Enhancing Graph U-Nets for Mesh-Agnostic Spatio-Temporal Flow Prediction

This study aims to overcome the conventional deep-learning approaches based on convolutional neural networks, whose applicability to complex geometries and unstructured meshes is limited due to their inherent mesh dependency. We propose novel approaches to improve mesh-agnostic spatio-temporal prediction of transient flow fields using graph U-Nets, enabling accurate prediction on diverse mesh configurations. Key enhancements to the graph U-Net architecture, including the Gaussian mixture model convolutional operator and noise injection approaches, provide increased flexibility in modeling node dynamics: the former reduces prediction error by 95\% compared to conventional convolutional operators, while the latter improves long-term prediction robustness, resulting in an error reduction of 86\%. We also investigate transductive and inductive-learning perspectives of graph U-Nets with proposed improvements. In the transductive setting, they effectively predict quantities for unseen nodes within the trained graph. In the inductive setting, they successfully perform in mesh scenarios with different vortex-shedding periods, showing 98\% improvement in predicting the future flow fields compared to a model trained without the inductive settings. It is found that graph U-Nets without pooling operations, i.e. without reducing and restoring the node dimensionality of the graph data, perform better in inductive settings due to their ability to learn from the detailed structure of each graph. Meanwhile, we also discover that the choice of normalization technique significantly impacts graph U-Net performance.

Towards Reliable Uncertainty Quantification via Deep Ensembles in Multi-output Regression Task

Deep ensemble is a simple and straightforward approach for approximating Bayesian inference and has been successfully applied to many classification tasks. This study aims to comprehensively investigate this approach in the multi-output regression task to predict the aerodynamic performance of a missile configuration. By scrutinizing the effect of the number of neural networks used in the ensemble, an obvious trend toward underconfidence in estimated uncertainty is observed. In this context, we propose the deep ensemble framework that applies the post-hoc calibration method, and its improved uncertainty quantification performance is demonstrated. It is compared with Gaussian process regression, the most prevalent model for uncertainty quantification in engineering, and is proven to have superior performance in terms of regression accuracy, reliability of estimated uncertainty, and training efficiency. Finally, the impact of the suggested framework on the results of Bayesian optimization is examined, showing that whether or not the deep ensemble is calibrated can result in completely different exploration characteristics. This framework can be seamlessly applied and extended to any regression task, as no special assumptions have been made for the specific problem used in this study.

Physics-aware Reduced-order Modeling of Transonic Flow via $β$-Variational Autoencoder

Autoencoder-based reduced-order modeling has recently attracted significant attention, owing to the ability to capture underlying nonlinear features. However, its uninterpretable latent variables (LVs) severely undermine the applicability to various physical problems. This study proposes physics-aware reduced-order modeling using a $\beta$-variational autoencoder to address this issue. The presented approach can quantify the rank and independence of LVs, which is validated both quantitatively and qualitatively using various techniques. Accordingly, LVs containing interpretable physical features were successfully identified. It was also verified that these "physics-aware" LVs correspond to the physical parameters that are the generating factors of the dataset, i.e., the Mach number and angle of attack in this study. Moreover, the effects of these physics-aware LVs on the accuracy of reduced-order modeling were investigated, which verified the potential of this method to alleviate the computational cost of the offline stage by excluding physics-unaware LVs.

Inverse design optimization framework via a two-step deep learning approach: application to a wind turbine airfoil

Though inverse approach is computationally efficient in aerodynamic design as the desired target performance distribution is specified, it has some significant limitations that prevent full efficiency from being achieved. First, the iterative procedure should be repeated whenever the specified target distribution changes. Target distribution optimization can be performed to clarify the ambiguity in specifying this distribution, but several additional problems arise in this process such as loss of the representation capacity due to parameterization of the distribution, excessive constraints for a realistic distribution, inaccuracy of quantities of interest due to theoretical/empirical predictions, and the impossibility of explicitly imposing geometric constraints. To deal with these issues, a novel inverse design optimization framework with a two-step deep learning approach is proposed. A variational autoencoder and multi-layer perceptron are used to generate a realistic target distribution and predict the quantities of interest and shape parameters from the generated distribution, respectively. Then, target distribution optimization is performed as the inverse design optimization. The proposed framework applies active learning and transfer learning techniques to improve accuracy and efficiency. Finally, the framework is validated through aerodynamic shape optimizations of the airfoil of a wind turbine blade, where inverse design is actively being applied. The results of the optimizations show that this framework is sufficiently accurate, efficient, and flexible to be applied to other inverse design engineering applications.