Data-Driven Fluid Flow Simulations by Using
Convolutional Neural Network
Kazuhiko Kakuda (B) , Yuto Morimasa, Tomoyuki Enomoto, Wataru Okaniwa,
and Shinichiro Miura
Nihon University, Narashino, Chiba 275-8575, Japan
kakuda.kazuhiko@nihon-u.ac.jp
Abstract. In this paper, we present the data-driven fluid flow simulations using the
deep CNN (Convolutional Neural Network) with the parametric softsign activation functions. To simulate the fluid flow problems, the particle-method approach
based on SPH (Smoothed Particle Hydrodynamics) is used herein. The GPUimplementation consists mainly of the search for neighboring particles in the
locally uniform grid cell using hash function. We construct significantly the deep
CNN architectures with novel activation functions, so-called parametric softsign.
Numerical results demonstrate the workability and validity of the present approach
through the dam-breaking fluid flow simulations with free surface.
Keywords: Particle method · Fluid simulation · Data-driven · CNN · Activation
functions · Parametric softsign
1 Introduction
In the massive simulation-based fields of science and engineering, it is indispensable
to demonstrate the fluid flow behavior in real-time. To simulate effectively the largescale fluid flow problems, there are significantly particle-based approaches, such as SPH
(Smoothed Particle Hydrodynamics) [1, 7], MPS (Moving Particle Semi-implicit) [4],
and so forth.
Recently, the data-driven fluid flow approaches have increasingly become an important strategy for solving efficiently various problems, such as physics-based fluid simulation using the regression forests [5], the parameterized fluid simulations using the
generative neural network [3], the RANS turbulence modelling using the tensor basis
neural network [6], and so forth. In our previous work, we have proposed newly the parametric softsign activation functions [2] to avoid zero-values in negative part of ReLU
used widely in CNN (Convolutional Neural Network).
The purpose of this paper is to present the data-driven fluid flow approach by using the
deep CNN with the parametric softsign activation functions. As the particle-based fluid
simulation, we adopt the GPU-based SPH method with quantic-spline kernel functions
[8]. The GPU-implementation consists mainly of the search for neighboring particles in
the locally uniform grid cell using hash function. On the other hand, we construct the
latent space network [3] based on the deep CNN using some datasets obtained from the
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
S. N. Atluri and I. Vušanovi´ c (Eds.): ICCES 2020, MMS 97, pp. 14–19, 2021.
https://doi.org/10.1007/978-3-030-64690-5_2
Convolutional Neural Network
Kazuhiko Kakuda (B) , Yuto Morimasa, Tomoyuki Enomoto, Wataru Okaniwa,
and Shinichiro Miura
Nihon University, Narashino, Chiba 275-8575, Japan
kakuda.kazuhiko@nihon-u.ac.jp
Abstract. In this paper, we present the data-driven fluid flow simulations using the
deep CNN (Convolutional Neural Network) with the parametric softsign activation functions. To simulate the fluid flow problems, the particle-method approach
based on SPH (Smoothed Particle Hydrodynamics) is used herein. The GPUimplementation consists mainly of the search for neighboring particles in the
locally uniform grid cell using hash function. We construct significantly the deep
CNN architectures with novel activation functions, so-called parametric softsign.
Numerical results demonstrate the workability and validity of the present approach
through the dam-breaking fluid flow simulations with free surface.
Keywords: Particle method · Fluid simulation · Data-driven · CNN · Activation
functions · Parametric softsign
1 Introduction
In the massive simulation-based fields of science and engineering, it is indispensable
to demonstrate the fluid flow behavior in real-time. To simulate effectively the largescale fluid flow problems, there are significantly particle-based approaches, such as SPH
(Smoothed Particle Hydrodynamics) [1, 7], MPS (Moving Particle Semi-implicit) [4],
and so forth.
Recently, the data-driven fluid flow approaches have increasingly become an important strategy for solving efficiently various problems, such as physics-based fluid simulation using the regression forests [5], the parameterized fluid simulations using the
generative neural network [3], the RANS turbulence modelling using the tensor basis
neural network [6], and so forth. In our previous work, we have proposed newly the parametric softsign activation functions [2] to avoid zero-values in negative part of ReLU
used widely in CNN (Convolutional Neural Network).
The purpose of this paper is to present the data-driven fluid flow approach by using the
deep CNN with the parametric softsign activation functions. As the particle-based fluid
simulation, we adopt the GPU-based SPH method with quantic-spline kernel functions
[8]. The GPU-implementation consists mainly of the search for neighboring particles in
the locally uniform grid cell using hash function. On the other hand, we construct the
latent space network [3] based on the deep CNN using some datasets obtained from the
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
S. N. Atluri and I. Vušanovi´ c (Eds.): ICCES 2020, MMS 97, pp. 14–19, 2021.
https://doi.org/10.1007/978-3-030-64690-5_2