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Shape-Based Nonlinear Model Reduction for 1D Conservation Laws

By Denis Nikitin, Carlos Canudas de Wit and Paolo Frasca

Abstract

International audienceWe present a novel method for model reduction of one-dimensional conservation law to the dynamics of the parameters describing the approximate shape of the solution. Depending on the parametrization, each parameter has a well-defined physical meaning. The obtained ODE system can be used for the estimation and control purposes. The model reduction is performed by minimizing the divergence of flows between the original and reduced systems, and we show that this is equivalent to the minimization of the Wasserstein distance derivative. The method is then tested on the heat equation and on the LWR (Lighthill-Whitham-Richards) model for vehicle traffic

Topics: Model reduction, partial differential equations, traffic control, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Publisher: HAL CCSD
Year: 2020
OAI identifier: oai:HAL:hal-02952161v1
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