Data-Augmented Numerical Integration in State Prediction: Rule Selection

TL;DR

This paper introduces a data-augmented numerical integration method for nonlinear stochastic system state prediction, utilizing neural networks to select optimal integration rules and improve prediction accuracy.

Contribution

It presents a novel data-informed rule selection approach that combines mathematical and data-driven methods for enhanced state prediction in nonlinear stochastic systems.

Findings

Improved accuracy in state prediction for nonlinear stochastic systems.

Effective neural network-based selection of integration rules.

Combines mathematical rigor with data-driven adaptability.

Abstract

This paper deals with the state prediction of nonlinear stochastic dynamic systems. The emphasis is laid on a solution to the integral Chapman-Kolmogorov equation by a deterministic-integration-rule-based point-mass method. A novel concept of reliable data-augmented, i.e., mathematics- and data-informed, integration rule is developed to enhance the point-mass state predictor, where the trained neural network (representing data contribution) is used for the selection of the best integration rule from a set of available rules (representing mathematics contribution). The proposed approach combining the best properties of the standard mathematics-informed and novel data-informed rules is thoroughly discussed.