Learning slosh dynamics by means of data
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.
Computational Mechanics