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Physics-informed machine learning with smoothed particle hydrodynamics: Hierarchy of reduced Lagrangian models of turbulence

Michael Woodward1,2,3,*, Yifeng Tian3, Criston Hyett1,2,3, Chris Fryer3, Mikhail Stepanov1,2, Daniel Livescu3, and Michael Chertkov1,2,†

  • 1Graduate Interdisciplinary Program in Applied Mathematics, University of Arizona, Tucson, Arizona 85721, USA
  • 2Department of Mathematics, University of Arizona, Tucson, Arizona 85721, USA
  • 3Computer, Computational and Statistical Sciences Division, LANL, Los Alamos, New Mexico 87544, USA

  • *mwoodward@math.arizona.edu
  • †chertkov@math.arizona.edu
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Phys. Rev. Fluids 8, 054602 – Published 5 May, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.054602

Abstract

Building efficient, accurate, and generalizable reduced-order models of developed turbulence remains a major challenge. This manuscript approaches this problem by developing a hierarchy of parameterized reduced Lagrangian models for turbulent flows, and it investigates the effects of enforcing physical structure through smoothed particle hydrodynamics (SPH) versus relying on neural networks (NNs) as universal function approximators. Starting from NN parametrizations of a Lagrangian acceleration operator, this hierarchy of models gradually incorporates a weakly compressible and parameterized SPH framework, which enforces physical symmetries, such as Galilean, rotational, and translational invariances. Within this hierarchy, two new parameterized smoothing kernels are developed to increase the flexibility of the learn-able SPH simulators. For each model we experiment with different loss functions which are minimized using gradient based optimization, where efficient computations of gradients are obtained by using automatic differentiation and sensitivity analysis. Each model within the hierarchy is trained on two data sets associated with weakly compressible homogeneous isotropic turbulence: (1) a validation set using weakly compressible SPH; and (2) a high-fidelity set from direct numerical simulations. Numerical evidence shows that encoding more SPH structure improves generalizability to different turbulent Mach numbers and time shifts, and that including the novel parameterized smoothing kernels improves the accuracy of SPH at the resolved scales.

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Outline

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Phys. Rev. Fluids 8, 054602– Published 5 May, 2023
  • Received 14 September 2022
  • Accepted 28 March 2023
Article part of CHORUS
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