To tackle heterogeneous time-dependent problems, an algorithm that constructs problem-adapted basis functions in an embarrassingly parallel and local manner in time has recently been proposed in [Schleuss, Smetana, ter Maat, SIAM J. Sci. Comput., 2022+]. Several simulations of the problem are performed for only few time steps in parallel by starting at different, randomly drawn start time points. For this purpose, data-dependent probability distributions that are based on the (time-dependent) data functions of the problem, such as leverage scores, are employed. In this paper, we suggest as a key new contribution to perform a deterministic time point selection based on the (discrete) empirical interpolation method (DEIM) within the proposed algorithm. In numerical experiments we investigate the performance of a DEIM based time point selection and compare it to the leverage score sampling approach.

翻译：针对异构时间依赖问题，近期[Schleuss, Smetana, ter Maat, SIAM J. Sci. Comput., 2022+]提出了一种以时间局部且高度并行的方式构造问题自适应基函数的算法。该算法通过从随机选取的不同起始时间点并行执行问题模拟，仅需少量时间步即可完成。为此，采用基于问题（时间依赖）数据函数（如leverage分数）的数据驱动概率分布。本文提出一项关键新贡献：在算法中引入基于（离散）经验插值法（DEIM）的确定性时间点选取策略。通过数值实验，我们研究了基于DEIM的时间点选取性能，并将其与leverage分数采样方法进行对比。