论文标题
从低分辨率测量中重建准本地数值有效模型
Reconstruction of quasi-local numerical effective models from low-resolution measurements
论文作者
论文摘要
我们考虑基于粗测量的强烈异质介质中重建有效模型的有效模型的逆问题。该方法是由准本地数值有效的远期模型激励的，这些模型超出周期性假设和规模分离是可靠的。这项工作的目的是证明与这些有效模型相关的矩阵表示形式的识别。一方面，在直接重建是由于粗数据量表与要重建的微观量之间的不匹配而无法匹配的情况下，这提供了合理的替代物。另一方面，该方法使我们能够在数值同质化的背景下研究对某些非本地性的要求。在一系列数值实验中说明了反转过程及其性能的算法方面。
We consider the inverse problem of reconstructing an effective model for a prototypical diffusion process in strongly heterogeneous media based on coarse measurements. The approach is motivated by quasi-local numerical effective forward models that are provably reliable beyond periodicity assumptions and scale separation. The goal of this work is to show that an identification of the matrix representation related to these effective models is possible. On the one hand, this provides a reasonable surrogate in cases where a direct reconstruction is unfeasible due to a mismatch between the coarse data scale and the microscopic quantities to be reconstructed. On the other hand, the approach allows us to investigate the requirement for a certain non-locality in the context of numerical homogenization. Algorithmic aspects of the inversion procedure and its performance are illustrated in a series of numerical experiments.
