Models with dominant advection always posed a difficult challenge for projection-based reduced order modelling. Many methodologies that have recently been proposed are based on the pre-processing of the full-order solutions to accelerate the Kolmogorov N-width decay thereby obtaining smaller linear subspaces with improved accuracy. These methods however must rely on the knowledge of the characteristic speeds in phase space of the solution, limiting their range of applicability to problems with explicit functional form for the advection field. In this work we approach the problem of automatically detecting the correct pre-processing transformation in a statistical learning framework by implementing a deep-learning architecture. The purely data-driven method allowed us to generalise the existing approaches of linear subspace manipulation to non-linear hyperbolic problems with unknown advection fields. The proposed algorithm has been validated against simple test cases to benchmark its performances and later successfully applied to a multiphase simulation.
翻译:最近提出的许多方法都基于对加速科尔莫戈罗夫N-width衰减的全序解决办法的预处理,从而获得更精准的较小线性子空间,但这些方法必须依靠对解决办法阶段空间的特性速度的了解,将其适用范围限制在对冲领域具有明显功能形式的问题的可适用性。在这项工作中,我们通过实施深层学习结构,处理在统计学习框架中自动发现正确的预处理变的问题。纯粹以数据为驱动的方法使我们能够将线性子空间操纵的现有方法推广到非线性双向问题和未知的对冲场。提议的算法已经根据简单的测试案例加以验证,以衡量其性能,随后成功地应用于多阶段模拟。