MAD-TENSOR · Machine-learned Atomic Descriptors combined with TENSOR Networks unlocks predictive computational design of alloys

Metallic alloys form the backbone of modern infrastructure and technology in our society. Hence, alloys must be understood, not only by their macroscopic behavior, but rather through consideration of the interactions between many length scales, from angstroms to meters. In general, understanding cannot be developed by experiments alone, beyond observations of snapshots, but must be combined with atomistic simulations that can provide a deeper understanding of the nanoscale mechanisms that govern the dynamics observed in experiments.Machine-learning potentials (MLIPs) have been a breakthrough for providing the quantitative accuracy of quantum mechanics to atomistic simulations, required to predict the correct mechanisms. However, developing a universal MLIP that is quantitative over the whole composition space has thus far not been achieved. Current available approaches lack either computational efficiency or accuracy. Another breakthrough is required.To address these challenges, I propose to develop a novel architecture for potentials, equivariant tensor networks (ETNs), based on low-rank representations of high-dimensional tensors to reduce the number of parameters in approximating multidimensional functions. The two distinguishing features of ETNs that are key for developing predictive universal potentials are (i) high-dimensional convolutions represented using low-rank tensor networks, (ii) their factorization into small, equally-sized, but highly repetitive, operations which are lucrative for massive parallelization on modern HPC architectures, such as GPUs.Moreover, ETNs will allow to solve two additional urgent problems: (a) efficiently adding magnetic degrees freedom to the MLIP's functional form to compute magnetic properties with atomistic simulations, (b) the creation of an ""averaged"" ETN potential that allows to compute material properties of random alloys without requiring sampling over thousands of simulations of the true random alloy.""