In this paper, we show how convolutional neural networks (CNN) can
be used in regression and classification learning problems for noisy and non-noisy
functional data. The main idea is to transform the functional data into a 28 by 28
image. We use a specific but typical architecture of a convolutional neural network
to perform all the regression exercises of parameter estimation and functional form
classification. First, we use some functional case studies of functional data with and
without random noise to showcase the strength of the new method. In particular,
we use it to estimate exponential growth and decay rates, the bandwidths of sine
and cosine functions, and the magnitudes and widths of curve peaks. We also use it
to classify the monotonicity and curvatures of functional data, the algebraic versus
exponential growth, and the number of peaks of functional data. Second, we apply
the same convolutional neural networks to Lyapunov exponent estimation in noisy
and non-noisy chaotic data, in estimating rates of disease transmission from epidemic
curves, and in detecting the similarity of drug dissolution profiles. Finally, we apply
the method to real-life data to detect Parkinson’s disease patients in a classification
problem. We performed ablation analysis and compared the new method with other
commonly used neural networks for functional data and showed that it outperforms
them in all applications. Although simple, the method shows high accuracy and is
promising for future use in engineering and medical applications.