# Hybrid Modeling for Stream Flow Estimation: Integrating Machine Learning and Federated Learning
## 3 Material and Experimental Methods
### Federated Learning for Stream Flow Rate Estimation
By incorporating diverse data inputs--each station contributing its array of contextual factors, geographical characteristics, and variables--the model's generalization capabilities are significantly enriched. This augmentation equips the model to predict effectively within the purview of various scenarios and accomplish this task with remarkable precision. Furthermore, the scope of federated learning transcends the immediate realm of hydrological predictions. The applicability of this technique extends expansively to domains where data privacy preservation stands as a paramount concern and prediction accuracy is of non-negotiable significance. Industries such as healthcare, finance, and energy management are poised to benefit substantially from this approach. Undoubtedly, the proposed federated learning methodology signifies a transformative advancement in the domain of predictive modeling. It symbolizes a departure from conventional techniques, often streamlining data for analytical convenience. Conversely, it champions the integration of multifaceted data sources, harnessing this diversity to enhance predictive prowess. By advocating for the sacrosancity of data privacy while concurrently realizing predictive accuracy, this methodology forges a path that empowers data-driven insights, all while upholding the sanctity of confidential information. As seen in Figure 8, the use of federated learning for the purpose of estimating stream flow has a multitude of advantages. Firstly, it facilitates the utilization of data derived from many geographical sites, hence including a diverse range of hydrological attributes. Additionally, this solution addresses the issue of privacy issues related to data sharing, rendering it appropriate for settings where maintaining data secrecy is of utmost importance. Furthermore, the implementation of this collaborative learning technique enables the exchange of knowledge among various stations, hence leading to the development of a more precise model for the estimation of stream flow rate. FL-SFRE, an acronym for federated learning for stream flow rate estimation, is a highly promising approach towards achieving sustainable water resource management and effective environmental monitoring. This technology facilitates accurate prognostications while safeguarding confidential information acquired from diverse geographic regions. Through the utilization of federated learning, it is possible to attain precise and dependable estimations of stream flow rates. This advancement holds the potential to enhance water resource management and conservation efforts significantly, hence ensuring the sustainability of these valuable resources for future generations [68; 69; 70]. In our research, we implemented the innovative approach of federated learning to estimate stream flow rates using data collected from two distinct stream gauging stations: Besdegirmen (E12A003) in the Sakarya Basin's Porsuk Stream sub-basin and Melekbahce (E21A033) in the Upper Euphrates basin's Munzur water sub-basin. The primary objective was to develop a predictive model for stream flow rate estimation while ensuring the confidentiality and privacy of data at each station. The application of FL-SFRE involved a well-defined process. Initially, we partitioned the data collected by both stream gauging stations, ensuring that no raw data were exchanged between them or with a central server. Instead, data subsets were created, and each station retained its data locally for analysis. Figure 8: Federated learning for stream flow estimation. To initiate the federated learning process, a global machine learning model was initialized with shared weights and biases. The subsequent step involved the independent training of this global model at each station, using their respective local data, and employing the federated averaging algorithm. During this training phase, model updates, or gradients, were exchanged between stations rather than raw data.