In recent years, the domain of fast flow field prediction has been vastly dominated by pixel-based convolutional neural networks. Yet, the recent advent of graph convolutional neural networks (GCNNs) has attracted considerable attention in the computational fluid dynamics (CFD) community. In this contribution, we proposed a GCNN structure as a surrogate model for laminar flow prediction around two-dimensional (2D) obstacles. Unlike traditional convolution on image pixels, the graph convolution can be directly applied on body-fitted triangular meshes, hence yielding an easy coupling with CFD solvers. The proposed GCNN model is trained over a dataset composed of CFD-computed laminar flows around 2000 random 2D shapes. Accuracy levels are assessed on reconstructed velocity and pressure fields around out-of-training obstacles and are compared with that of standard U-net architectures, especially in the boundary layer area.

In the past couple of years, the interest of the fluid mechanics community for deep reinforcement learning techniques has increased at fast pace, leading to a growing bibliography on the topic. Due to its ability to solve complex decision-making problems, deep reinforcement learning has especially emerged as a valuable tool to perform flow control, but recent publications also advertise the great potential for other applications, such as shape optimization or microfluidics. The present work proposes an exhaustive review of the existing literature and is a follow-up to our previous review on the topic. The contributions are regrouped by the domain of application and are compared together regarding algorithmic and technical choices, such as state selection, reward design, time granularity, and more. Based on these comparisons, general conclusions are drawn regarding the current state-of-the-art, and perspectives for future improvements are sketched.

Instabilities arise in a number of flow configurations. One such manifestation is the development of interfacial waves in multiphase flows, such as those observed in the falling liquid film problem. Controlling the development of such instabilities is a problem of both academic interest and industrial interest. However, this has proven challenging in most cases due to the strong nonlinearity and high dimensionality of the underlying equations. In the present work, we successfully apply Deep Reinforcement Learning (DRL) for the control of the one-dimensional depth-integrated falling liquid film. In addition, we introduce for the first time translational invariance in the architecture of the DRL agent, and we exploit locality of the control problem to define a dense reward function. This allows us to both speed up learning considerably and easily control an arbitrary large number of jets and overcome the curse of dimensionality on the control output size that would take place using a naïve approach. This illustrates the importance of the architecture of the agent for successful DRL control, and we believe this will be an important element in the effective application of DRL to large two-dimensional or three-dimensional systems featuring translational, axisymmetric, or other invariance.

This research gauges the capabilities of deep reinforcement learning (DRL) techniques for direct optimal shape design in computational fluid dynamics (CFD) systems. It uses policy based optimization, a single-step DRL algorithm intended for situations where the optimal policy to be learnt by a neural network does not depend on state. The numerical reward fed to the neural network is computed with an in-house stabilized finite elements environment combining variational multi-scale modeling of the governing equations, immerse volume method, and multi-component anisotropic mesh adaptation. Several cases are tackled in two and three dimensions, for which shapes with fixed camber line, angle of attack, and cross-sectional area are generated by varying a chord length and a symmetric thickness distribution (and possibly extruding in the off-body direction). At a zero incidence, the proposed DRL-CFD framework successfully reduces the drag of the equivalent cylinder (i.e., the cylinder of same cross-sectional area) by 48% at a Reynolds numbers in the range of a few hundreds. At an incidence of 30°, it increases the lift to drag ratio of the equivalent ellipse by 13% in two dimensions and 5% in three dimensions at a chord Reynolds numbers in the range of a few thousands. Although the low number of degrees of freedom inevitably constrains the range of attainable shapes, the optimal is systematically found to perform just as well as a conventional airfoil, despite DRL starting from the ground up and having no a priori knowledge of aerodynamic concepts. Such results showcase the potential of the method for black-box shape optimization of practically meaningful CFD systems. Since the resolution process is agnostic to details of the underlying fluid dynamics, they also pave the way for a general evolution of reference shape optimization strategies for fluid mechanics and any other domain where a relevant reward function can be defined.

The availability of accurate and efficient numerical simulation tools has become of utmost importance for the design and optimization phases of existing industrial processes. The latter requires the computation of multiple physical fields governed by coupled systems of partial differential equations and tends to require large computational resources. Recently, the coupling of machine learning techniques with numerical simulation tools has allowed lifting part of this computational burden, by replacing parts of the resolution process with trained neural networks, whose execution cost is far less than their traditional counterparts. In this work, an auto-encoder convolutional neural network is suggested to reduce the resolution cost of the forced cooling of a hot workpiece in a confined space by modeling the scalar transport equation coupled to the Navier–Stokes equations. Although the proposed model was trained on a relatively limited amount of data, it was able to generalize accurately for different cooling setups with different inlet locations, thus leading to a reliable deep learning-assisted numerical solver.