Modeling Carbon Release of Brazilian Highest Economic Pole and Major Urban Emitter: Comparing Classical Methods and Artificial Neural Networks
Abstract
:1. Introduction
1.1. Global Carbon Emissions and Economic Indicators
1.2. Literature Review
1.3. Purpose of the Study
2. Materials and Methods
3. Results and Discussion
3.1. Descriptive Analysis and Multivariate Linear Regression Models
3.2. Elastic-Net Regression Method
3.3. Multilayer Perceptron Neural Network
3.4. Comparative Analysis
4. Conclusions and Policy Implications
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
Number of Non-Zero Coefficients | R2 | Number of Non-Zero Coefficients | R2 |
---|---|---|---|
4 | 0.9234 | 4 | 0.9157 |
4 | 0.9233 | 4 | 0.9144 |
4 | 0.9233 | 4 | 0.9129 |
4 | 0.9233 | 4 | 0.911 |
4 | 0.9233 | 4 | 0.9089 |
4 | 0.9233 | 4 | 0.9063 |
4 | 0.9233 | 4 | 0.9033 |
4 | 0.9233 | 4 | 0.8997 |
4 | 0.9232 | 4 | 0.8954 |
4 | 0.9232 | 4 | 0.8903 |
4 | 0.9232 | 4 | 0.8843 |
4 | 0.9231 | 4 | 0.8772 |
4 | 0.9231 | 4 | 0.8688 |
4 | 0.9231 | 4 | 0.8588 |
4 | 0.923 | 4 | 0.8471 |
4 | 0.9229 | 4 | 0.8333 |
4 | 0.9229 | 4 | 0.817 |
4 | 0.9228 | 4 | 0.798 |
4 | 0.9227 | 4 | 0.7757 |
4 | 0.9226 | 4 | 0.7496 |
4 | 0.9224 | 4 | 0.7193 |
4 | 0.9223 | 3 | 0.6868 |
4 | 0.9221 | 3 | 0.6504 |
4 | 0.9219 | 3 | 0.6087 |
4 | 0.9217 | 3 | 0.5612 |
4 | 0.9214 | 3 | 0.5071 |
4 | 0.9211 | 3 | 0.4457 |
4 | 0.9207 | 3 | 0.3765 |
4 | 0.9203 | 2 | 0.3064 |
4 | 0.9198 | 2 | 0.2516 |
4 | 0.9192 | 1 | 0.1916 |
4 | 0.9185 | 1 | 0.1322 |
4 | 0.9177 | 1 | 0.0682 |
4 | 0.9168 | 0 | 0 |
Coefficients | |
---|---|
Intercept | 88,219,707 |
GDP | 36,946,643 |
GDP2 | 4,234,893 |
EN | 508,937.2 |
EN2 | 19,410,830 |
Bias 1 | Weights | |
---|---|---|
−2.8754 | 4.7578 | 1.2974 |
2.2133 | −1.5901 | 3.3818 |
−1.3108 | 0.111 | −3.3552 |
0.6798 | 4.5322 | −3.643 |
−3.2999 | −3.8249 | −0.9763 |
2.5992 | 3.9668 | −1.2442 |
Bias 2 | Weights 2 | |||||
---|---|---|---|---|---|---|
0.3126 | 1.3675 | −1.2193 | −0.2508 | −1.1435 | 1.1634 | 2.2346 |
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Performed Tests | |
---|---|
Structures | The number of neurons of hidden layer varied from 1 to 20 |
Algorithms | Levenberg–Marquardt (trainlm) and Scaled Conjugate Gradient (trainscg) |
Activation functions | linear (purelin), hyperbolic tangent sigmoid (tansig) and logarithmic sigmoid (logsig) |
Total trained architectures | 156 |
ID | Predictors | β0 | β1 | β2 | β3 | β4 | Adjusted-R2 | MAPE (%) |
---|---|---|---|---|---|---|---|---|
1 | GDP + EN | 9.28 × 107 ** | 5.75 × 10−5 ** | - | −5.32 × 10−1 | - | 0.68 | 5.50 |
