论文标题
通过张量投票增强了无模型数据驱动的计算机制
Model-free Data-Driven Computational Mechanics Enhanced by Tensor Voting
论文作者
论文摘要
最初由Kirchdoerfer＆Ortiz（2016）引入的数据驱动的计算范式通过将局部线性切线空间纳入数据集来扩展。这些切线空间是通过Mordohai＆Medioni（2010）引入的张量投票方法构建的，该方法改善了数据集的基础结构的学习。张量投票是一种基于实例的机器学习技术，它积累了从最近的邻居中积累投票，以建立二阶张量，编码切线和正常的基础数据结构。这里提出的二阶数据驱动范式是一种用于距离最小化和熵最大化数据驱动方案的插入方法。与其前身一样，所得的方法旨在最大程度地减少相位空间上适当定义的自由能，但受到兼容性和平衡约束的影响。由于数据结构分析是在离线步骤中执行的，因此该方法的实现是直接且在数值上有效的。提出了所选的数值示例，这些示例建立了通过张量投票对理想和嘈杂数据集增强的数据驱动求解器的高阶收敛属性。
The data-driven computing paradigm initially introduced by Kirchdoerfer & Ortiz (2016) is extended by incorporating locally linear tangent spaces into the data set. These tangent spaces are constructed by means of the tensor voting method introduced by Mordohai & Medioni (2010) which improves the learning of the underlying structure of a data set. Tensor voting is an instance-based machine learning technique which accumulates votes from the nearest neighbors to build up second-order tensors encoding tangents and normals to the underlying data structure. The here proposed second-order data-driven paradigm is a plug-in method for distance-minimizing as well as entropy-maximizing data-driven schemes. Like its predecessor, the resulting method aims to minimize a suitably defined free energy over phase space subject to compatibility and equilibrium constraints. The method's implementation is straightforward and numerically efficient since the data structure analysis is performed in an offline step. Selected numerical examples are presented that establish the higher-order convergence properties of the data-driven solvers enhanced by tensor voting for ideal and noisy data sets.
