A novel high level canonical piecewise linear model based on the simplicial partition and its application

- PWL has attracted more and more concerns due to its integral nonlinearity and linearity in subregions.
- There is the so-called curse of partitions for compact PWL models when training.
- An improved simplicial partition strategy and a novel high level canonical PWL model are proposed in this paper.
- The numerical and simulation experiments validate the effectiveness of our proposed model.

The piecewise linear (PWL) model has attracted more and more attention in recent research because it can handle complex nonlinearity while maintaining linearity in local regions. A large number of compact representations for PWL modeling have been introduced, such as hinging hyperplanes and its generalized version. However, the existing methods usually give rise to many and complex subregions, which is an issue known as “curse of partitions”, and hampered practical applications of PWL models. In this paper, a novel high level canonical PWL model is presented to tackle the curse of partitions. In more detail, an improved simplicial partition strategy with alterable intervals is proposed to improve the model representation capability. The proposed PWL model guarantees an unchangeable topology during training and thus a limited number of subregions after training. Several numerical experiments, and a simulated chemical process, are used to demonstrate the effectiveness of the proposed model.