CIRA Guide to Custom Loss Functions for Neural Networks in Environmental Sciences -- Version 1

Neural networks are increasingly used in environmental science applications. Furthermore, neural network models are trained by minimizing a loss function, and it is crucial to choose the loss function very carefully for environmental science applications, as it determines what exactly is being optimized. Standard loss functions do not cover all the needs of the environmental sciences, which makes it important for scientists to be able to develop their own custom loss functions so that they can implement many of the classic performance measures already developed in environmental science, including measures developed for spatial model verification. However, there are very few resources available that cover the basics of custom loss function development comprehensively, and to the best of our knowledge none that focus on the needs of environmental scientists. This document seeks to fill this gap by providing a guide on how to write custom loss functions targeted toward environmental science applications. Topics include the basics of writing custom loss functions, common pitfalls, functions to use in loss functions, examples such as fractions skill score as loss function, how to incorporate physical constraints, discrete and soft discretization, and concepts such as focal, robust, and adaptive loss. While examples are currently provided in this guide for Python with Keras and the TensorFlow backend, the basic concepts also apply to other environments, such as Python with PyTorch. Similarly, while the sample loss functions provided here are from meteorology, these are just examples of how to create custom loss functions. Other fields in the environmental sciences have very similar needs for custom loss functions, e.g., for evaluating spatial forecasts effectively, and the concepts discussed here can be applied there as well. All code samples are provided in a GitHub repository.