论文标题
多孔介质中的参数流问题的Waserstein模型减少方法
Waserstein model reduction approach for parametrized flow problems in porous media
论文作者
论文摘要
这项工作的目的是为参数化的多孔介质方程构建一个减少阶模型。这种类型的问题的主要挑战是，溶液歧管的kolmogorov宽度通常很缓慢，因此使通常的线性模型级减少方法不合适。在这项工作中，我们研究了基于Wasserstein Barycenters在非保守问题的情况下，根据使用Wasserstein Barycenters提出的方法的适应。一维测试案例中的数值示例说明了这种方法的优点和局限性，并提出了我们打算将来要探索的进一步研究方向。
The aim of this work is to build a reduced-order model for parametrized porous media equations. The main challenge of this type of problems is that the Kolmogorov width of the solution manifold typically decays quite slowly and thus makes usual linear model-order reduction methods inappropriate. In this work, we investigate an adaptation of the methodology proposed in a previous work, based on the use of Wasserstein barycenters, to the case of non-conservative problems. Numerical examples in one-dimensional test cases illustrate the advantages and limitations of this approach and suggest further research directions that we intend to explore in the future.
