Stationary Flow Predictions Using Convolutional Neural Networks

Surrogate convolutional neural network models for steady computational fluid dynamics simulations

“…Here, w is the width of the input image and the output images and h is the corresponding height. Our approach is inspired by the work of Guo, Li, and Iorio [16] and has already been presented partly in [10]. Convolutional neural networks [25] are specialized neural networks for data with a tensor product grid-like topology; see also [13,Chapter 9].…”

“…Therefore, we will use two different image representations of the geometry, i.e., a signed distance function (SDF) representation and a binary representation; cf. [10,16]. Both representations are 256 × 128 px images.…”

“…In contrast to most other approaches, we are interested in geometry-dependent flow predictions, where the geometry is used as the input for the neural network and the whole flow field is obtained as the output. Our approach is inspired by the work of Guo, Li, and Iorio [16] and has already been partly presented in [10]. As in the original work [16], we employ convolutional neural networks (CNNs) in order to map from an image of the geometry to images of the resulting flow field, making use of the strengths of CNNs in processing image data.…”

Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models

“…1. the extraction of relevant flow features, such as recirculation regions or boundary layers through convolutional neural networks (CNNs) [24]; 2. the construction of inexpensive, non-intrusive approximations for output quantities of interest for fluid flows [25], or to velocity and pressure field, obtained through Reynolds-averaged Navier-Stokes (RANS) equations [26,27,28]; 3. data-driven turbulence models in RANS equations through a physics-informed machine learning approach [29], or data-driven eddy viscosity closure models in Large Eddy Simulations (LES) [30]; 4. the setting of closure models to stabilize a POD-Galerkin ROM [31] by using, e.g., recurrent neural networks (RNNs) to predict the impact of the unresolved scales on the resolved scales [32], or correction models to adapt a ROM to describe scenarios quite far from the ones seen during the training stage [33]; 5. the reconstruction of a high-resolution flow field from limited flow information [34], as well as the assimilation of flow measurements and computational flow dynamics models derived from first physical principles. This task can be cast in the framework of the so-called physics-informed neural networks [35,36], where NNs are trained to solve supervised learning tasks while respecting the fluid dynamics equations, or tackled by means of Bayesian neural networks [37]; 6. the nonintrusive estimation of POD coefficients through, e.g., feedforward NNs [38,39,40] or probabilistic NNs [41].…”

Towards high-accuracy deep learning inference of compressible turbulent flows over aerofoils

“…For many approaches, convolutional neural networks (CNNs) provide an important building block, e.g., for lightweight approximations of steady flows [7]. Aiming for the goal of accurate predictions of flow solutions, state-of-the-art deep learning methods and architectures have been developed for the inference of Reynolds-averaged Navier-Stokes solutions as well as steady laminar flow fields [8,9,10]. More recently, trained deep neural network models that infer flow fields have also been used as surrogate models to optimise shapes [11].…”