Researchers at The University of New Mexico and Los Alamos National Laboratory have introduced a new computational approach designed to solve one of the most difficult problems in statistical physics. Their system, called the Tensors for High-dimensional Object Representation (THOR) AI framework, uses tensor network algorithms to handle extremely large mathematical calculations known as configurational integrals, along with the partial differential equations needed to analyze materials.
These calculations are essential for predicting the thermodynamic and mechanical behavior of materials. To make the system more powerful, the researchers combined the framework with machine learning potentials that capture how atoms interact and move. This integration allows scientists to model materials accurately and efficiently across a wide range of physical environments.
"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," said Los Alamos senior AI scientist Boian Alexandrov, who led the project. "Accurately determining the thermodynamic behavior deepens our scientific understanding of statistical mechanics and informs key areas such as metallurgy."
Why Configurational Integrals Are So Difficult to Compute
For decades, researchers have depended on indirect computational techniques such as molecular dynamics and Monte Carlo simulations to estimate configurational integrals. These methods attempt to reproduce the movement of atoms by simulating enormous numbers of interactions over extended periods.
The main obstacle comes from what scientists call the "curse of dimensionality." As the number of variables grows, the complexity of the calculations increases exponentially. Even the most advanced supercomputers struggle with this challenge. As a result, simulations often run for weeks while still providing only approximate answers.
Dimiter Petsev, a professor in the UNM Department of Chemical and Biological Engineering, frequently collaborates with Alexandrov on materials science research. When Alexandrov described the computational strategy his team had developed, Petsev realized that the technique might offer a way to directly evaluate the configurational integral in statistical mechanics.
"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 Makes High-Dimensional Calculations Practical
THOR AI converts this seemingly unmanageable problem into something that can be solved efficiently. It does this by expressing the massive high-dimensional dataset of the integrand as a sequence of smaller connected pieces. The framework relies on a mathematical strategy known as "tensor train cross interpolation" to achieve this compression.
Researchers also developed a specialized version of the method that detects key crystal symmetries within the material. By identifying these patterns, THOR AI dramatically reduces the amount of computation required. Calculations that once demanded thousands of hours can now be completed in seconds without sacrificing accuracy.
Faster Simulations for Materials Science and Physics
The team tested THOR AI on several materials systems. These included metals such as copper, noble gases under extreme pressure such as argon in crystalline state, and the complex solid-solid phase transition of tin. In each case, the new method reproduced results previously obtained from advanced Los Alamos simulations while running more than 400 times faster.
The framework also integrates smoothly with modern machine learning atomic models, allowing it to analyze materials under a wide variety of conditions. Because of this flexibility, researchers say THOR AI could become a valuable tool across materials science, physics and chemistry.
"This breakthrough replaces century-old simulations and approximations of configurational integral with a first-principles calculation," said Duc Truong, Los Alamos scientist and lead author of the study published in Physical Review Materials. "THOR AI opens the door to faster discoveries and a deeper understanding of materials."
The THOR Project is available on GitHub .
