从低分辨率测量重建准局部数值有效模式
Reconstruction of quasi-local numerical effective models from low-resolution measurements
摘要：
本文研究了基于粗糙测量的强非均匀介质中典型扩散过程的有效模型重建问题。该方法的动机是准本地数值有效的正演模型，可证明可靠的周期性假设和尺度分离。这项工作的目标是表明，这些有效的模型相关的矩阵表示的识别是可能的。一方面，这提供了一个合理的替代的情况下，直接重建是不可行的，由于粗数据尺度和微观量之间的不匹配，以重建。另一方面，该方法允许我们调查的要求，在一定的非局部性的背景下，数值均匀化。在一系列的数值实验中说明了反演过程及其性能的数学方面。
英文摘要：
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.
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