Density Propagation with Characteristics-based Deep Learning

TL;DR

This paper introduces a deep learning-based method for efficiently propagating uncertainty in high-dimensional nonlinear dynamic systems by encoding PDF evolution equations, reducing data requirements.

Contribution

It presents a novel data-driven approach that combines deep learning with PDF evolution equations to handle high-dimensional uncertainty propagation with less training data.

Findings

Successfully applied to a six-dimensional rigid body system

Demonstrated robustness evaluation of a feedback controller

Reduced need for large training datasets

Abstract

Uncertainty propagation in nonlinear dynamic systems remains an outstanding problem in scientific computing and control. Numerous approaches have been developed, but are limited in their capability to tackle problems with more than a few uncertain variables or require large amounts of simulation data. In this paper, we propose a data-driven method for approximating joint probability density functions (PDFs) of nonlinear dynamic systems with initial condition and parameter uncertainty. Our approach leverages on the power of deep learning to deal with high-dimensional inputs, but we overcome the need for huge quantities of training data by encoding PDF evolution equations directly into the optimization problem. We demonstrate the potential of the proposed method by applying it to evaluate the robustness of a feedback controller for a six-dimensional rigid body with parameter uncertainty.