In this study, we implement a low-rank approximation of Moment Tensor Potential (MTP) based on the tensor train (TT) decomposition. The implemented tensor-factorized MTP (TFMTP) and the original MTP model are actively trained via a MaxVol-based algorithm during molecular dynamics simulations of a four-component molten salt mixture, LiF-NaF-KF (FLiNaK), and geometry optimizations of a five-component equiatomic Mo-Nb-Ta-W-V random alloy. We demonstrate that under a 1.5-fold compression, TFMTP requires two times fewer configurations for fitting than the original MTP model, while maintaining an indistinguishable level of accuracy. These actively trained MTP and TFMTP models are further used to evaluate the density and viscosity of FLiNaK at temperatures ranging from 600 to 1200 K, as well as the elastic constants and bulk modulus of the Mo-Nb-Ta-W-V alloy at zero temperature. For both atomic systems, the differences in physical properties predicted by MTP and TFMTP are negligible.
This work systematically investigates the tensor train (TT) compressibility of grid-represented Hartree-Fock (HF) and Density Functional Theory (DFT) orbitals across a range of molecular systems and TT formats (standard, quantized, and z-permuted quantized). To overcome limitations of current TT solvers, we employ a no...
Ruslan A. Mallaev, D. Morozov, Dmitry A. Zheltkov et al.· Journal of Chemical Physics· 0 citations
We propose a parameter-reduced version of magnetic Moment Tensor Potential (mMTP) based on various matrix and tensor decompositions. The resulting compressed magnetic machine-learning potential reduces the number of parameters by a factor of approximately 1.5-3 without compromising predictive performance on the validat...
Alexey S. Kotykhov, Alexander V. Shapeev, Maxim V. Rakhuba et al.· 0 citations
General-purpose machine-learning force fields (MLFFs) for materials are now trained on the order of $100$ million structures, assuming transferability requires such scale. We test this premise on OMat24, the largest available materials dataset, by training MACE models on subsets of $6.5$ million atoms, less than $1\%$...
Evgeny Moerman, Igor Poltavsky, Anton Charkin-Gorbulin et al.· 0 citations
Abstract.
Approximating a tensor in the tensor train (TT) format has many important applications in scientific computing. Rounding a TT tensor involves further compressing a tensor that is already in the TT format. This paper proposes new randomized algorithms for TT-rounding that use sketches based on Khatri-Rao prod...
Hussam Al Daas, Grey Ballard, L. Grigori et al.· SIAM Journal on Scientific C...· 0 citations
In recent years, there are many surrogates for tensor tubal rank. In this paper, we propose a hybrid norm consisting of the weighted nuclear norm and the weighted Frobenius norm (WTNFN) of a tensor. The WTNFN is a surrogate for tensor tubal rank, and studies the weighted tensor nuclear and Frobenius norm minimization (...
Xiang-Yi Wang, Wei-Gao Jiang· Advances in Applied Mathemat...· 0 citations
We propose a randomized, streamable algorithm that computes a tensor-train approximation of a matrix-vector product without ever forming the full intermediate tensor. We develop three contraction strategies for streaming tensor-train approximation (STTA): sequential, fused, and pre-sketched. We focus on the regime of l...
Alberto Bucci, S. Güttel, J. Pearson· 0 citations
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