The need of solving industrial problems using faster and less computationally expensive techniques is becoming a requirement to cope with the present digital transformation of most industries. Recently, data is conquering the domain of engineering with different purposes: (i) defining data-driven models of materials, processes, structures and systems, whose physics-based models, when they exists, remain too inaccurate; (ii) enriching the existing physics-based models within the so-called hybrid paradigm; and (iii) using advanced machine learning and artificial intelligence techniques for scales bridging (upscaling), that is, for creating models that operating at the coarse-grained scale (cheaper in what respect the computational resources) enables integrating the fine-scale richness. The present work addresses the last item, aiming at enhancing standard structural models (defined in 2D shell geometries) for accounting all the fine-scale details (3D with rich through-the-thickness behaviors). For this purpose, two main strategies will be combined: (i) the in-plane-out-of-plane proper generalized decomposition -PGD- serving to provide the fine-scale richness; and (ii) advance machine learning techniques able to learn and extract the regression relating the input parameters with those high-resolution detailed descriptions.

From the simplest models to complex deep neural networks, modeling turbulence with machine learning techniques still offers multiple challenges. In this context, the present contribution proposes a robust strategy using patch-based training to learn turbulent viscosity from flow velocities and demonstrates its efficient use on the Spalart–Allmaras turbulence model. Training datasets are generated for flow past two-dimensional obstacles at high-Reynolds numbers and used to train an auto-encoder type convolutional neural network with local patch inputs. Compared to a standard training technique, patch-based learning not only yields increased accuracy but also reduces the computational cost required for training.

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, which 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