Sunwoong Yang

Yu-Eop Kang, Sunwoong Yang, Kwanjung Yee

Autoencoder-based reduced-order modeling (ROM) has recently attracted significant attention, owing to its ability to capture underlying nonlinear features. However, two critical drawbacks severely undermine its scalability to various physical applications: entangled and therefore uninterpretable latent variables (LVs) and the blindfold determination of latent space dimension. In this regard, this study proposes the physics-aware ROM using only interpretable and information-intensive LVs extracted by $β$-variational autoencoder, which are referred to as physics-aware LVs throughout this paper. To extract these LVs, their independence and information intensity are quantitatively scrutinized in a two-dimensional transonic flow benchmark problem. Then, the physical meanings of the physics-aware LVs are thoroughly investigated and we confirmed that with appropriate hyperparameter $β$, they actually correspond to the generating factors of the training dataset, Mach number and angle of attack. To the best of the authors' knowledge, our work is the first to practically confirm that $β$-variational autoencoder can automatically extract the physical generating factors in the field of applied physics. Finally, physics-aware ROM, which utilizes only physics-aware LVs, is compared with conventional ROMs, and its validity and efficiency are successfully verified.

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.

Sunwoong Yang, Hojin Kim, Yoonpyo Hong et al.

This study explores the potential of physics-informed neural networks (PINNs) for the realization of digital twins (DT) from various perspectives. First, various adaptive sampling approaches for collocation points are investigated to verify their effectiveness in the mesh-free framework of PINNs, which allows automated construction of virtual representation without manual mesh generation. Then, the overall performance of the data-driven PINNs (DD-PINNs) framework is examined, which can utilize the acquired datasets in DT scenarios. Its scalability to more general physics is validated within parametric Navier-Stokes equations, where PINNs do not need to be retrained as the Reynolds number varies. In addition, since datasets can be often collected from different fidelity/sparsity in practice, multi-fidelity DD-PINNs are also proposed and evaluated. They show remarkable prediction performance even in the extrapolation tasks, with $42\sim62\%$ improvement over the single-fidelity approach. Finally, the uncertainty quantification performance of multi-fidelity DD-PINNs is investigated by the ensemble method to verify their potential in DT, where an accurate measure of predictive uncertainty is critical. The DD-PINN frameworks explored in this study are found to be more suitable for DT scenarios than traditional PINNs from the above perspectives, bringing engineers one step closer to seamless DT realization.

Jeesuk Shin, Cheolwoong Kim, Sunwoong Yang et al.

Severe accidents (SAs) in nuclear power plants have been analyzed using thermal-hydraulic (TH) system codes such as MELCOR and MAAP. These codes efficiently simulate the progression of SAs, while they still have inherent limitations due to their inconsistent finite difference schemes. The use of empirical schemes incorporating both implicit and explicit formulations inherently induces unidirectional coupling in multi-physics analyses. The objective of this study is to develop a novel numerical method for TH system codes using physics-informed neural network (PINN). They have shown strength in solving multi-physics due to the innate feature of neural networks-automatic differentiation. We propose a node-assigned PINN (NA-PINN) that is suitable for the control volume approach-based system codes. NA-PINN addresses the issue of spatial governing equation variation by assigning an individual network to each nodalization of the system code, such that spatial information is excluded from both the input and output domains, and each subnetwork learns to approximate a purely temporal solution. In this phase, we evaluated the accuracy of the PINN methods for the hydrodynamic module. In the 6 water tank simulation, PINN and NA-PINN showed maximum absolute errors of 1.678 and 0.007, respectively. It should be noted that only NA-PINN demonstrated acceptable accuracy. To the best of the authors' knowledge, this is the first study to successfully implement a system code using PINN. Our future work involves extending NA-PINN to a multi-physics solver and developing it in a surrogate manner.

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%).

Sunwoong Yang, Youngkyu Lee, Namwoo Kang

This study presents an enhanced multi-fidelity Deep Operator Network (DeepONet) framework for efficient spatio-temporal flow field prediction when high-fidelity data is scarce. Key innovations include: a merge network replacing traditional dot-product operations, achieving 50.4% reduction in prediction error and 7.57% accuracy improvement while reducing training time by 96%; a transfer learning multi-fidelity approach that freezes pre-trained low-fidelity networks while making only the merge network trainable, outperforming alternatives by up to 76% and achieving 43.7% better accuracy than single-fidelity training; and a physics-guided subsampling method that strategically selects high-fidelity training points based on temporal dynamics, reducing high-fidelity sample requirements by 40% while maintaining comparable accuracy. Comprehensive experiments across multiple resolutions and datasets demonstrate the framework's ability to significantly reduce required high-fidelity dataset size while maintaining predictive accuracy, with consistent superior performance against conventional benchmarks.

