Learned Turbulence Modelling with Differentiable Fluid Solvers: Physics-based Loss-functions and Optimisation Horizons

Abstract

In this paper, we train turbulence models based on convolutional neural networks. These learned turbulence models improve under-resolved low resolution solutions to the incompressible Navier-Stokes equations at simulation time. Our study involves the development of a differentiable numerical solver that supports the propagation of optimisation gradients through multiple solver steps. The significance of this property is demonstrated by the superior stability and accuracy of those models that unroll more solver steps during training. Furthermore, we introduce loss terms based on turbulence physics that further improve the model accuracy. This approach is applied to three two-dimensional turbulence flow scenarios, a homogeneous decaying turbulence case, a temporally evolving mixing layer, and a spatially evolving mixing layer. Our models achieve significant improvements of long-term a-posteriori statistics when compared to no-model simulations, without requiring these statistics to be directly included in the learning targets. At inference time, our proposed method also gains substantial performance improvements over similarly accurate, purely numerical methods.

arXiv commentPublished in the Journal of Fluid Mechanics (JFM), code & data available at: https://github.com/tum-pbs/differentiable-piso

References in corpus (11)

• Turbulence Modeling in the Age of Data
• Deep learning for universal linear embeddings of nonlinear dynamics
• Machine learning accelerated computational fluid dynamics
• Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows
• Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networks
• Deep Neural Networks for Data-Driven Turbulence Models
• Sub-grid modelling for two-dimensional turbulence using neural networks
• Inverse energy cascade in three-dimensional isotropic turbulence
• Training convolutional neural networks to estimate turbulent sub-grid scale reaction rates
• Embedded training of neural-network sub-grid-scale turbulence models
• High-order methods for decaying two-dimensional homogeneous isotropic turbulence

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