Approximation of high dimensional functions is in the focus of machine learning and data-based scientific computing. In many applications, empirical risk minimisation techniques over nonlinear model classes are employed. Neural networks, kernel methods and tensor decomposition techniques are among the most popular model classes. We provide a numerical study comparing the performance of these methods on various high-dimensional functions with focus on optimal control problems, where the collection of the dataset is based on the application of the State-Dependent Riccati Equation.

翻译：高维函数的逼近是机器学习与基于数据的科学计算领域的核心问题。在许多应用中，通常采用基于非线性模型类的经验风险最小化技术。神经网络、核方法与张量分解技术属于最常用的模型类别。本文针对最优控制问题场景，通过数值实验对比了这些方法在不同高维函数上的表现性能，其中数据集是基于状态相关Riccati方程的应用采集的。