Researchers at The University of New Mexico and Los Alamos National Laboratory have introduced a new computational framework that addresses a longstanding problem in statistical physics. The Tensors for High-dimensional Object Representation (THOR) AI framework uses tensor network algorithms to compress and evaluate large configurational integrals and partial differential equations, which are important for determining the thermodynamic and mechanical properties of materials.
The THOR AI framework integrates with machine learning potentials to model interatomic interactions and dynamic behavior, allowing accurate modeling of materials under various physical conditions.
Boian Alexandrov, senior AI scientist at Los Alamos who led the project, explained, “The configurational integral — which captures particle interactions — is notoriously difficult and time-consuming to evaluate, particularly in materials science applications involving extreme pressures or phase transitions. Accurately determining the thermodynamic behavior deepens our scientific understanding of statistical mechanics and informs key areas such as metallurgy.”
Previously, scientists used approximate methods like molecular dynamics and Monte Carlo simulations to estimate the configurational integral. These methods simulate many atomic motions over long periods to address the complexity that increases rapidly with more dimensions. Such calculations can require weeks on supercomputers but still face significant limitations.
Dimiter Petsev, professor in the UNM Department of Chemical and Biological Engineering, said he saw potential for these computational methods when Alexandrov described them. “Traditionally, solving the configurational integral directly has been considered impossible because the integral often involves dimensions on the order of thousands. Classical integration techniques would require computational times exceeding the age of the universe, even with modern computers,” Petsev said. “Tensor network methods, however, offer a new standard of accuracy and efficiency against which other approaches can be benchmarked.”
THOR AI addresses this challenge by representing high-dimensional data as smaller connected components using tensor train cross interpolation. A custom version identifies important crystal symmetries so that calculations can be completed in seconds instead of thousands of hours without losing accuracy.
When applied to metals like copper or noble gases such as argon under high pressure—and for calculating tin’s solid-solid phase transition—THOR AI produced results consistent with top Los Alamos simulations but did so more than 400 times faster. It also works well with machine learning-based atomic models.
Duc Truong, Los Alamos scientist and lead author of a study published in Physical Review Materials, stated: “This breakthrough replaces century-old simulations and approximations of configurational integral with a first-principles calculation. THOR AI opens the door to faster discoveries and a deeper understanding of materials.”
The THOR Project is available on GitHub.
