**7. Conclusions**

Summing up, three di fferent forecasting approaches have been implemented in order to develop models for predicting energy demand of natural gas. Investigative analysis took place for an ANN, a LSTM, and the proposed DNN implementations in order to find a desired architecture for each method. Fifteen cities all around Greece were tested, each one with a dataset of measurements that spanned from 3 to 7 years. The investigated cities di ffer both in size as well as in geographical location, amplifying as much as possible the variability of each use case examined. Despite the fact that this study is focused on cities that are only in Greece, the proposed methodology is highly generalizable for any other city that can provide su fficient amount of data, both measurable and behavioral.

The goal of this study was to propose an e fficient neural network implementation that utilizes a variety of quantitative and qualitative inputs, as well as a deep architecture with many layers and nodes, to demonstrate how social factors can improve the performance of the model and increase the accuracy of its forecasts. The proposed methodology has outperformed both the simple ANN approach as well as the state-of-the-art LSTM approach even though both still o ffer good accuracy in most cases. The inclusion of social factors in the proposed DNN approach o ffered consistently more generalized, high-accuracy results. This derives from the fact that by exploring longer forecasts, the four-year ahead forecast was achieved only with the proposed DNN implementation, while the LSTM could only provide accurate results up to two years ahead, and the ANN was deviating systematically.

Applying a combination of multi-parametric social factors, by also taking advantage of the memory cells structure of the LSTM implementation will be the base of the future work that will aim to outperform the DNN implementation. Additional Fuzzy Cognitive Maps structures will be also considered for increasing the interpretability of the models and how the inputs a ffect the performance.

**Author Contributions:** Conceptualization, A.A., E.P. and D.B.; methodology, A.A.; software, A.A.; validation, A.A., E.P. and D.B.; formal analysis, A.A.; investigation, A.A.; resources, E.P.; data curation, A.A.; writing—original draft preparation, A.A.; writing—review and editing, A.A., E.P., and D.B.; visualization, A.A; supervision, E.P. and D.B.; project administration, D.B. All authors have read and agree to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

## **Appendix A Appendix**

**Figure A1.** *Cont*.

**Figure A1.** *Cont*.

**Figure A1.** *Cont*.

**Figure A1.** *Cont*.

**Figure A1.** *Cont*.

**Figure A1.** Correlation of the energy demand and the mean temperature for the training set and the test set for all the examined cities.
