Effective data reduction techniques are crucial for enhancing computational efficiency in complex industrial processes such as forging. In this study, we investigate various discretization and mesh adaptivity strategies using Proper Orthogonal Decomposition (POD) to optimize data reduction fidelity in forging simulations. We focus particularly on r-adaptivity techniques, which ensure a consistent number of elements throughout the field representation, filling a gap in existing research that predominantly concentrates on h-adaptivity. Our investigation compares isotropic mesh approaches with anisotropic mesh adaptations, including gradient-based, isolines-based, and spring-energy-based methods. Through numerical simulations and analysis, we demonstrate that these anisotropic techniques provide superior fidelity in representing deformation fields compared to isotropic meshes. These improvements are achieved while maintaining a similar level of model reduction efficiency. This enhancement in representation leads to improved data reduction quality, forming the foundation for data-driven models. This research contributes to advancing the understanding of mesh adaptivity approaches and their potential applications in data-driven modeling across various industrial domains.

中文翻译：

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增强锻造过程中的数据表示：研究具有适当正交分解缩减的离散化和 R 自适应策略


有效的数据缩减技术对于提高复杂工业过程（如锻造）的计算效率至关重要。在本研究中，我们使用适当正交分解 （POD） 研究了各种离散化和网格自适应策略，以优化锻造仿真中的数据缩减保真度。我们特别关注 r 自适应技术，该技术可确保整个场表示中元素数量的一致性，填补了主要关注 h 自适应性的现有研究中的空白。我们的研究将各向同性网格方法与各向异性网格适应进行了比较，包括基于梯度、基于等值线和基于弹簧能量的方法。通过数值模拟和分析，我们证明，与各向同性网格相比，这些各向异性技术在表示变形场方面提供了卓越的保真度。这些改进是在保持类似级别的模型缩减效率的同时实现的。这种表示的增强可以提高数据缩减质量，从而为数据驱动模型奠定基础。这项研究有助于促进对网格自适应方法及其在各种工业领域的数据驱动建模中的潜在应用的理解。