Deploying deep learning in OpenFOAM with TensorFlow

We outline the development of a data science module within OpenFOAM which allows for the in-situ deployment of trained deep learning architectures for general-purpose predictive tasks. This module is constructed with the TensorFlow C API and is integrated into OpenFOAM as an application that may be linked at run time. Notably, our formulation precludes any restrictions related to the type of neural network architecture (i.e., convolutional, fully-connected, etc.). This allows for potential studies of complicated neural architectures for practical CFD problems. In addition, the proposed module outlines a path towards an open-source, unified and transparent framework for computational fluid dynamics and machine learning.

[1]  Vishwas Rao,et al.  Machine-Learning for Nonintrusive Model Order Reduction of the Parametric Inviscid Transonic Flow past an airfoil. , 2020 .

[2]  Prasanna Balaprakash,et al.  Recurrent Neural Network Architecture Search for Geophysical Emulation , 2020, SC20: International Conference for High Performance Computing, Networking, Storage and Analysis.

[3]  Kookjin Lee,et al.  Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders , 2018, J. Comput. Phys..

[4]  Karthik Duraisamy,et al.  Turbulence Modeling in the Age of Data , 2018, Annual Review of Fluid Mechanics.

[5]  Jean-Luc Aider,et al.  Closed-loop separation control using machine learning , 2014, Journal of Fluid Mechanics.

[6]  Paris Perdikaris,et al.  Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations , 2019, J. Comput. Phys..

[7]  R. Goodman,et al.  Application of neural networks to turbulence control for drag reduction , 1997 .

[8]  Heng Xiao,et al.  Quantifying and reducing model-form uncertainties in Reynolds-averaged Navier-Stokes simulations: A data-driven, physics-informed Bayesian approach , 2015, J. Comput. Phys..

[9]  Michele Milano,et al.  Application of machine learning algorithms to flow modeling and optimization , 1999 .

[10]  E. Jennings,et al.  A turbulent eddy-viscosity surrogate modeling framework for Reynolds-Averaged Navier-Stokes simulations , 2020 .

[11]  Prasanna Balaprakash,et al.  Time-series learning of latent-space dynamics for reduced-order model closure , 2019, Physica D: Nonlinear Phenomena.

[12]  A. Mohan,et al.  Compressed Convolutional LSTM: An Efficient Deep Learning framework to Model High Fidelity 3D Turbulence , 2019, 1903.00033.

[13]  Soshi Kawai,et al.  Kriging-model-based uncertainty quantification in computational fluid dynamics , 2014 .

[14]  Heng Xiao,et al.  Physics-informed covariance kernel for model-form uncertainty quantification with application to turbulent flows , 2019, Computers & Fluids.

[15]  Omer San,et al.  Machine learning closures for model order reduction of thermal fluids , 2018, Applied Mathematical Modelling.

[16]  Hrvoje Jasak,et al.  A tensorial approach to computational continuum mechanics using object-oriented techniques , 1998 .

[17]  Kai Fukami,et al.  Assessment of supervised machine learning methods for fluid flows , 2020 .

[18]  Heng Xiao,et al.  Recent progress in augmenting turbulence models with physics-informed machine learning , 2019, Journal of Hydrodynamics.

[19]  P. Durbin,et al.  Zonal Eddy Viscosity Models Based on Machine Learning , 2019, Flow, Turbulence and Combustion.

[20]  Louis J. Durlofsky,et al.  Error modeling for surrogates of dynamical systems using machine learning , 2017 .

[21]  Yike Guo,et al.  A Reduced Order Deep Data Assimilation model , 2020 .

[22]  B. Weigand,et al.  Towards a general data-driven explicit algebraic Reynolds stress prediction framework , 2019, International Journal of Heat and Fluid Flow.

[23]  Pierre Baldi,et al.  A Fortran-Keras Deep Learning Bridge for Scientific Computing , 2020, Sci. Program..

