In a nutshell, quantized tensor decompositions (QTDs) are a combination of reshaping lower-dimensional arrays to higher-dimensional ones and representing the resulting multidimensional arrays using tensor decompositions. QTDs have proven useful for approximating functions exhibiting, for example, point singularities, boundary layers, or multiple length scales. This observation makes it tempting to apply them to solving PDEs. Nevertheless, it appears that severe stability issues occur when trying to solve discretized PDEs in a quantized tensor format. In this talk, I will discuss how to overcome this issue for certain PDEs. I will also present new theoretical results on approximating functions with QTDs and showcase several application areas.
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