This study presents an enhanced multi-fidelity deep operator network (DeepONet) framework for efficient spatio-temporal flow field prediction, with particular emphasis on practical scenarios where high-fidelity data is scarce. We introduce several key innovations to improve the framework's efficiency and accuracy. First, we enhance the DeepONet architecture by incorporating a merge network that enables more complex feature interactions between operator and coordinate spaces, achieving a 50.4% reduction in prediction error compared to traditional dot-product operations. We further optimize the architecture through temporal positional encoding and point-based sampling strategies, achieving a 7.57% improvement in prediction accuracy while reducing training time by 96% through efficient sampling and automatic mixed precision training. Building upon this foundation, we develop a transfer learning-based multi-fidelity framework that leverages knowledge from pre-trained low-fidelity models to guide high-fidelity predictions. Our approach freezes the pre-trained branch and trunk networks while making only the merge network trainable during high-fidelity training, preserving valuable low-fidelity representations while efficiently adapting to high-fidelity features. Through systematic investigation, we demonstrate that this fine-tuning strategy not only significantly outperforms linear probing and full-tuning alternatives but also surpasses conventional multi-fidelity frameworks by up to 76%, while achieving up to 43.7% improvement in prediction accuracy compared to single-fidelity training. The core contribution lies in our novel time-derivative guided sampling approach: it maintains prediction accuracy equivalent to models trained with the full dataset while requiring only 60% of the original high-fidelity samples.

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.

This study addresses the critical challenge of error accumulation in spatio-temporal auto-regressive predictions within scientific machine learning models by introducing innovative temporal integration schemes and adaptive multi-step rollout strategies. We present a comprehensive analysis of time integration methods, highlighting the adaptation of the two-step Adams-Bashforth scheme to enhance long-term prediction robustness in auto-regressive models. Additionally, we improve temporal prediction accuracy through a multi-step rollout strategy that incorporates multiple future time steps during training, supported by three newly proposed approaches that dynamically adjust the importance of each future step. By integrating the Adams-Bashforth scheme with adaptive multi-step strategies, our graph neural network-based auto-regressive model accurately predicts 350 future time steps, even under practical constraints such as limited training data and minimal model capacity -- achieving an error of only 1.6% compared to the vanilla auto-regressive approach. Moreover, our framework demonstrates an 83% improvement in rollout performance over the standard noise injection method, a standard technique for enhancing long-term rollout performance. Its effectiveness is further validated in more challenging scenarios with truncated meshes, showcasing its adaptability and robustness in practical applications. This work introduces a versatile framework for robust long-term spatio-temporal auto-regressive predictions, effectively mitigating error accumulation across various model types and engineering discipline.

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.

This paper proposes a framework that optimizes the linkage mechanism of the quasi-serial manipulator for target tasks. This process is explained through a case study of 2-degree-of-freedom linkage mechanisms, which significantly affect the workspace of the quasi-serial manipulator. First, a vast quasi-serial mechanism is generated with a workspace satisfying a target task and it converts it into a 3D CAD model. Then, the workspace and required torque performance of each mechanism are evaluated through kinematic and dynamic analysis. A deep learning-based surrogate model is leveraged to efficiently predict mechanisms and performance during the optimization process. After model training, a multi-objective optimization problem is formulated under the mechanical and dynamic conditions of the manipulator. The design goal of the manipulator is to recommend quasi-serial mechanisms with optimized kinematic (workspace) and dynamic (joint torque) performance that satisfies the target task. To investigate the underlying physics from the obtained Pareto solutions, various data mining techniques are performed to extract design rules that can provide practical design guidance. Finally, the manipulator was designed in detail for realization with 3D printed parts, including topology optimization. Also, the task-based optimized manipulator is verified through a payload test. Based on these results, the proposed framework has the potential for other real applications as realized cases and provides a reasonable design plan through the design rule extraction.

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.

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.

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.