[24]  Benjamin Peherstorfer,et al.  Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems , 2019, Physica D: Nonlinear Phenomena.

[25]  Jamey D. Jacob,et al.  Sub-grid scale model classification and blending through deep learning , 2018, Journal of Fluid Mechanics.

[26]  J. Templeton,et al.  Reynolds averaged turbulence modelling using deep neural networks with embedded invariance , 2016, Journal of Fluid Mechanics.

[27]  S. Girimaji,et al.  Turbulence closure modeling with data-driven techniques: physical compatibility and consistency considerations , 2020, 2004.03031.

[28]  Karthik Duraisamy,et al.  Machine Learning-augmented Predictive Modeling of Turbulent Separated Flows over Airfoils , 2016, ArXiv.

[29]  P. Moin,et al.  A dynamic subgrid‐scale eddy viscosity model , 1990 .

[30]  K. Taira,et al.  Super-resolution reconstruction of turbulent flows with machine learning , 2018, Journal of Fluid Mechanics.

[31]  Steven L. Brunton,et al.  Machine Learning Control – Taming Nonlinear Dynamics and Turbulence , 2016, Fluid Mechanics and Its Applications.

[32]  J. Templeton.  Evaluation of machine learning algorithms for prediction of regions of high Reynolds averaged Navier Stokes uncertainty , 2015 .

[33]  A. Mohan,et al.  A Deep Learning based Approach to Reduced Order Modeling for Turbulent Flow Control using LSTM Neural Networks , 2018, 1804.09269.

[34]  Takaaki Murata,et al.  Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes , 2020, Theoretical and Computational Fluid Dynamics.

[35]  Omer San,et al.  Extreme learning machine for reduced order modeling of turbulent geophysical flows. , 2018, Physical review. E.

[36]  Han Gao,et al.  A Bi-fidelity Ensemble Kalman Method for PDE-Constrained Inverse Problems , 2020, ArXiv.

[37]  Louis J. Durlofsky,et al.  A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problems , 2019, J. Comput. Phys..

[38]  Nicholas Geneva,et al.  Quantifying model form uncertainty in Reynolds-averaged turbulence models with Bayesian deep neural networks , 2018, J. Comput. Phys..

[39]  Jinlong Wu,et al.  Physics-informed machine learning approach for augmenting turbulence models: A comprehensive framework , 2018, Physical Review Fluids.

[40]  P. Spalart.  A One-Equation Turbulence Model for Aerodynamic Flows , 1992 .

[41]  Yuji Hattori,et al.  Searching for turbulence models by artificial neural network , 2016, 1607.01042.

[42]  Petros Koumoutsakos,et al.  Machine Learning for Fluid Mechanics , 2019, Annual Review of Fluid Mechanics.

[43]  Jian-Xun Wang,et al.  Physics-constrained bayesian neural network for fluid flow reconstruction with sparse and noisy data , 2020, Theoretical and Applied Mechanics Letters.

[44]  Prasanna Balaprakash,et al.  Non-autoregressive time-series methods for stable parametric reduced-order models , 2020, 2006.14725.

[45]  George Em Karniadakis,et al.  Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations , 2020, Science.

[46]  Kai Fukami,et al.  Probabilistic neural networks for fluid flow surrogate modeling and data recovery , 2020 .

[47]  O. San,et al.  Data assimilation empowered neural network parametrizations for subgrid processes in geophysical flows , 2020, 2006.08901.

[48]  Robert J. Martinuzzi,et al.  Machine learning strategies applied to the control of a fluidic pinball , 2020, Physics of Fluids.

[49]  Xi-yun Lu,et al.  Deep learning methods for super-resolution reconstruction of turbulent flows , 2020, Physics of Fluids.

[50]  Kai Fukami,et al.  Convolutional neural network based hierarchical autoencoder for nonlinear mode decomposition of fluid field data , 2020, Physics of Fluids.

[51]  Luning Sun,et al.  Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data , 2019, Computer Methods in Applied Mechanics and Engineering.