electrical demand prediction, based on data provided by the International Organization for Standardization (ISO) of Great Britain.  
The remainder of this article is organized as follows: Section 2 presents neural network tuning via the Hessian. Better tuning of the Hessian using mini-batches is explained in Section 3. Section 4 shows the comparison results of steepest descent, steepest descent with mini-batches, Hessian, and Hessian with mini-batches for electrical demand prediction. Conclusions and future work are presented in Section 5.