论文标题
数据驱动的通过特征增强基于可变缩放的薄板样物的外推驱动
Data-driven extrapolation via feature augmentation based on variably scaled thin plate splines
论文作者
论文摘要
数据驱动的外推需要根据可用数据的功能模型的定义，并且具有对未知动力学的可靠预测的应用范围。由于数据可能散布，因此我们将注意力集中在具有互联网的优势的内核模型上。确切地说，所提出的数值方法利用了所谓的可变缩放内核（VSK），这些核（VSK）被引入以基于离散数据实现类似功能增强的策略。由于数据可能存在不确定性，并且由于我们有兴趣建模所考虑的动力学的行为，因此我们通过山脊回归寻求正则化解决方案。为了关注多谐波花纹，我们研究了它们在VSK设置中的实现，并在Beppo-Levi空间中提供了错误界限。然后对该方法的性能进行测试，该功能在拉普拉斯变换反转框架中常见的功能。还进行了与支持向量回归（SVR）的比较，并表明该方法是有效的，特别是因为它不需要训练复杂的建筑结构。
The data driven extrapolation requires the definition of a functional model depending on the available data and has the application scope of providing reliable predictions on the unknown dynamics. Since data might be scattered, we drive our attention towards kernel models that have the advantage of being meshfree. Precisely, the proposed numerical method makes use of the so-called Variably Scaled Kernels (VSKs), which are introduced to implement a feature augmentation-like strategy based on discrete data. Due to the possible uncertainty on the data and since we are interested in modelling the behaviour of the considered dynamics, we seek for a regularized solution by ridge regression. Focusing on polyharmonic splines, we investigate their implementation in the VSK setting and we provide error bounds in Beppo-Levi spaces. The performances of the method are then tested on functions which are common in the framework of the Laplace transform inversion. Comparisons with Support Vector Regression (SVR) are also carried out and show that the proposed method is effective particularly since it does not require to train complex architecture constructions.
