Hossein Haghbin

In this research, the design and evaluation of functional neural networks for analyzing functional data have been addressed. Functional data, which consist of a set of functions defined on a continuous domain, have widespread applications in various scientific fields, and their analysis requires specific approaches. The main objective of this thesis is to develop deep neural network architectures capable of efficiently processing functional data as well as combinations of functional and scalar data. Various neural network architectures, including functional-to-scalar, functional-to-functional, and scalar-to-functional layers, have been designed and analyzed. These architectures have been adapted for different types of input and output data, including functional and scalar data. Moreover, the unique characteristics of each architecture and the methods for estimating their parameters have been explored. Functional-to-scalar layers have been expanded using basis functions, while other layers have been designed by directly modeling functional and scalar data. The proposed models have been evaluated on real-world Teacator datasets, which include spectral and chemical data. The results demonstrated that the proposed architectures, especially when functional and scalar data are combined as inputs, outperform standard models such as LSTM. This research, by introducing a set of novel functional neural network architectures, provides a framework for more precise analysis and modeling of functional data and can be applied in various fields, including environmental sciences, medicine, and engineering.