Sun-Woong Yang

Sunwoong Yang, Kwanjung Yee

This study aims to comprehensively investigate the deep ensemble approach, an approximate Bayesian inference, in the multi-output regression task for predicting the aerodynamic performance of a missile configuration. To this end, the effect of the number of neural networks used in the ensemble, which has been blindly adopted in previous studies, is scrutinized. As a result, an obvious trend towards underestimation of uncertainty as it increases is observed for the first time, and in this context, we propose the deep ensemble framework that applies the post-hoc calibration method to improve its uncertainty quantification performance. It is compared with Gaussian process regression and is shown to have superior performance in terms of regression accuracy ($\uparrow55\sim56\%$), reliability of estimated uncertainty ($\uparrow38\sim77\%$), and training efficiency ($\uparrow78\%$). Finally, the potential impact of the suggested framework on the Bayesian optimization is briefly examined, indicating that deep ensemble without calibration may lead to unintended exploratory behavior. This UQ 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.

Jiyong Kim, Sunwoong Yang, Namwoo Kang

This study introduces a novel point-wise diffusion model that processes spatio-temporal points independently to efficiently predict complex physical systems with shape variations. This methodological contribution lies in applying forward and backward diffusion processes at individual spatio-temporal points, coupled with a point-wise diffusion transformer architecture for denoising. Unlike conventional image-based diffusion models that operate on structured data representations, this framework enables direct processing of any data formats including meshes and point clouds while preserving geometric fidelity. We validate our approach across three distinct physical domains with complex geometric configurations: 2D spatio-temporal systems including cylinder fluid flow and OLED drop impact test, and 3D large-scale system for road-car external aerodynamics. To justify the necessity of our point-wise approach for real-time prediction applications, we employ denoising diffusion implicit models (DDIM) for efficient deterministic sampling, requiring only 5-10 steps compared to traditional 1000-step and providing computational speedup of 100 to 200 times during inference without compromising accuracy. In addition, our proposed model achieves superior performance compared to image-based diffusion model: reducing training time by 94.4% and requiring 89.0% fewer parameters while achieving over 28% improvement in prediction accuracy. Comprehensive comparisons against data-flexible surrogate models including DeepONet and Meshgraphnet demonstrate consistent superiority of our approach across all three physical systems. To further refine the proposed model, we investigate two key aspects: 1) comparison of final physical states prediction or incremental change prediction, and 2) computational efficiency evaluation across varying subsampling ratios (10%-100%).