Functional Deep Learning With Application to Forecasting Precipitation in Macau

Abstract

Precipitation prediction is a popular topic in the feld of weather forecasting, as it provides many benefts for various occupations. For example, farmers can use rainfall prediction to plan crop planting and irrigation, thus maximizing rainfall usage and improving yield and quality in agriculture. Additionally, precipitation prediction can aid in disaster prevention and reduction efforts by enabling authorities to take early action to reduce the harm of natural disasters such as floods and landslides. Several commonly used methods for precipitation prediction exist, including the time series method, Bayesian method, and artifcial neural network method. Each of these methods has its advantages and disadvantages that need to be improved upon. For instance, the time series method processes precipitation data individually and does not incorporate other factors such as humidity or wind speed, potentially missing useful information. Additionally, this method is sensitive to data noise and outliers, requiring complex data preprocessing and fltering. On the other hand, the Bayesian method relies heavily on model assumptions and prior distribution choices, which can signifcantly impact predicted results. Furthermore, the predictive power of this method may be weak for cases with few data samples or insuffcient prior knowledge. Lastly, the artifcial neural network method requires a large number of parameters and lacks interpretability, making it challenging to explain the reasoning behind the results. In this article, we introduce the functional neural network (FuncNN) as a potential solution to these problems. The FuncNN method is capable of handling multi covariates, eliminating the need to fnd a suitable prior distribution as with the Bayesian method. Furthermore, FuncNN requires fewer parameters than the artifcial neural network method while also improving interpretability.