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DTSTART;VALUE=DATE:20251106T140000
DTEND;VALUE=DATE:20251106T140000
UID:18821@agenda.unifr.ch
DESCRIPTION:We present a divide–et–impera extension of the (Quantics) Tensor Cross \nInterpolation (TCI) algorithm that adaptively partitions a high\ndimensional tensor into a collection of low-rank tensor train (TT) patches. \nEach patch is compressed with an explicit bond-dimension cap χpatch, \nthat triggers finer partitioning of the configuration space wherever the \ninput tensor has more interesting features (higher local rank). The local \ncap χpatch not only reduces the memory footprint of the tensor-train \nrepresentation of functions with sharply local features, but also tames the \nO(χ4) cost of MPO-MPO contractions by decomposing the global \nproduct into many rank-≤χpatch sub-contractions; in this context, the \nchoice of MPO patching scheme is essential, as it can markedly \nenhance—or, if poorly chosen, limit—the overall efficiency of patched \ncontractions. \nWe derive closed-form bounds that relate χpatch and the patch count \nNpatch to the memory and run-time advantage over a monolithic TCI or \nMPO contraction, and identify an “over-patching” regime that arises if \nthe cap is chosen too small. The theoretical estimates are validated by \ncomprehensive benchmarks and the advantage is tested on three \nnotorious bottlenecks ofmany-bodyphysics related to the Hubbard \nmodel: (i) the approximaton of a two-dimensional Matsubara Green’s \nfunction, (ii) the computation of the bare susceptibility χ0(q,iω) (bubble \ndiagram), and (iii) vertex contractions entering the Bethe-Salpeter \nequation for the single-impurity Anderson model. In all cases the patched \nstrategy yields significant memory savings together with speed-ups of \nnearly an order of magnitude, enabling computations that remain out of \npractical reach for the monolithic method. 
SUMMARY:Efficient Tensor Compression through Adaptive Patched  Quantics Tensor Cross Interpolation
CATEGORIES:Séminaire
LOCATION:PER 08\, 2.73\, Chemin du Musée 3\, 1700 Fribourg
URL;VALUE=URI:https://agenda.unifr.ch/e/fr/18821
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