图指令神经网络用于基于稀疏网格的不连续检测器
Graph-Instructed Neural Networks for Sparse Grid-Based Discontinuity Detectors
AI总结：
本文提出基于图指令神经网络和稀疏网格的不连续检测方法，适用于高维域，通过递归算法和数值实验验证了其高效性和鲁棒泛化能力。
摘要：
本文提出了一种检测不连续函数不连续界面的新方法。该方法利用图指令神经网络（GINNs）和稀疏网格，以解决维度大于3的域中的不连续检测问题。GINNs经过训练，用于识别稀疏网格上的问题点，利用基于网格构建的图结构，实现高效且准确的不连续检测性能。我们还引入了一种用于通用稀疏网格检测器的递归算法，该算法具有收敛特性和易于应用的特点。在维度n=2和n=4的函数上的数值实验证明了GINNs在检测不连续界面方面的效率和鲁棒泛化能力。值得注意的是，训练好的GINNs具有可移植性和多功能性，允许集成到各种算法中并在用户之间共享。
英文摘要：
In this paper, we present a novel approach for detecting the discontinuity interfaces of a discontinuous function. This approach leverages Graph-Instructed Neural Networks (GINNs) and sparse grids to address discontinuity detection also in domains of dimension larger than 3. GINNs, trained to identify troubled points on sparse grids, exploit graph structures built on the grids to achieve efficient and accurate discontinuity detection performances. We also introduce a recursive algorithm for general sparse grid-based detectors, characterized by convergence properties and easy applicability. Numerical experiments on functions with dimensions n = 2 and n = 4 demonstrate the efficiency and robust generalization properties of GINNs in detecting discontinuity interfaces. Notably, the trained GINNs offer portability and versatility, allowing integration into various algorithms and sharing among users.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
