esa-sceva/satcom-chunk-collection huggingface dataset:
# Linear System Identification and Vibration Control of End-Effector for Industrial Robots
## 3 Linear System Identification  
### Theoretical Design of Linear System Identification  
Basing on the state space model of the system, the discrete state space model of linear time invariant system is assumed to be as follows,  
\[x_{k+1}=Ax_{k}+Bu_{k}+w_{k} \tag{1}\]  
\[y_{k}=Cx_{k}+Du_{k}+v_{k} \tag{2}\]  
where:  
\(x_{k}\)--the n-dimensional state vector of the system  
\(y_{k}\)--the L-dimensional output observation vector  
\(u_{k}\)--the m-dimensional input observation vector, \(A\in R^{n\times m},\ C\in R^{n\times l},\ D\in R^{l\times m}\)  
\(\omega_{k}\)--the n-dimensional input noise vector  
\(v_{k}\)--the L-dimensional measurement noise vector.  
\([u(k),y(k)]\)--the input-output sequence of SISO object at time k  
The parameter vector is defined as  
\[\theta=\left[vec(A)^{T},vec(B,G)^{T},vec(C)^{T},vec(D)^{T}\right]^{T}\in R^{d} \tag{3}\]  
The vector length \(d=n^{2}+n(m+l)+lm\) is the total number of system parameters. \(vec(A)\) is the straightening operation. The identification of system state space can be expressed as the estimate of the parameter matrix \(A\), \(B\), \(C\), \(D\) by giving the input-output observation sequence \((U_{N},Y_{N})\), so as to minimize the value of the objective function as  
\[J_{N}(\theta)=\sum_{k=1}^{n}\left\|y_{k}-\overset{\wedge}{y}_{k\
eq k-1}(\theta )\right\|_{2}^{2}=\sum_{k=1}^{n}\left\|e_{k}(\theta)\right\|_{2}^{2} \tag{4}\]  
Basing on subspace identification method, the extended objective matrix of structure is proposed as  
\[\Gamma_{a}=\left[C\ CA\ \cdots\ CA^{a-1}\right]^{T} \tag{5}\]  
Hankel matrix of impulse response  
\[H_{t,a,b}=\left[\begin{array}{cccc}h_{t}&h_{t+1}&L&h_{t+b-1}\\ h_{t+1}&h_{t+2}&L&h_{t+b}\\ M&M&M&M\\ h_{t+a-1}&h_{t+a}&L&h_{t+a+b-2}\end{array}\right] \tag{6}\]  
According to the corresponding time, the Hankel matrix is \(U_{p}=U_{1,s,T}\) in the past which at present is \(U_{c}=U_{s,1,T}\) and \(U_{f}=U_{s+1,s,T}\) in the future. Hankel matrices defining the future measurement noise and input noise are denoted as \(M_{f}\), \(N_{f}\). The state sequence of a system is defined as  
\[X_{s}=\left[\begin{array}{cccc}x_{s+1}&x_{s+2}&\cdots&x_{s+T}\end{array}\right] \tag{7}\]  
Basing on the input-output matrix equation of the system \(Y_{f}=\Gamma_{s}X_{s}+\Phi_{s}U_{f}+\Phi_{s}{}^{w}M_{f}+N_{f}\). Removing \(M_{f},N_{f}\) and Hankel matrices \(U_{f}\) by projection method gets \(O_{s}=\Gamma_{s}X_{s}\).  
Basing on the estimated state sequence \(X_{s}\) and extended observability matrix \(\Gamma_{s}\). The parameter matrix \(A\), \(B\), \(C\), \(D\) of the system state space model can be obtained by solving the equations with the least square method of N4 SID regression.  