Sunwoong Yang, Ricardo Vinuesa, Namwoo Kang

This study addresses the critical challenge of error accumulation in spatio-temporal auto-regressive (AR) predictions within scientific machine learning models by exploring temporal integration schemes and adaptive multi-step rollout strategies. We introduce the first implementation of the two-step Adams-Bashforth method specifically tailored for data-driven AR prediction, leveraging historical derivative information to enhance numerical stability without additional computational overhead. To validate our approach, we systematically evaluate time integration schemes across canonical 2D PDEs before extending to complex Navier-Stokes cylinder vortex shedding dynamics. Additionally, we develop three novel adaptive weighting strategies that dynamically adjust the importance of different future time steps during multi-step rollout training. Our analysis reveals that as physical complexity increases, such sophisticated rollout techniques become essential, with the Adams-Bashforth scheme demonstrating consistent robustness across investigated systems and our best adaptive approach delivering an 89% improvement over conventional fixed-weight methods while maintaining similar computational costs. For the complex Navier-Stokes vortex shedding problem, despite using an extremely lightweight graph neural network with just 1,177 trainable parameters and training on only 50 snapshots, our framework accurately predicts 350 future time steps reducing mean squared error from 0.125 (single-step direct prediction) to 0.002 (Adams-Bashforth with proposed multi-step rollout). Our integrated methodology demonstrates an 83% improvement over standard noise injection techniques and maintains robustness under severe spatial constraints; specifically, when trained on only a partial spatial domain, it still achieves 58% and 27% improvements over direct prediction and forward Euler methods, respectively.

Dongeon Lee, Sunwoong Yang, Jae-Won Oh et al.

Environmental pollution and fossil fuel depletion have prompted the need for renewable energy-based power generation. However, its stability is often challenged by low energy density and non-stationary conditions. Wave energy converters (WECs), in particular, need reliable real-time wave height prediction to address these issues caused by irregular wave patterns, which can lead to the inefficient and unstable operation of WECs. In this study, we propose an AI-powered reliable real-time wave height prediction model that integrates long short-term memory (LSTM) networks for temporal prediction with deep ensemble (DE) for robust uncertainty quantification (UQ), ensuring high accuracy and reliability. To further enhance the reliability, uncertainty calibration is applied, which has proven to significantly improve the quality of the quantified uncertainty. Using real operational data from an oscillating water column-wave energy converter (OWC-WEC) system in Jeju, South Korea, the model achieves notable accuracy (R2 > 0.9), while increasing uncertainty quality by over 50% through simple calibration technique. Furthermore, a comprehensive parametric study is conducted to explore the effects of key model hyperparameters, offering valuable guidelines for diverse operational scenarios, characterized by differences in wavelength, amplitude, and period. These results demonstrate the model's capability to deliver reliable predictions, facilitating digital twin of the ocean.

Sunwoong Yang, Ricardo Vinuesa, Namwoo Kang

This study aims to overcome the limitations of conventional deep-learning approaches based on convolutional neural networks in complex geometries and unstructured meshes by exploring the potential of Graph U-Nets for unsteady flow-field prediction. We present a comprehensive investigation of Graph U-Nets, originally developed for classification tasks, now tailored for mesh-agnostic spatio-temporal forecasting of fluid dynamics. Our focus is on enhancing their performance through systematic hyperparameter tuning and architectural modifications. 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 demonstrate the effectiveness of these enhancements in both transductive and inductive learning settings, showcasing the adaptability of Graph U-Nets to various flow conditions and mesh structures. This work contributes to the field of reduced-order modeling for computational fluid dynamics by establishing Graph U-Nets as a viable and flexible alternative to convolutional neural networks, capable of accurately and efficiently predicting complex fluid flow phenomena across diverse scenarios.

Sunwoong Yang, Sanga Lee, Kwanjung Yee

The inverse approach is computationally efficient in aerodynamic design as the desired target performance distribution is prespecified. However, it has some significant limitations that prevent it from achieving full efficiency. 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 wind turbine airfoil. Their results show that this framework is accurate, efficient, and flexible to be applied to other inverse design engineering applications.