Physics-Informed Geometric Operators to Support Surrogate, Dimension Reduction and Generative Models for Engineering Design

In this work, we propose a set of physics-informed geometric operators (GOs) to enrich the geometric data provided for training surrogate/discriminative models, dimension reduction, and generative models, typically employed for performance prediction, dimension reduction, and creating data-driven parameterisations, respectively. However, as both the input and output streams of these models consist of low-level shape representations, they often fail to capture shape characteristics essential for performance analyses. Therefore, the proposed GOs exploit the differential and integral properties of shapes--accessed through Fourier descriptors, curvature integrals, geometric moments, and their invariants--to infuse high-level intrinsic geometric information and physics into the feature vector used for training, even when employing simple model architectures or low-level parametric descriptions. We showed that for surrogate modelling, along with the inclusion of the notion of physics, GOs enact regularisation to reduce over-fitting and enhance generalisation to new, unseen designs. Furthermore, through extensive experimentation, we demonstrate that for dimension reduction and generative models, incorporating the proposed GOs enriches the training data with compact global and local geometric features. This significantly enhances the quality of the resulting latent space, thereby facilitating the generation of valid and diverse designs. Lastly, we also show that GOs can enable learning parametric sensitivities to a great extent. Consequently, these enhancements accelerate the convergence rate of shape optimisers towards optimal solutions.

Generative VS non-Generative Models in Engineering Shape Optimization

In this work, we perform a systematic comparison of the effectiveness and efficiency of generative and non-generative models in constructing design spaces for novel and efficient design exploration and shape optimization. We apply these models in the case of airfoil/hydrofoil design and conduct the comparison on the resulting design spaces. A conventional Generative Adversarial Network (GAN) and a state-of-the-art generative model, the Performance-Augmented Diverse Generative Adversarial Network (PaDGAN), are juxtaposed with a linear non-generative model based on the coupling of the Karhunen-Lo\`eve Expansion and a physics-informed Shape Signature Vector (SSV-KLE). The comparison demonstrates that, with an appropriate shape encoding and a physics-augmented design space, non-generative models have the potential to cost-effectively generate high-performing valid designs with enhanced coverage of the design space. In this work, both approaches are applied to two large foil profile datasets comprising real-world and artificial designs generated through either a profile-generating parametric model or deep-learning approach. These datasets are further enriched with integral properties of their members' shapes as well as physics-informed parameters. Our results illustrate that the design spaces constructed by the non-generative model outperform the generative model in terms of design validity, generating robust latent spaces with none or significantly fewer invalid designs when compared to generative models. We aspire that these findings will aid the engineering design community in making informed decisions when constructing designs spaces for shape optimization, as we have show that under certain conditions computationally inexpensive approaches can closely match or even outperform state-of-the art generative models.

ShipHullGAN: A generic parametric modeller for ship hull design using deep convolutional generative model

In this work, we introduce ShipHullGAN, a generic parametric modeller built using deep convolutional generative adversarial networks (GANs) for the versatile representation and generation of ship hulls. At a high level, the new model intends to address the current conservatism in the parametric ship design paradigm, where parametric modellers can only handle a particular ship type. We trained ShipHullGAN on a large dataset of 52,591 \textit{physically validated} designs from a wide range of existing ship types, including container ships, tankers, bulk carriers, tugboats, and crew supply vessels. We developed a new shape extraction and representation strategy to convert all training designs into a common geometric representation of the same resolution, as typically GANs can only accept vectors of fixed dimension as input. A space-filling layer is placed right after the generator component to ensure that the trained generator can cover all design classes. During training, designs are provided in the form of a shape-signature tensor (SST) which harnesses the compact geometric representation using geometric moments that further enable the inexpensive incorporation of physics-informed elements in ship design. We have shown through extensive comparative studies and optimisation cases that ShipHullGAN can generate designs with augmented features resulting in versatile design spaces that produce traditional and novel designs with geometrically valid and practically feasible shapes.