TY - JOUR
T1 - Machine-Learning Methods on Noisy and Sparse Data
AU - Poulinakis, Konstantinos
AU - Drikakis, Dimitris
AU - Kokkinakis, Ioannis W.
AU - Spottswood, Stephen Michael
N1 - Funding Information:
This material is based upon work supported by the Air Force Office of Scientific Research under award numbers FA8655-22-1-7026 and FA9550-19-1-7018. The authors thank Dr David Swanson (Air Force Office of Scientific Research-European Office of Aerospace) for their support. The funding was awarded to D.D. through the University of Nicosia Research Foundation.
Publisher Copyright:
© 2023 by the authors.
PY - 2023/1
Y1 - 2023/1
N2 - Experimental and computational data and field data obtained from measurements are often sparse and noisy. Consequently, interpolating unknown functions under these restrictions to provide accurate predictions is very challenging. This study compares machine-learning methods and cubic splines on the sparsity of training data they can handle, especially when training samples are noisy. We compare deviation from a true function f using the mean square error, signal-to-noise ratio and the Pearson (Formula presented.) coefficient. We show that, given very sparse data, cubic splines constitute a more precise interpolation method than deep neural networks and multivariate adaptive regression splines. In contrast, machine-learning models are robust to noise and can outperform splines after a training data threshold is met. Our study aims to provide a general framework for interpolating one-dimensional signals, often the result of complex scientific simulations or laboratory experiments.
AB - Experimental and computational data and field data obtained from measurements are often sparse and noisy. Consequently, interpolating unknown functions under these restrictions to provide accurate predictions is very challenging. This study compares machine-learning methods and cubic splines on the sparsity of training data they can handle, especially when training samples are noisy. We compare deviation from a true function f using the mean square error, signal-to-noise ratio and the Pearson (Formula presented.) coefficient. We show that, given very sparse data, cubic splines constitute a more precise interpolation method than deep neural networks and multivariate adaptive regression splines. In contrast, machine-learning models are robust to noise and can outperform splines after a training data threshold is met. Our study aims to provide a general framework for interpolating one-dimensional signals, often the result of complex scientific simulations or laboratory experiments.
KW - deep neural networks
KW - feedforward neural networks
KW - interpolation
KW - machine learning
KW - MARS
KW - noisy data
KW - sparse data
KW - splines
UR - http://www.scopus.com/inward/record.url?scp=85145920087&partnerID=8YFLogxK
U2 - 10.3390/math11010236
DO - 10.3390/math11010236
M3 - Article
AN - SCOPUS:85145920087
SN - 2227-7390
VL - 11
JO - Mathematics
JF - Mathematics
IS - 1
M1 - 236
ER -