This work proposes the extended functional tensor train (EFTT) format for compressing and working with multivariate functions on tensor product domains. Our compression algorithm combines tensorized Chebyshev interpolation with a low-rank approximation algorithm that is entirely based on function evaluations. Compared to existing methods based on the functional tensor train format, the adaptivity of our approach often results in reducing the required storage, sometimes considerably, while achieving the same accuracy. In particular, we reduce the number of function evaluations required to achieve a prescribed accuracy by up to over 96% compared to the algorithm from [Gorodetsky, Karaman and Marzouk, Comput. Methods Appl. Mech. Eng., 347 (2019)].

翻译：本文提出扩展函数张量列（EFTT）格式，用于压缩和处理张量积域上的多元函数。我们的压缩算法结合了张量切比雪夫插值与完全基于函数评估的低秩逼近算法。与现有基于函数张量列格式的方法相比，我们方法的自适应性通常能够在保持相同精度的同时减少所需存储量，有时甚至显著降低。特别地，与[Gorodetsky, Karaman and Marzouk, Comput. Methods Appl. Mech. Eng., 347 (2019)]中的算法相比，我们在达到指定精度所需的函数评估次数上最多减少了96%以上。