2 | GDP2 + EN2 | 7.87 × 107 *** | - | 4.58 × 10−17 ** | - | −1.16 × 10−9 | 0.75 | 4.79 |
3 | GDP + EN + EN2 | 4.84 × 108 *** | 4.59 × 10−5 *** | - | −1.36 × 10 *** | 1.08 × 10−7 *** | 0.91 | 2.68 |
4 | GDP + GDP2 + EN | 4.83 × 107 * | −1.36 × 10−4 * | 1.41 × 10−16 ** | 1.02 | - | 0.81 | 4.01 |
5 | GDP + GDP2 + EN + EN2 | 4.43 × 108 *** | 1.81 × 10−5 | 2.10× 10−17 | −1.22 × 10 ** | 9.85 × 10−8 ** | 0.90 | 2.66 |
Cross Validation (Train) | Test | Predictions | ||||
---|---|---|---|---|---|---|
RMSE | R2 | RMSE | R2 | RMSE | MAPE | R2 |
4.44 (±0.78) | 0.913 (±0.07) | 4.65 | 0.868 | 2.95 | 2.67% | 0.923 |
Models’ characteristics | Train | Validation | Test | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
#ID | Algorithm | Structure | AF | R2 | MAPE (%) | OF | R2 | MAPE (%) | OF | R2 | MAPE (%) | OF |
47 | trainscg | 2-6-1 | tansig; purelin | 0.988 | 1.05 | 3.09 × 1012 | 1.000 | 0.23 | 6.98 × 1010 | 1.000 | 0.04 | 1.76 × 109 |
65 | trainscg | 2-8-1 | tansig; purelin | 0.987 | 1.18 | 3.21 × 1012 | 0.997 | 0.48 | 2.06 × 1011 | 0.998 | 0.74 | 5.00 × 1011 |
98 | trainlm | 2-15-1 | logsig; purelin | 0.960 | 1.97 | 8.56 × 1012 | 0.999 | 2.46 | 7.32 × 1012 | 0.999 | 0.37 | 1.10 × 1011 |
R2 | APE (Max) | APE (Median) | MAPE (%) | |
---|---|---|---|---|
ID47 MLP ANN | 1.00 | 5.48 | 0.13 | 0.76 *** |
Elastic-net Regression | 0.92 | 9.34 | 1.74 | 2.67 |
ID3 MLR model | 0.91 | 9.63 | 1.34 | 2.68 |
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Debone, D.; Martins, T.D.; Miraglia, S.G.E.K. Modeling Carbon Release of Brazilian Highest Economic Pole and Major Urban Emitter: Comparing Classical Methods and Artificial Neural Networks. Climate 2022, 10, 9. https://doi.org/10.3390/cli10010009
Debone D, Martins TD, Miraglia SGEK. Modeling Carbon Release of Brazilian Highest Economic Pole and Major Urban Emitter: Comparing Classical Methods and Artificial Neural Networks. Climate. 2022; 10(1):9. https://doi.org/10.3390/cli10010009
Chicago/Turabian StyleDebone, Daniela, Tiago Dias Martins, and Simone Georges El Khouri Miraglia. 2022. "Modeling Carbon Release of Brazilian Highest Economic Pole and Major Urban Emitter: Comparing Classical Methods and Artificial Neural Networks" Climate 10, no. 1: 9. https://doi.org/10.3390/cli10010009
APA StyleDebone, D., Martins, T. D., & Miraglia, S. G. E. K. (2022). Modeling Carbon Release of Brazilian Highest Economic Pole and Major Urban Emitter: Comparing Classical Methods and Artificial Neural Networks. Climate, 10(1), 9. https://doi.org/10.3390/cli10010009