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In this study, we explore the use of deep learning methods to perform functional regression models, highlighting their potential in analyzing and predicting functional data. Recent advancements in neural operators have paved the way for models like the Fourier Neural Operator (FNO) and Neural Operator Flows (OpFlow), which are capable of learning complex mappings between infinitedimensional function spaces. Additionally, we discuss the Function Direct Neural Network model (FDNN), Deep Functional Multiple index Models (DFMM) and Adaptive Functional Neural Network (AdaFNN) to increase the flexibility of functional regression tasks. We present a comparative analysis of these deep functional networks, on simulations and on two case studies: Tecator and Building Occupancy datasets.

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Comparison of Deep Learning Methods for Functional Data

  • 会议论文

  • 发表日期：

    2025年

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  • Nouhaila Goujili,
  • Matthieu Saumard,
  • Maher Jridi

摘要

In this study, we explore the use of deep learning methods to perform functional regression models, highlighting their potential in analyzing and predicting functional data. Recent advancements in neural operators have paved the way for models like the Fourier Neural Operator (FNO) and Neural Operator Flows (OpFlow), which are capable of learning complex mappings between infinitedimensional function spaces. Additionally, we discuss the Function Direct Neural Network model (FDNN), Deep Functional Multiple index Models (DFMM) and Adaptive Functional Neural Network (AdaFNN) to increase the flexibility of functional regression tasks. We present a comparative analysis of these deep functional networks, on simulations and on two case studies: Tecator and Building Occupancy datasets.