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Abstract
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In this talk, we provide a comprehensive review of the latest advancements in applying deep learning techniques to functional data analysis (FDA). We explore the extension of classical neural network models, particularly Multi-Layer Perceptron (MLPs), to functional data in three ways: functional inputs with scalar outputs, scalar vector inputs with functional outputs, and functional inputs with functional outputs. Additionally, we discuss the development of Functional Neural Networks (FNNs) that incorporate both functional and scalar inputs, as well as functional outputs. Our review also covers methodologies for integrating functional data into deep neural networks, emphasizing how dynamic functional weights enhance interpretability and predictive performance in various applications. Through this survey, we aim to highlight the potential and challenges of deep learning in FDA, providing insights into both theoretical advancements and practical implementations confirmed by real data applications and simulation studies.
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