\[\left[\begin{array}{cc}\begin{array}{cc}\wedge&\wedge\\ A&B\\ \wedge&\wedge\\ C&D\end{array}\end{array}\right]=\underset{A,B,C,D}{\text{argmin}}\left[ \begin{array}{cc}X_{s+1}\\ Y_{c}\end{array}\right]-\left[\begin{array}{cc}A&B\\ C&D\end{array}\right]\left[\begin{array}{cc}X_{s}\\ U_{c}\end{array}\right]_{F}^{2} \tag{8}\]
## 3 Results and Discussion
### Effects of Infill Patterns on SR
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Point**} & \multicolumn{4}{c}{**Grid Pattern**} & \multicolumn{4}{c}{**Zigzag Pattern**} \\ \cline{2-9}  & **Part** & \(\text{R}_{\text{a}}\) (\(\upmu\)m) & **Part** & \(\text{R}_{\text{a}}\) (\(\upmu\)m) & **Part** & \(\text{R}_{\text{a}}\) (\(\upmu\)m) & **Part** & \(\text{R}_{\text{a}}\) (\(\upmu\)m) \\ \hline
1 & & 2.37 & & 2.54 & & 6.78 & & 2.78 \\
2 & & 2.17 & & 2.77 & & 5.6 & & 3.3 \\
3 & CAD & 2.45 & FDM & 2.93 & & 6.11 & FDM & 3.4 \\
4 & 30\% & 3.49 & 30\% & 3.14 & CAD & 5.63 & 30\% & 2.93 \\
5 & 30\% & 3.1 & & 2.89 & 30\% & 7.3 & & 2.27 \\ Average & & 2.72 & & 2.85 & & 6.28 & & 2.94 \\ Standard & & 0.56 & & 0.22 & & 0.74 & & 0.45 \\ deviation & & 2.52 & & 3.07 & & 4.83 & & 3.73 \\
2 & & 2.19 & & 3.57 & & 4.88 & & 3.81 \\
3 & & 2.25 & FDM & 2.42 & & 4.5 & FDM & 2.94 \\
4 & & 2.78 & 60\% & 2.02 & CAD & 4.7 & 50\% & 3.47 \\
5 & & 2.54 & & 2.3 & & 4.3 & & 3.26 \\ Average & & 2.45 & & 2.67 & & 4.64 & & 3.45 \\ Standard & & 0.24 & & 0.63 & & 0.24 & & 0.36 \\ deviation & & & & & & & \\ \hline \hline \multicolumn{9}{c}{**Trangle pattern**} \\ \hline
1 & & 2.12 & & 3.11 & & 3.47 & & 3.12 \\
2 & & 2.86 & & 3.33 & & 2.64 & & 3.7 \\
3 & CAD & 2.4 & FDM & 3.25 & & 3.78 & FDM & 4.17 \\
4 & 20\% & 2.78 & 20\% & 3.61 & CAD & 3.4 & 10\% & 4.96 \\
5 & 2.62 & & 3.17 & 10\% & 2.77 & & 3.81 \\ Average & & 2.55 & & 3.29 & & 3.21 & & 3.95 \\ Standard & & 0.30 & & 0.20 & & 0.49 & & 0.68 \\ deviation & & & & & & & \\ \hline
1 & & 1.97 & & 3.08 & & 2.83 & & 3.11 \\
2 & & 2.23 & & 3.89 & & 3.03 & & 3.85 \\
3 & CAD & 2.38 & FDM & 2.74 & & 3.13 & FDM & 4.41 \\
4 & 30\% & 2.56 & 30\% & 3.47 & 40\% & 2.87 & 40\% & 3.9 \\
5 & 2.77 & & 2.22 & & 3.04 & & 2.82 \\ Average & & 2.38 & & 3.08 & & 2.98 & & 3.62 \\ Standard & & & 0.31 & & 0.64 & & 0.13 & & 0.64 \\ deviation & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The average SR of printed samples.
# Feasibility of LoRa for Smart Home Indoor Localization
## 2 Literature Review
### Radio Frequency Identification Device (RFID)
The active tags contain a radio transceiver and a button-cell battery used to power the transceiver. Thus, the active RFID has a broader reception range and costs more than passive RFID. The SpotON system [6] is the first localization system based on active RFID technology. This system integrates the RSSI technology, the aggregation algorithm, and the payload distribution measurement to calculate the indoor location. However, the SpotON system is limited by small applicable range (less than 16 m\({}^{2}\)) and high energy consumption of tags (2 AA batteries in 30 h). Another well-known indoor localization sensing system based on the active RFID is the LANDMARC system [52]. The researchers for the system have developed an algorithm to estimate the relations between physical distance, power levels, and signal strengths. Yet, the accuracy of LANDMARC system highly depends on the density of reference tags. To reaching one-meter average error, installation of four readers and one reference tag per square meter is needed. Many methods [53] were developed based on the LANDMARC system. For example, [PERSON] et al. [40] used a backtracking algorithm to identify reference tags for the LANDMARC to reduce the requirements of the density of tags and improve localization accuracy. Some studies adopted the active RFID system for smart home applications. [PERSON] et al. [54] proposed an indoor positioning system to track users' movement and direction in a smart home environment. The active RFID tags are assigned in the positioning area, and an RFID antenna is attached to the user. This study analyzed the active tags' overlapping sensing areas to better match the signal strength and various areas. When a user roves in an area, the user moves toward or away from the tags inevitably changing the received signal strengths. Though this study could calculate the moving direction based on the relative signal strength of the active tags, this approach may not be a solid solution for smart home applications because of an unrealistic assumption of perfectly circular shapes of the sensing areas. Furthermore, this study did not address the movements or obstacles that cause RSSI fluctuation and lower accuracy.
