## 4 Neural Network Model and Training  
### Current State of Research  
Approaches to detect or predict the aging state of a battery can roughly be classified into three categories:  
1. Model-based approaches often use algebraic or differential equations to model the physical and/or electrochemical behavior of battery degradation. In general, they are very accurate, but complex and require special measuring equipment to gather the necessary information.
2. Data-driven approaches treat the mechanisms within the battery as a black box. Instead, they use historical data to build a mathematical model and evaluate the aging state by statistical or ML methods. They are very flexible, only have to satisfy a few assumptions, but need a lot of data to accurately generate the model.
3. Hybrid approaches exploit the respective assets of both model-based and data-driven approaches.  
A comprehensive review with descriptions, examples, advantages and disadvantages of all categories can be found in [PERSON] et al [2]. Regarding the application to field data an overview can be found in [3].  
The electrochemical modeling of batteries achieved many scientific insights about battery behavior and aging processes. Most work is based on the Doyle-Fuller-Newman (DFM) model [4; 5]. The Single Particle Model is a simplification of this model and widely used [6; 7; 8]. It reduces the computational effort and makes it more applicable to state estimation tasks. Like other DFM models, it still requires deep knowledge about electrochemical parameters of the cell. There are only few attempts to apply this model to field data [9].  
Several \"classic\" ML methods have been adapted for and applied to batteries to predict the SOC and SOH, e.g., Bayesian and Gaussian processes, Kalman filters, (Deep) Neural Networks, Random Tree/Forest, Regression, Support Vector Machine and combinations of these. [PERSON] et al. [10] recently published a survey of the mentioned methods.  
In hybrid approaches, physical or heuristic models are combined with data driven models. The later update the relevant parameters to simulate aging effects. Using equivalent circuit models (ECMs) together with extended Kalman filters was investigated extensively [11; 12]. Current research is focusing on finding most robust estimation approaches [13; 14].  
Because of its comparatively high flexibility and accuracy, the neural network approach is very popular [15]. However, it is most often applied to lab data, either obtained by measurement campaigns with artificial parameters or synthetic drive cycles [16; 17; 18; 19]. Of the  
Figure 3: Data split for model training and validation.  
small number of publications which used actual field data [20; 21], many analyzed charge sections to diagnose aging [22; 23; 24].  
Working with field data usually entails having little information about the used cell and limited laboratory information. We therefore have chosen a hybrid approach, that uses a structured neural network coupled with an ECM. While there are some examples in the literature which also employ this strategy [25] none have explored how the training of the network could benefit from the additional information of an entire vehicle fleet.