Probabilistic regression is an approach that incorporates uncertainty into the prediction model. Instead of predicting a single output value, it predicts a distribution over possible output values, providing a measure of confidence in the predictions. This method is particularly useful when the data contains inherent noise or uncertainty. In this study, the regression model can be expressed as: 𝐶 = 𝑓(𝒗) + 𝜖, (1) where 𝜖~𝒩(0, 𝜎 ′2 ) denotes the noise, which is a normal distribution with mean zero and variance 𝜎 ′2 . Moreover, 𝐶 and 𝒗 are representing the capacity loss and training features vectors for each of the cycle and calendar aging models, respectively. In our study, based on the findings of to , we utilize accelerated time, State of Charge (SOC), and temperature (T) as the feature vectors for training the calendar aging predictor. Furthermore, following the methodology outlined in , we employ full equivalent cycle (FEC), charge and discharge rates, SOC, and Depth of Cycle (DOC) as the training features for the cyclic aging predictor. Given a training dataset 𝒟 = {(𝒗 𝑖 , 𝐶 𝑖 )|𝑖 = 1, … , 𝑛}, we aim to estimate the hyperparameters 𝜃 of the kernel function. This estimation is done by minimizing the negative loglikelihood function using the Adam optimizer . The negative log-likelihood function measures the "unlikeliness" of the observed data under the model, and minimizing it helps in fitting the model parameters. This function in our model is expressed as: