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 very large mathematical calculations known as constitutive 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 this framework with the potential of machine learning to capture how atoms interact and move. This integration enables scientists to accurately and efficiently model materials across a wide range of physical environments.
“Constitutive integrals that capture particle interactions are notoriously difficult and time-consuming to evaluate, especially in materials science applications involving extreme pressures and phase transitions,” said Boian Aleksandrov, a senior AI scientist at Los Alamos who led the project. “Accurately determining thermodynamic behavior deepens the scientific understanding of statistical mechanics and informs important fields such as metallurgy.”
Why calculating constituent integrals is so difficult
For decades, researchers have used indirect computational techniques such as molecular dynamics and Monte Carlo simulations to estimate configuration integrals. These methods attempt to reproduce the movement of atoms by simulating a huge number of interactions over long periods of time.
The main obstacle arises from what scientists call the “curse of dimensionality.” As the number of variables increases, the computational complexity increases exponentially. Even the most advanced supercomputers struggle with this challenge. As a result, simulations are often run over several weeks and still provide only approximate answers.
Professor Dimiter Petsev of the United Nations University School of Chemical and Biological Engineering is a frequent collaborator with Alexandrov on materials science research. When Alexandrov described the computational strategy his team had developed, Petsev realized that this technique could provide a way to directly evaluate constitutive integrals in statistical mechanics.
“It has traditionally been thought that it is impossible to solve configuration integrals directly because the integrals often have dimensions on the order of several thousand orders of magnitude. Classical integration methods require computational times that exceed the age of the universe, even with modern computers,” Petsev said. “However, Tensor network techniques provide a new standard of accuracy and efficiency against which other approaches can be benchmarked.”
THOR AI brings high-dimensional calculations to practical use
THOR AI transforms this seemingly intractable problem into one that can be efficiently solved. This is done by representing a large high-dimensional dataset of integrands as a sequence of small, connected parts. The framework relies on a mathematical strategy known as “tensor train interpolation” to achieve this compression.
The researchers have also developed a specialized version of this method to detect important crystal symmetries within materials. By identifying these patterns, THOR AI significantly reduces the amount of computation required. Calculations that once took thousands of hours can now be completed in seconds without sacrificing accuracy.
Accelerate materials science and physics simulations
The team tested THOR AI on several material systems. These include complex solid-solid phase transitions in metals such as copper, noble gases under extreme pressure such as argon in the crystalline state, and tin. In both cases, 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 you to analyze materials under a variety of conditions. This flexibility could make THOR AI a valuable tool across materials science, physics, and chemistry, the researchers said.
“This breakthrough replaces century-old simulations and shape integral approximations with ab initio calculations,” said Duc Truong, a Los Alamos scientist and lead author of the study published in Physical Review Materials. “THOR AI opens the door to faster discovery and deeper understanding of materials.”
The THOR project is available on GitHub.
