# A novel Multiplicative Polynomial Kernel for Volterra series identification

## TL;DR

This paper introduces a new kernel-based regularization method for Volterra series identification, improving the selection of influential monomials and enhancing prediction accuracy in nonlinear system modeling.

## Contribution

It proposes a novel multiplicative polynomial kernel for Volterra models, with parameter estimation via marginal likelihood, outperforming existing methods in monomial selection and prediction.

## Key findings

- Better monomial selection improves model accuracy
- Numerical experiments demonstrate superior prediction capabilities
- Kernel approach effectively handles curse of dimensionality

## Abstract

Volterra series are especially useful for nonlinear system identification, also thanks to their capability to approximate a broad range of input-output maps. However, their identification from a finite set of data is hard, due to the curse of dimensionality. Recent approaches have shown how regularized kernel-based methods can be useful for this task. In this paper, we propose a new regularization network for Volterra models identification. It relies on a new kernel given by the product of basic building blocks. Each block contains some unknown parameters that can be estimated from data using marginal likelihood optimization. In comparison with other algorithms proposed in the literature, numerical experiments show that our approach allows to better select the monomials that really influence the system output, much increasing the prediction capability of the model.