Methods and Applications of Analysis

Volume 26 (2019)

Number 3

Special Issue in Honor of Roland Glowinski (Part 2 of 2)

Guest Editors: Xiaoping Wang (Hong Kong University of Science and Technology) and Xiaoming Yuan (The University of Hong Kong)

Parameter identification of a fluid-structure system by deep-learning with an Eulerian formulation

Pages: 281 – 290



Olivier Pironneau (Laboratoire J.-L. Lions , University of Paris VI, Paris, France)


A simple fluid-structure problem is considered as a test to assess the feasibility of deep-learning algorithms for parameter identification. Tensorflow by Google is used and as it is a stochastic algorithm, provision must be made for the robustness of the large displacement fluidstructure simulator with respect to a wide range of values for the Lamé coefficients and the density of the solid. Hence an Eulerian monolithic solver is introduced. The numerical tests validate the deep-learning approach.


parameter identification, fluid-structure interaction, genetic algorithm, neural network, deep learning

2010 Mathematics Subject Classification

35Q30, 65N30, 68T01, 90C15

In honor of Roland Glowinski’s 80th birthday

Received 25 December 2017

Received revised 30 July 2019

Published 2 April 2020