## 8 Security and Privacy Risk Assessment
### Security and Privacy Risk Assessment at the Requirements Analysis Phase  
The objective of conducting a security and privacy risk assessment at the requirement analysis phase is to identify the risks, evaluate the identified risks, apply risk treatment to identify the risks which will require controls to mitigate and develop the security and privacy requirements. The initial product requirements and risk assessment approach will be taken as an input to conduct the security and privacy risk assessment at this phase. Figure 6 illustrates the steps to conduct a risk assessment at the requirements analysis phase.  
Below is the list of key tasks to be conducted during the risk assessment at the requirements analysis phase:  
* Apply risk analysis to identify the risk.
* Evaluate each risk to identify the acceptable and unacceptable risks.
* Update list of security and privacy requirements for unacceptable risk.
# Sentiment Interaction Distillation Network for Image Sentiment Analysis
## 4 Experiment
### Implementation Details  
Following [7], we selected the VGG16 [32] as the backbone and initialized it with the parameters pretrained on the ImageNet. Specifically, the input images were randomly cropped and resized into 224 \(\times\) 224. During the training period, the images were also flipped random horizontal for data enhancement. We chose SGD as the optimizer on the FI dataset and set the momentum to 0.9. The initial learning rate was set to 0.01, which is 0.1 times per 20 epochs.  
We employed two stacked GCN layers in the sentiment interaction branch whose dimensions of output are 1024 and 2048. We expressed the features of each input node in the graph using a 512-dimensional vector. To extract object features, we applied the panoptic segmentation model (Resnet-101 with FPN) [37] pretrained by Detectron2 to detect object boundary and category. The confidence score threshold of detection was set to 0.6. Given the boundaries of output, we applied intensity and GLCM to obtain features from the corresponding regions. Specifically, we quantized the brightness to 0-255 and obtained a 256-dimensional intensity distribution chart. Then, we computed GLCM at 45\({}^{\circ}\), which was reshaped to 256. Finally, we concatenated the intensity features and texture features, which result an object feature of \(1\times 512\).  
Referring to previous work [7], we applied the same split and test strategy for these datasets without specific division. Specifically, the multilabel datasets, FI and EmotionROI, need to be divided into positive and negative to execute the sentiment polarity classification. The EmotionROI dataset has six emotion categories: joy, surprise, anger, disgust, fear, and sadness. We relabel the joy and surprise as positive and relabel the anger, disgust, fear, and sadness as negative. In FI dataset, eight emotion categories are divided into binary labels based on [PERSON]'s emotion wheel model [38]--amusement, awe, contentment, and excitement are labeled as positive, and anger, disgust, fear, and sadness are labeled as negative. For small-scale datasets, including EmotionROI, Twitter I, and Twitter II, we referred to the commonly used strategy in sentiment analysis [7; 8; 34] and set the initial weights with the model parameters trained on FI, then fine-tuned the model on small datasets.  
For the trade-off parameter in the loss function, we set \(\lambda\) to 0.1, which is tuned on the FI validation set.
# A Novel Chimp Optimization Algorithm with Refraction Learning and Its Engineering Applications
## 5 Experimental Results
### Experiments on 23 Widely Used Test Functions  
As shown in Table 2, in the unimodal benchmark test functions (\(F1\)-\(F7\)): the overall performance of the proposed algorithm RL-ChOA is better than other algorithms on the unimodal benchmark problem. RL-ChOA can perform best compared to other algorithms except for three benchmark test functions (\(F5\)-\(F7\)) and find the optimal value in four benchmark test functions (\(F1\)-\(F4\)). The SMIGWO achieves the best performance on two benchmark test functions (\(F5\) and \(F6\)). The WChOA obtains the best solution on the one benchmark test function (\(F7\)). In addition, KEEL software [74] was used for the Friedman rank, and the results are shown in Table 6 RL-ChOA achieved the best place.  
