Data-Driven Fluid Flow Simulations by Using Convolutional
19
(a) Loss for the reconstructed results
(b) Loss for the results divided by autoencoder
Fig. 5. Loss time-history for the reconstructed velocity fields.
Table 2. Comparison of SPH simulation time and our approach time.
SPH simulation time [s]
(12,500 time steps)
Our CNN approach time [s]
80.568 [s]
0.58 [s]
Speed up [×]
138.91
6 Conclusions
We have presented the data-driven fluid flow approach by using the deep CNN with the
parametric softsign activation functions. We have adopted the SPH approach as the fluid
simulation, and constructed the latent space network based on the deep CNN with the
parametric softsign activation functions. The qualitative agreement between the present
result and the ground truth image appears also satisfactory.
References
1. Gingold, R.A., Monaghan, J.J.: Smoothed particle hydrodynamics: theory and application to
non-spherical stars. Mon. Not. R. Astr. Soc. 181, 375–389 (1977)
2. Kakuda, K., Enomoto, T., Miura, S.: Nonlinear activation functions in CNN based on fluid
dynamics and its applications. CMES: Comput. Model. Eng. Sci. 118(1), 1–14 (2019)
3. Kim, B., Azevedo, V.C., Thuerey, N., Kim, T., Gross, M., Solenthaler, B.: Deep Fluids: A
generative network for parameterized fluid simulations. Eurographics 38(2), 59–70 (2019)
4. Koshizuka, S., Oka, Y.: Moving-particle semi-implicit method for fragmentation of incompressible fluid. Nucl. Sci. Eng. 123, 421–434 (1996)
5. Ladicky, L., Jeong, S., Solenthaler, B., Pollefeys, M., Gross, M.: Data-driven fluid simulations
using regression forests. ACM Trans. Graph. 34(6), 1–9 (2015)
6. Ling, J., Kurzawski, A., Templeton, J.: Reynolds averaged turbulence modelling using deep
neural networks with embedded invariance. J. Fluid Mech. 807, 155–166 (2016)
7. Lucy, L.B.: A numerical approach to the testing of the fission hypothesis. Astron. J. 82(12),
1013–1024 (1977)
8. Morris, J.P., Fox, P.J., Zhu, Y.: Modeling low reynolds number incompressible flows using
SPH. J. Comput. Phys. 136, 214–226 (1997)
19
(a) Loss for the reconstructed results
(b) Loss for the results divided by autoencoder
Fig. 5. Loss time-history for the reconstructed velocity fields.
Table 2. Comparison of SPH simulation time and our approach time.
SPH simulation time [s]
(12,500 time steps)
Our CNN approach time [s]
80.568 [s]
0.58 [s]
Speed up [×]
138.91
6 Conclusions
We have presented the data-driven fluid flow approach by using the deep CNN with the
parametric softsign activation functions. We have adopted the SPH approach as the fluid
simulation, and constructed the latent space network based on the deep CNN with the
parametric softsign activation functions. The qualitative agreement between the present
result and the ground truth image appears also satisfactory.
References
1. Gingold, R.A., Monaghan, J.J.: Smoothed particle hydrodynamics: theory and application to
non-spherical stars. Mon. Not. R. Astr. Soc. 181, 375–389 (1977)
2. Kakuda, K., Enomoto, T., Miura, S.: Nonlinear activation functions in CNN based on fluid
dynamics and its applications. CMES: Comput. Model. Eng. Sci. 118(1), 1–14 (2019)
3. Kim, B., Azevedo, V.C., Thuerey, N., Kim, T., Gross, M., Solenthaler, B.: Deep Fluids: A
generative network for parameterized fluid simulations. Eurographics 38(2), 59–70 (2019)
4. Koshizuka, S., Oka, Y.: Moving-particle semi-implicit method for fragmentation of incompressible fluid. Nucl. Sci. Eng. 123, 421–434 (1996)
5. Ladicky, L., Jeong, S., Solenthaler, B., Pollefeys, M., Gross, M.: Data-driven fluid simulations
using regression forests. ACM Trans. Graph. 34(6), 1–9 (2015)
6. Ling, J., Kurzawski, A., Templeton, J.: Reynolds averaged turbulence modelling using deep
neural networks with embedded invariance. J. Fluid Mech. 807, 155–166 (2016)
7. Lucy, L.B.: A numerical approach to the testing of the fission hypothesis. Astron. J. 82(12),
1013–1024 (1977)
8. Morris, J.P., Fox, P.J., Zhu, Y.: Modeling low reynolds number incompressible flows using
SPH. J. Comput. Phys. 136, 214–226 (1997)