Hybrid additive modeling with partial dependence for supervised regression and dynamical systems forecasting

TL;DR

This paper introduces a hybrid additive modeling approach using partial dependence for supervised regression and dynamical systems forecasting, reducing regularization needs and improving interpretability.

Contribution

It proposes a novel hybrid training method based on partial dependence, applicable to various models and dynamical systems, with comprehensive performance evaluation.

Findings

Hybrid models outperform purely data-driven models in accuracy.

Partial dependence-based training reduces the need for complex regularization.

The approach is effective for both standard regression and dynamical systems forecasting.

Abstract

Learning processes by exploiting restricted domain knowledge is an important task across a plethora of scientific areas, with more and more hybrid training methods additively combining data-driven and model-based approaches. Although the obtained models are more accurate than purely data-driven models, the optimization process usually comes with sensitive regularization constraints. Furthermore, while such hybrid methods have been tested in various scientific applications, they have been mostly tested on dynamical systems, with only limited study about the influence of each model component on global performance and parameter identification. In this work, we introduce a new hybrid training approach based on partial dependence, which removes the need for intricate regularization. Moreover, we assess the performance of hybrid modeling against traditional machine learning methods on standard regression problems. We compare, on both synthetic and real regression problems, several approaches for training such hybrid models. We focus on hybrid methods that additively combine a parametric term with a machine learning term and investigate model-agnostic training procedures. Therefore, experiments are carried out with different types of machine learning models, including tree-based models and artificial neural networks. We also extend our partial dependence optimization process for dynamical systems forecasting and compare it to existing schemes.