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Parametrized Shape Optimization using Surrogate Fluid Models

Fast and efficient structure optimization based on parametrized shapes in surrogate fluid simulation environment.

Keywords: surrogate modeling, deep learning, fluid simulation, optimization

Incompressible fluids governed by the Navier-Stokes equations are often computationally expensive to simulate, hence we look towards surrogate modeling, replacing conventional simulation using efficient machine learning approaches, for practical applications, such as shape optimization [1]. This is already a popular field in aerodynamics for airfoil lift/drag optimization, which we want to now apply in the context of more complex structures. We also want to start with a supervised learning approach for the surrogate model, then move towards semi-supervised or unsupervised settings, to potentially allow us better generalizability in the fluid domain. The shape parametrization can be based on previous work, such as using Wasserstein barycenters for shape interpolation [2]. This comes with the limitation that it only interpolates between known shapes, as a result this approach can be extended, if time allows it, by e.g. deep generative models [3].
References:
[1] Chen, L.W., Cakal, B.A., Hu, X. and Thuerey, N., 2021. Numerical investigation of minimum drag profiles in laminar flow using deep learning surrogates. Journal of Fluid Mechanics, 919.
[2] Ma, P., Du, T., Zhang, J.Z., Wu, K., Spielberg, A., Katzschmann, R.K. and Matusik, W., 2021. Diffaqua: A differentiable computational design pipeline for soft underwater swimmers with shape interpolation. ACM Transactions on Graphics (TOG), 40(4), pp.1-14.
[3] Li, R., Li, X., Hui, K.H. and Fu, C.W., 2021. SP-GAN: Sphere-guided 3D shape generation and manipulation. ACM Transactions on Graphics (TOG), 40(4), pp.1-12.

Incompressible fluids governed by the Navier-Stokes equations are often computationally expensive to simulate, hence we look towards surrogate modeling, replacing conventional simulation using efficient machine learning approaches, for practical applications, such as shape optimization [1]. This is already a popular field in aerodynamics for airfoil lift/drag optimization, which we want to now apply in the context of more complex structures. We also want to start with a supervised learning approach for the surrogate model, then move towards semi-supervised or unsupervised settings, to potentially allow us better generalizability in the fluid domain. The shape parametrization can be based on previous work, such as using Wasserstein barycenters for shape interpolation [2]. This comes with the limitation that it only interpolates between known shapes, as a result this approach can be extended, if time allows it, by e.g. deep generative models [3].

References:

[1] Chen, L.W., Cakal, B.A., Hu, X. and Thuerey, N., 2021. Numerical investigation of minimum drag profiles in laminar flow using deep learning surrogates. Journal of Fluid Mechanics, 919.

[2] Ma, P., Du, T., Zhang, J.Z., Wu, K., Spielberg, A., Katzschmann, R.K. and Matusik, W., 2021. Diffaqua: A differentiable computational design pipeline for soft underwater swimmers with shape interpolation. ACM Transactions on Graphics (TOG), 40(4), pp.1-14.

[3] Li, R., Li, X., Hui, K.H. and Fu, C.W., 2021. SP-GAN: Sphere-guided 3D shape generation and manipulation. ACM Transactions on Graphics (TOG), 40(4), pp.1-12.

- Literature review on surrogate modeling and shape optimization
- Reproduce some previous works on shape optimization within trained surrogate model
- Identify limitations of surrogate model (e.g. sampling efficiency, move from supervised to semi-supervised training, etc.) and extend the existing neural network model
- (If time allows) Expand upon the shape parametrization method to allow a more expressive shape-space

- Literature review on surrogate modeling and shape optimization - Reproduce some previous works on shape optimization within trained surrogate model - Identify limitations of surrogate model (e.g. sampling efficiency, move from supervised to semi-supervised training, etc.) and extend the existing neural network model - (If time allows) Expand upon the shape parametrization method to allow a more expressive shape-space

Please contact Mike Y. Michelis (michelism@ethz.ch) for further details. Submit your CV, your BSc and MSc transcripts, and one or two reference contacts.

Please contact Mike Y. Michelis (michelism@ethz.ch) for further details. Submit your CV, your BSc and MSc transcripts, and one or two reference contacts.