Multi-fidelity generative deep learning turbulent flows

Abstract

In computational fluid dynamics, there is an inevitable trade off between accuracy and computational cost. In this work, a novel multi-fidelity deep generative model is introduced for the surrogate modeling of high-fidelity turbulent flow fields given the solution of a computationally inexpensive but inaccurate low-fidelity solver. The resulting surrogate is able to generate physically accurate turbulent realizations at a computational cost magnitudes lower than that of a high-fidelity simulation. The deep generative model developed is a conditional invertible neural network, built with normalizing flows, with recurrent LSTM connections that allow for stable training of transient systems with high predictive accuracy. The model is trained with a variational loss that combines both data-driven and physics-constrained learning. This deep generative model is applied to non-trivial high Reynolds number flows governed by the Navier-Stokes equations including turbulent flow over a backwards facing step at different Reynolds numbers and turbulent wake behind an array of bluff bodies. For both of these examples, the model is able to generate unique yet physically accurate turbulent fluid flows conditioned on an inexpensive low-fidelity solution.

Conditional variational autoencoders for probabilistic wind turbine blade fatigue estimation using Supervisory, Control, and Data Acquisition data

“…In the offered case study, we demonstrated this idea on short‐term fatigue damage equivalent loads for wind turbines. Other wind‐energy related problems where CVAEs may find application are, for instance, wind farm level SCADA data modeling 48 or turbulence modeling 84,85 where finer turbulence scales are resolved in a data‐driven manner in place of the mostly empirical and mathematically simplified standard classical approaches.…”

Enforcing Imprecise Constraints on Generative Adversarial Networks for Emulating Physical Systems

“…This work is complementary to the work presented in a companion paper that studied enforcing statistical constraints [36]. While precise constraints have previously been used as regularization in various fields (e.g., natural language processing [37], lake temperature modeling [38,39], general dynamical systems [25], fluid flow simulations [9,11,12,40], and more specifically in turbulent flow simulations and generation [41][42][43]), the effects, performances, and best practices of imposing imprecise constraints in generative models still need further investigations.…”

Multi-fidelity reduced-order surrogate modelling

“…A wide range of MF surrogate modelling techniques have been developed based on Gaussian processes [41][42][43] and neural networks (NNs) [44][45][46][47][48]. They have found recent applications in many areas of scientific computing, including uncertainty quantification, inference and optimization [49][50][51][52][53][54][55]. Nevertheless, MF techniques often become impractical when approximating high-dimensional systems, thereby limiting their ability to directly approximate the full solution fields of PDEs.…”