Yong-Hyuk Kim

Maritime search and rescue requires probabilistic decision-making under uncertainty about a drifting target’s location and constraints on search resources. Classical search theory provides a basis for allocating search effort through the probability of containment, probability of detection, and probability of success. Advances in numerical modeling and artificial intelligence have expanded the capabilities of drift prediction and search planning, but improvements in prediction accuracy do not necessarily translate into better search outcomes. This structured narrative review examines the development of these research streams and their coupling through probability representations, including probability-of-containment maps. An illustrative evidence map of ten selected cases distinguishes implemented coupling from evidence that isolates the downstream effects of prediction changes. The cases provide limited evidence tracing these effects through probability representation, planning, and operational outcomes under common evaluation conditions. The synthesis organizes evaluation into four stages: Prediction Gain, Information Gain, Decision Gain, and Operational Gain. Decision Gain denotes improved plan quality under a common evaluation criterion, rather than a change in the plan alone. The review outlines common evaluation conditions and a factorial comparison for separating prediction-side, planning-side, and combined effects. These recommendations support evaluation of whether artificial-intelligence-based prediction improvements lead to better search decisions, detection outcomes, and resource use.

In maritime search and rescue (SAR), rapid and accurate prediction of a castaway’s drift trajectory is essential because survival probability decreases sharply over time. However, conventional physics-based drift prediction models often exhibit substantial uncertainty because they cannot fully capture complex environmental drivers and the diverse characteristics of drifting objects. To address this limitation, this study proposes a machine learning-based drift prediction framework that integrates observed surface drifter data, OpenDrift simulations, and environmental forcings (wind velocity and current velocity). Within this framework, physics-based drift models and historical observations are treated as structured knowledge that guides the learning process. Five prediction models (linear regression, support vector regression, multi-layer perceptron, light gradient boosting model, and long short-term memory) are employed for direct trajectory prediction and correction of OpenDrift forecasts. The framework further incorporates time-series feature expansion, feature selection using SHapley Additive exPlanations, and incremental learning to adapt to previously unseen drifting objects. In addition, an ensemble strategy is introduced that combines genetic algorithm-based weight optimization with dynamic updates via the weighted majority algorithm, enabling robust performance under real-world maritime uncertainty. Experiments using 2021–2023 surface drifter observations show that the proposed framework reduces mean absolute error by more than 70% and improves normalized cumulative Lagrangian separation by more than 80% compared with OpenDrift. These results demonstrate that the proposed framework not only enables reliable drift prediction but also serves as a practical, knowledge-driven decision support system for maritime SAR operations, supporting more efficient search and rescue planning.

Virtual reality (VR) has emerged as a complex technological domain that demands high levels of realism and interactivity. At the core of this immersive experience lies a broad spectrum of mathematical modeling techniques. This survey explores how mathematical foundations support and enhance key VR components, including physical simulations, 3D spatial analysis, rendering pipelines, and user interactions. We review differential equations and numerical integration methods (e.g., Euler, Verlet, Runge–Kutta (RK4)) used to simulate dynamic environments, as well as geometric transformations and coordinate systems that enable seamless motion and viewpoint control. The paper also examines the mathematical underpinnings of real-time rendering processes and interaction models involving collision detection and feedback prediction. In addition, recent developments such as physics-informed neural networks, differentiable rendering, and neural scene representations are presented as emerging trends bridging classical mathematics and data-driven approaches. By organizing these elements into a coherent mathematical framework, this work aims to provide researchers and developers with a comprehensive reference for applying mathematical techniques in VR systems. The paper concludes by outlining the open challenges in balancing accuracy and performance and proposes future directions for integrating advanced mathematics into next-generation VR experiences.