SamplerID — interpolating millions of points of low-rank functions

A C++17 library for learning tensor-network surrogates of expensive multivariate functions f(i_0, ..., i_{N-1}) -> T from a small number of evaluations.

The headline feature is a variant of Tensor Cross Interpolation (TCI) allowing user-provided pivots: you can sample millions of points separately and later combine the learned tensor trains without losing information. The cost scales linearly with the number of pivots.

What's inside

Core decomposition

• Interpolative decomposition (ID) of a matrix via rank-revealing pivoted QR (LAPACK geqp3)

Tensor trains (chain topology)

• TensorTrain<T> — basic TT container with eval, sum, overlap, and norm.
• tt_id<T> — TCI-style TT construction using row/column ID (instead of CUR). DMRG-style left/right sweeps.
• addPivotsAllBonds — linear-cost interpolation of a batch of global pivots. Sample independently, then merge.
• block_tt_id<T> — learn n functions simultaneously into one TT with a "fat" core of local dim n * d_center at the sweep center; all other cores stay the usual shape [r, d, r'].

Tree tensor networks

• TreeTopology — pure topology: ordered neighbors per node, a root, a phys set tagging physical nodes. Two edge iterators leaves_to_root and root_to_leaves to generate chain-like algorithms.
• TensorTree<T> — tensor-tree container with eval, sum, overlap, norm. All contractions are written as a chain-like sweep over leaves_to_root(): the tree recursion lives in the iterator, the loop body sees only one edge at a time.
• tree_tt_id<T> — ID-based construction of a tree tensor network, generalizing tt_id to arbitrary tree topologies (chain, Y-tree, binary tree, …). Same addPivotsAllBonds API for batched pivots.

Quantics

• Quantics grid and QTT learning on top of tt_id.

Building & testing

cmake -S . -B build
cmake --build build -j
ctest --test-dir build

LibTorch is downloaded on the fly if no local libtorch/ is found. Test binaries: test_interp_decomp, test_tt, test_q_tt_id, test_block_tt_id, test_tree_tt_id.

Dependencies

• LibTorch (C++) — tensor manipulation
• LAPACK — pivoted QR, SVD, triangular solves
• Catch2 v3 — testing (fetched by CMake)