This paper introduces a methodology for optimizing neural network models using a combination of continuous and categorical binary indices in the context of precipitation forecasting. Traditional metrics like Probability of Detection (POD) and False Alarm Rate (FAR) are popular for evaluating precipitation models, but they are not differentiable, making them unsuitable for gradient-based optimization. The authors propose differentiable versions of these metrics using the sigmoid function, which allows for smooth and continuous optimization. This approach enables the training of deep learning models to improve the skill of precipitation forecasts. The methodology involves a multi-objective loss function that combines continuous and categorical binary indices. The authors test this approach by training a neural network to estimate precipitation using geopotential height data as input. The model is evaluated using well-known metrics such as ROC curves and the Area Under the Curve (AUC). The results show that the proposed differentiable indices can be used to optimize the performance of neural network models, achieving better skill than traditional methods. The study demonstrates that the proposed differentiable indices can be integrated into the loss function of gradient descent-based models, allowing for the optimization of both continuous and categorical metrics. The experiments show that the model's performance can be improved by balancing the weights of different indices, such as POD and POFD. The results indicate that the best performance is achieved with a specific combination of these indices, leading to a high AUC score. The paper also discusses the use of a U-net architecture for learning spatial relationships between geopotential height and precipitation. The model is trained on the ERA-Interim dataset, which provides reanalysis data for weather forecasting. The results show that the proposed methodology can effectively optimize the performance of neural network models for precipitation forecasting, making it a valuable tool for improving weather prediction accuracy.This paper introduces a methodology for optimizing neural network models using a combination of continuous and categorical binary indices in the context of precipitation forecasting. Traditional metrics like Probability of Detection (POD) and False Alarm Rate (FAR) are popular for evaluating precipitation models, but they are not differentiable, making them unsuitable for gradient-based optimization. The authors propose differentiable versions of these metrics using the sigmoid function, which allows for smooth and continuous optimization. This approach enables the training of deep learning models to improve the skill of precipitation forecasts. The methodology involves a multi-objective loss function that combines continuous and categorical binary indices. The authors test this approach by training a neural network to estimate precipitation using geopotential height data as input. The model is evaluated using well-known metrics such as ROC curves and the Area Under the Curve (AUC). The results show that the proposed differentiable indices can be used to optimize the performance of neural network models, achieving better skill than traditional methods. The study demonstrates that the proposed differentiable indices can be integrated into the loss function of gradient descent-based models, allowing for the optimization of both continuous and categorical metrics. The experiments show that the model's performance can be improved by balancing the weights of different indices, such as POD and POFD. The results indicate that the best performance is achieved with a specific combination of these indices, leading to a high AUC score. The paper also discusses the use of a U-net architecture for learning spatial relationships between geopotential height and precipitation. The model is trained on the ERA-Interim dataset, which provides reanalysis data for weather forecasting. The results show that the proposed methodology can effectively optimize the performance of neural network models for precipitation forecasting, making it a valuable tool for improving weather prediction accuracy.