Learning slosh dynamics by means of data

  • B. Moya
  • D. Gonzalez
  • I. Alfaro
  • F. Chinesta
  • E. CuetoEmail author
Original Paper


In this work we study several learning strategies for fluid sloshing problems based on data. In essence, a reduced-order model of the dynamics of the free surface motion of the fluid is developed under rigorous thermodynamics settings. This model is extracted from data by exploring several strategies. First, a linear one, based on the employ of Proper Orthogonal Decomposition techniques is analyzed. Second, a strategy based on the employ of Locally Linear Embedding is studied. Finally, Topological Data Analysis is employed to the same end. All the three distinct possibilities rely on a numerical integration scheme to advance the dynamics in time. This thermodynamically consistent integrator is developed on the basis of the General Equation for Non-Equilibrium Reversible–Irreversible Coupling, GENERIC [M. Grmela and H.C Oettinger (1997). Phys. Rev. E. 56 (6): 6620–6632], framework so as to guarantee the satisfaction of first principles (particularly, the laws of thermodynamics). We show how the resulting method employs a few degrees of freedom, while it allows for a realistic reconstruction of the fluid dynamics of sloshing processes under severe real-time constraints. The proposed method is shown to run faster than real time in a standard laptop.


Data-driven fluid simulation Model order reduction GENERIC formalism Real-time simulation 



This work has been supported by the Regional Government of Aragon and the European Social Fund, research group T24 17R. The support given by the ESI Group to F. Ch. through the Chair at ENSAM ParisTech, as well as the funding provided to E.C., D.G. and I.A. through the project “Simulated Reality: An intelligence augmentation system based on Hybrid Twins and Augmented Reality” is gratefully acknowledged.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • B. Moya
    • 1
  • D. Gonzalez
    • 1
  • I. Alfaro
    • 1
  • F. Chinesta
    • 2
  • E. Cueto
    • 1
    Email author
  1. 1.Aragon Institute of Engineering ResearchUniversidad de ZaragozaZaragozaSpain
  2. 2.ESi Chair and PIMM Lab. Ensam ParisTechParisFrance

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