A team of scientists from the University of New Mexico and Los Alamos National Laboratory has achieved what physicists once considered impossible using AI to solve some of the most complex equations in statistical physics within seconds. Their breakthrough, powered by a new AI framework known as THOR (Tensors for High-dimensional Object Representation), could fundamentally transform how researchers model the behavior of materials under extreme conditions.
For decades, physicists have struggled with the so-called configurational integral, a cornerstone equation that describes how particles interact and how materials behave under varying pressures, temperatures, and structural changes. Traditional simulation methods like molecular dynamics and Monte Carlo approximations have long been used to estimate these behaviors, but even the fastest supercomputers needed weeks of processing to produce limited results.
That bottleneck may now be history. The THOR AI framework uses a combination of tensor network algorithms and machine learning potentials to directly compute these massive equations with unprecedented speed and accuracy.
“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,” explained Boian Alexandrov, senior AI scientist at Los Alamos and lead researcher on the project. “Accurately determining the thermodynamic behavior deepens our scientific understanding of statistical mechanics and informs key areas such as metallurgy.”
Historically, solving the configurational integral directly was viewed as unachievable due to the curse of dimensionality where each added variable exponentially increases computational complexity. As Dimiter Petsev, professor at the University of New Mexico, put it:
“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.”
THOR AI sidesteps these limitations using a mathematical innovation known as tensor train cross interpolation. This technique breaks down the high-dimensional data cube of the equation into smaller, linked tensors essentially simplifying an impossible calculation into a manageable one.
According to the researchers, a custom version of this method also detects crystal symmetries, allowing THOR AI to compute the configurational integral in mere seconds, with no loss of precision.
When tested on metals such as copper, tin, and noble gases like argon, THOR AI produced results identical to those of Los Alamos’ best simulations but over 400 times faster. It even replicated tin’s solid-solid phase transition and matched predictions from high-pressure simulations of crystalline argon.
“This breakthrough replaces century-old simulations and approximations of the 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.