Density Propagation with Characteristics-based Deep Learning
This addresses a bottleneck in scientific computing and control for high-dimensional systems, though it appears incremental as it builds on existing deep learning approaches.
The paper tackled uncertainty propagation in nonlinear dynamic systems by proposing a data-driven deep learning method that approximates joint probability density functions without requiring large simulation data, demonstrating its potential on a six-dimensional rigid body control problem.
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.