As can be observed from Table 3, in the multi-modal benchmark test functions (\(F8\)-\(F13\)): RL-ChOA can obtain the best solution on the four benchmark test functions (\(F8\)-\(F11\)). SPTLBO can obtain the best solution on the one benchmark test function (\(F12\)). WChOA can get the best solution on the three benchmark test functions (\(F9\), \(F11\), and \(F12\)). SPTLBO can obtain the best solution on the one benchmark test function (\(F13\)). RL-ChOA outperforms other algorithms overall, and in Table 7, RL-ChOA ranks first in the Friedman rank.  
As can be observed from Table 4, in the fixed-dimension multi-modal benchmark functions (\(F14\)-\(F23\)): SPTLBO can get the best solution on the six benchmark test functions (\(F14\)-\(F19\)). MGWO can get the best solution on the four benchmark test functions (\(F16\)-\(F19\) and \(F23\)). SMIGWO can obtain the best solution on the five benchmark test function (\(F16\), \(F17\), \(F19\), \(F21\), and \(F22\)); RL-ChOA cannot perform well on these test functions, but RL-ChOA outperforms both original ChOA and WChOA in overall performance. As shown in Table 5, RL-ChOA ranks third in the Friedman rank.  
[PERSON]'s rank-sum test was used to verify the significant difference between RL-ChOA and the other five algorithms. The statistical results are shown in Table 8. The results prove that \(\alpha\) = 0.05, a significant difference can be observed in all cases, and RL-ChOA outperforms 12, 11, 7, 15, and 19 benchmark functions of SMIGWO, MGWO, SPTLBO, ChOA, and WChOA, respectively.
## 4 Results and Discussion
\begin{table}
\begin{tabular}{l l c c c c} \hline \hline
**Method** & **Source** & **Accuracy \%** & **Recall \%** & **Precision \%** & **F1-Measure \%** \\ \hline LR & [PERSON] et al. [23] & 83.3 & 86.3 & - & - \\ KNN & [PERSON] et al. [23] & 84.8 & 85 & - & - \\ SVM & [PERSON] et al. [23] & 83.2 & 78.2 & - & - \\ RF & [PERSON] et al. [23] & 80.3 & 78.2 & - & - \\ DT & [PERSON] et al. [23] & 82.3 & 78.5 & - & - \\ DL & [PERSON] et al. [23] & 94.2 & 82.3 & - & - \\ ML & [PERSON] et al. [24] & 70 & 73 & 72 & 79 \\ DNN & Miao and Miao [25] & 83.67 & 93.51 & 79.12 & 85.71 \\ GDO & [PERSON] et al. [26] & 97.07 & 97.15 & - & - \\ GA & Eisa and Alnaggar [27] & 64 & 66 & 65 & 70 \\ Swarm-ANN & [PERSON] et al. [28] & 95.78 & 95.21 & 95.21 & 95.21 \\ Fuzzy Expert System & Kasbe and Pippals [29] & 94.5 & - & - & - \\ MANAGE-HF & [PERSON] et al. [30] & 56 & 60 & 58 & 63 \\ BSN & Shakya and Joby [31] & 82 & 85 & 84 & 88 \\ MSABA & [PERSON] et al. [32] & 90 & 91 & 92 & 95 \\ GBDT & Current paper & 83 & 81 & 79 & 79.99 \\ SS-GBDT & Current paper & 95 & 96.8 & 95.8 & 96.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of SS-GBDT with the state-of-the-art. As shown in Figure 4, where the current SS-GBDT has a precision of 95.8%, the swarm optimized artificial neural networks [28] has marginally less precision (95.21%). However, the precision of SS-GBDT is about 38% better than MANAGE-HF [30] and 31% better than GA [27]. With respect to the ML framework [24] and DNN [25], the present precision is 24% and 17% better, respectively. Figure 4: Comparison of precision of the proposed SS-GBDT and the state-of-the-art, compared with ML [24], DNN [25], GA [27], Swarm-ANN [28], MANAGE-HF [30], BSN [31] and MSABA [32]. Figure 3: Comparison of accuracy of the proposed SS-GBDT and the state of the art, compared with LR [23], KNN [23], SVM [23], RF [23], DT [23], DL [23], ML [24], DNN [25], GDO [26], GA [27], Swarm-ANN [28], Fuzzy Expert System [29], MANAGE-HF [30], BSN [31] and MSABA [32]. The new methodology has a higher level of recall when compared to other methods; this can be seen in Figure 5, where the MANAGE-HF [30], GA [27], ML [24], BSNs [31], MSABA [32] and Swarm-ANN [28] have 36.8%, 30.8%, 23.8%, 11.8%, 5.8% and 1.6% lesser recall than the current SS-GBDT. The comparison of the F1-measure for various states of the art and the SS-GBDT is shown in Figure 6. In terms of the F1-measure, the present SS-GBDT is found to be about 33%, 26%, 17%, 8%, 1.3% and 1.1% superior to MANAGE-HF [30], GA [27], ML [24], BSNs [31], MSABA [32] and Swarm-ANN [28], respectively. Figure 5: Comparison of recall of the proposed SS-GBDT and the state of the art, compared with LR [23], KNN [23], SVM [23], RF [23], DT [23], DL [23], ML [24], DNN [25], GDO [26], GA [27], Swarm-ANN [28], MANAGE-HF [30], BSN [31] and MSABA [32]. Figure 6: Comparison of the F1-measure of the proposed SS-GBDT and the state of the art, compared with ML [24], DNN [25], GA [27], Swarm-ANN [28], MANAGE-HF [30], BSN [31] and MSABA [32].
# Code Obfuscation: A Comprehensive Approach to Detection, Classification, and Ethical Challenges
## 2 Challenges and Drawbacks of Code Obfuscation
### Knowledge Gaps and Research Question  
The literature provides substantial insights into techniques, metrics, quality measurement [11; 12; 13], and detection methods for code obfuscation. While previous studiesprimarily emphasize the theoretical foundations and metrics for evaluating obfuscation quality, this work adopts a practical perspective, integrating advanced detection models, real-world use cases, and ethical considerations into this analysis. Four critical gaps in the existing research are identified: 1. adaptive obfuscation detection models that can generalize effectively across different obfuscators; 2. practical methods for detecting and classifying code obfuscation; 3. actionable ethical guidelines for the use of obfuscation; and 4. countermeasures against the detection and classification of obfuscated code. This paper aims to address the research question, \"How can we effectively and ethically detect and classify code obfuscation techniques using machine learning models?\"
# Two Scenario-Based Heuristics for Stochastic Shift Design Problem with Task-Based Demand
## 4 Numerical Results
### The Effect of the Task Coverage \(\eta\) on the Performances of OSH and TSH  
The effect of the task coverage \(\eta\) on the performances of OSH and TSH is tested in this subsection. Fix the parameters \(\alpha=1\), \(\gamma=0.5\), \(\delta=3\), \(|\Omega|=5000\), \(\epsilon=0.0001\), \(\mathrm{N}=8000\), \(\mathrm{M}=8000\) and vary the value of \(\eta\) with \(\eta=0,\ 0.05,\ 0.1,\ \dots,\ 0.95,\ 1\). Carry out 20 times each experiment and calculate the average of these experiments result. In addition, regenerate the scenario set before starting each experiment.  
Figure 9 shows that as the task coverage \(\eta\) increases, the expected cost of the solutions found by both methods under their respective better parameters increases, which is the cost of additional resources to overcome the bad scenario. And when requiring a task coverage \(\eta\) of 1, the expected cost of shift plans found by both methods increases dramatically, due to the diminishing marginal benefit effect. Among them, the solutions found by TSH are always cost-advantageous, and the advantage is more pronounced the higher the task coverage \(\eta\) is. This is because OSH finds the feasible solution by relaxing the resource occupancy time of all tasks simultaneously, while TSH updates the feasible solution by iterating, which makes the cost of the shift plan found by TSH lower than that of OSH.  
Figure 8: The impact of scenario number M on the stability of the expected metrics of shift plan.  
Figure 9: The impact of the task coverage \(\eta\) on the performances of OSH and TSH.  
