  Functional principal component analysis (FPCA) is an important technique for
dimension reduction in functional data analysis (FDA). Classical FPCA method is
based on the Karhunen-Lo\`{e}ve expansion, which assumes a linear structure of
the observed functional data. However, the assumption may not always be
satisfied, and the FPCA method can become inefficient when the data deviates
from the linear assumption. In this paper, we propose a novel FPCA method that
is suitable for data with a nonlinear structure by neural network approach. We
construct networks that can be applied to functional data and explore the
corresponding universal approximation property. The main use of our proposed
nonlinear FPCA method is curve reconstruction. We conduct a simulation study to
evaluate the performance of our method. The proposed method is also applied to
two real-world data sets to further demonstrate its superiority.
