A thesis submitted in fulfillment of the requirements for the degree of Bechelor of Mathematics in the Department of Mathematics, Faculty of Science and Technology, University of Macau
Essay report refers to link[https://github.com/Ivan087/FYP_fda/blob/main/thesis/Functional%20Deep%20Learning%20With%20Application%20to%20Forecasting%20Precipitation%20in%20Macau.pdf]
Precipitation prediction is a popular topic in the field of weather forecasting, as it provides many benefits for various occupations. For example, farmers can use rain fall prediction to plan crop planting and irrigation, thus maximizing rainfall usage and improving yield and quality in agriculture. Additionally, precipitation predic tion 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 land slides. Several commonly used methods for precipitation prediction exist, includ ing the time series method, Bayesian method, and artificial neural network method. Each of these methods has its advantages and disadvantages that need to be im proved upon. For instance, the time series method processes precipitation data in dividually 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 filtering. On the other hand, the Bayesian method relies heavily on model assumptions and prior distri bution choices, which can significantly impact predicted results. Furthermore, the predictive power of this method may be weak for cases with few data samples or insufficient prior knowledge. Lastly, the artificial neural network method requires a large number of parameters and lacks interpretability, making it challenging to ex plain 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 find a suit able prior distribution as with the Bayesian method. Furthermore, FuncNN requires fewer parameters than the artificial neural network method while also improving interpretability.