In addition, the running time of OSH increases with the task coverage \(\eta\), while the running time of TSH remains relatively stable. This is because increasing the task coverage \(\eta\) increases the non-zero term in the M3 model used by OSH, which increases the running time of OSH, whereas TSH always first finds a shift plan with task coverage close to 1 before using dichotomization to find a shift plan that satisfies the task coverage \(\eta\) and performs well in terms of cost in the updating process. Besides, when the required task coverage \(\eta\) is 1, the running time of both methods drops dramatically. This is because the task coverage of the solutions found by both methods can only be close to 1. Both methods use backtracking to find a solution that satisfies the constraint (A9), so both algorithms terminate as soon as the initial backtracked solution does not satisfy the constraint (A9), which is why the running time is so short at this time.
## 4 Implementation and Performance Evaluation
### Performance Criterion  
The overall performance of the proposed approach was comprehensively assessed by using two deterministic performance metrics, i.e., RMSE and mean absolute error, and a heatmap representation of the correlation between the training and testing datasets was created as shown in Figure 7.  
\[\text{RMSE}=\sqrt{\frac{1}{N}\overline{\sum_{i=0}^{n}(R-P_{j})^{2}}} \tag{37}\]  
\[\text{MAE}=\frac{1}{N}\overline{\sum_{i=1}^{n}\left|R_{j}-P_{j}\right|} \tag{38}\]  
\[K=\frac{\sum\limits{(x-x)(y-y)}}{\sqrt{(x-x)^{2}\Sigma(y-y)^{2}}} \tag{39}\]
# A Study on the Electromagnetic-Temperature Coupled Analysis Method for In-Wheel Motors
## 3 Analysis of Coupling Factors  
To analyze the coupling of the electromagnetic and temperature field of an IWM more accurately, the coupling factors of electromagnetic and temperature characteristics were analyzed first, and the coupling relationship between the two fields was further clarified.
## Materials and Methods
### Plant Material and Extraction Procedures  
Fresh _C. longa_ rhizomes were purchased from a local market and authenticated by comparison with a voucher specimen (No. 224169) deposited at the INPA Herbarium (Herbarium of the National Institute of Amazonian Research, Manaus, AM, Brazil). The rhizomes (35 g) were crushed and subjected to sequential solid-liquid extraction using solvents of increasing polarity. Initially, the material was macerated in hexane (1 \(\times\) 90 mL) under agitation and protected from light. After 5 days, the solvent was replaced, and the extraction continued. The resulting liquid phase was evaporated under reduced pressure to obtain the hexane extract (HEXCURC). The solid plant residue remaining after hexane extraction was then sequentially extracted using dichloromethane (3 \(\times\) 90 mL), followed by ethanol (3 \(\times\) 90 mL), under the same conditions. The combined liquid phases from each solvent were evaporated under reduced pressure, yielding the dichloromethane extract (DCCURC) and the ethanol extract (ETOHCURC), respectively. The extraction yields were calculated as the ratio between the dry extract mass and the initial plant mass (% w/w), resulting in 0.6% for HEXCURC, 2.8% for DCCURC, and 3.9% for ETOHCURC.
# PSDFH: A Phase-Space-Based Depth from Hologram Extraction Method
## 4 Experimental Results
### Holographic Dataset  
For training the \(\mathcal{G}\) network, a large-scale dataset consisting of 4200 RGB holograms was obtained from three different scenes (piano, table, wood). The holograms were acquired using a layer-based method [16] with a resolution of \(1024\times 1024\), a pixel pitch of \(1\)\(\upmu\)m, and 1400 acquisition angles. The evaluation phase was performed on two sets: a test set consisting of 300 holograms evenly distributed over the training classes and a validation set consisting of 200 holograms from two additional scenes (cars, dice). Table 1 summarizes the depth in centimeters of each object that makes up each scene.  
For each hologram of the dataset, its 4D phase space representation \(L\) of size of \(N\times N\times M\times M\) and the associated phase space masks \(M_{b}\) of size \(N\times N\times M\times M\) are computed using 3D formulas proposed in [14]. Then, the two tensors \(L\) and \(M\) are reorganized as a 3D tensor of size \((N\times N)\times M\times M\) and used as the initial batch for the network training. Finally, for each iteration, a sub-sample of size 1024 is randomly sampled from the initial batch to constitute the final network input/output data.  
The network was trained for a total of 100 epochs, using the stochastic gradient descent and an exponential learning rate decay.