## 7 Conclusions  
Different statistical and machine-learning algorithms are commonly applied in various fields (such as in financial studies as well as in climatology, and so forth) to predict the future behavior of complex dynamic systems. However, no works are reported in the literature on their use for multi temporal geophysical data forecasting in near-surface applications.  
In this work, both variational methods (VAR) and machine-learning algorithms (Recurrent Neural Networks) were tested for predicting the values of cross-hole electrical resistivity data, taking in account measurements recorded during a tracer test monitoring experiments performed, respectively, during a previous work on a heterogeneous aquifer in the south of Italy [55] and in a new controlled laboratory experiment. The aim was to predict the geoelectrical variations induced by fluids/contaminant displacements in the subsoil.  
This study shows that VAR and RNN can be effective tools for predicting the values of cross-hole geoelectrical data for subsoil fluid transport monitoring in a relatively simple hydrogeological context where seasonal changes in temperature, subsoil saturation degree, and groundwater level variation are negligible. In particular, RNN showed a very good performance even with a small historical dataset.  
However, starting from a bigger historical dataset, and by entering more control factors and increasing the variables of subsurface response, it will be possible to extend the forecast to more than five previsions. In this manner, an efficient quantification of transport characteristics at a study site could follow from the integration of direct hydrological data, and a relatively \"small\" number of geoelectrical measurements and probabilistic previsions based on electrical images.  
Finally, we remark that the proposed methodology is potentially applicable also in the energetic sector for the reservoirs management during oil, gas, hydrogen, CO\({}_{2}\), and heat storage or extraction.  
Conceptualization, V.G., P.D. and E.R.; Data curation, V.G. and L.C.; Formal analysis, P.D.; Funding acquisition, E.R.; Investigation, V.G., L.C., G.D.M. and E.R.; Methodology, V.G., P.D., L.C., G.D.M. and E.R.; Project administration, E.R.; Software V.G., P.D. and L.C.; Supervision, E.R.; Validation, V.G., P.D. and E.R.; Visualization, V.G., P.D., L.C. and E.R.; Writing--original draft, V.G. and P.D.; Writing--review and editing, V.G., P.D., L.C. and E.R. All authors have read and agreed to the published version of the manuscript.  
Laboratory experiment was funded by the Basilicata Region, Progetto PO FSE Basilicata 2007-2013: \"Promozione della ricerca e dell'innovazione e sviluppo di relazioni con il sistema produttivo regionale\" DD n. 796/2013 Azione n. n. 15/AP/05/2013/REG.  
Not applicable.  
The data that support the findings of this study are available from the corresponding author upon request. Python codes are available from [PERSON] upon request.  
**Acknowledgments:** The filed experimental work was provided in collaboration with [PERSON] and [PERSON] of University of Calabria. Authors are grateful to the Director of the CNR-IMAA for the experimental phase in the Laboratory Hydrogeosite facility. Authors thank [PERSON] and [PERSON] for their support during the laboratory experiment.  
**Conflicts of Interest:** The authors declare no conflict of interest.