Comparison of universal approximators incorporating partial monotonicity by structure.
Neural networks applied in control loops and safety-critical domains have to meet more requirements than just the overall best function approximation. On the one hand, a small approximation error is required; on the other hand, the smoothness and the monotonicity of selected input-output relations have to be guaranteed. Otherwise, the stability of most of the control laws is lost. In this article we compare two neural network-based approaches incorporating partial monotonicity by structure, namely the Monotonic Multi-Layer Perceptron (MONMLP) network and the Monotonic MIN-MAX (MONMM) network. We show the universal approximation capabilities of both types of network for partially monotone functions. On a number of datasets, we investigate the advantages and disadvantages of these approaches related to approximation performance, training of the model and convergence.
Minin
Alexey
A
OOO Siemens, Monitoring and Preventive Control group, 191186 Saint-Petersburg, Volynskiy Per. Dom 3A liter A, Russia. alexey.minin@siemens.com
Velikova
Marina
M
Lang
Bernhard
B
Daniels
Hennie
H
D000465:Algorithms; D001185:Artificial Intelligence; D019295:Computational Biology; D003198:Computer Simulation; D016571:Neural Networks, Computer; D010363:Pattern Recognition, Automated