Density Propagation with Characteristics-based Deep Learning
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Authors
Nakamura-Zimmerer, Tenavi
Venturi, Daniele
Gong, Qi
Subjects
Advisors
Date of Issue
2019-11-22
Date
November 22, 2019
Publisher
ArXiv
Language
Abstract
Uncertainty propagation in nonlinear dynamic systems remains an outstanding
problem in scientific computing and control. Numerous approaches have been de veloped, 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.
Type
Preprint
Description
Series/Report No
Department
Applied Mathematics
Organization
Identifiers
NPS Report Number
Sponsors
Funder
Format
13 p.
Citation
Nakamura-Zimmerer, Tenavi, et al. "Density Propagation with Characteristics-based Deep Learning." arXiv preprint arXiv:1911.09311 (2019).
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.