AI tensor network-based computational framework cracks a 100-year-old physics challenge
September 16, 2025
Researchers from The University of New Mexico and Los Alamos National Laboratory have developed a novel computational framework that addresses a longstanding challenge in statistical physics. The Tensors for High-dimensional Object Representation (THOR) AI framework employs tensor network algorithms to efficiently compress and evaluate the extremely large configurational integrals and partial differential equations central to determining the thermodynamic and mechanical properties of materials. The framework was integrated with machine learning potentials, which encode interatomic interactions and dynamical behavior, enabling accurate and scalable modeling of materials across diverse physical conditions.
“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.”
Until now, scientists have relied on approximate methods such as molecular dynamics and Monte Carlo simulations to estimate the configurational integral. These approaches work indirectly, simulating countless atomic motions over long time scales in an effort to bypass the “curse of dimensionality” — the exponential growth of complexity in high-dimensional problems that overwhelms even the most powerful supercomputers. Such calculations often demand weeks of supercomputer time, yet still face significant limits.
Dimiter Petsev, professor in the UNM Department of Chemical and Biological Engineering, often collaborates with Alexandrov on topics in materials science. When Alexandrov described the unique computational methods his team had developed, it occurred to Petsev that the work could be applied to the configurational integral in statistical mechanics as a test problem.
“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.”
Fast and accurate compute of the configurational integral
THOR AI transforms this high-dimensional challenge into a tractable problem by representing the high-dimensional data cube of the integrand as a chain of smaller, connected components using a mathematical technique called “tensor train cross interpolation.” A custom variant of this method identifies the important crystal symmetries, enabling the configurational integral to be computed in seconds rather than thousands of hours — without loss of accuracy.
Applied to metals such as copper and noble gases at high pressure, like argon in crystalline state, as well as to the calculation of tin’s solid-solid phase transition, THOR AI reproduces results from the best Los Alamos simulations — but more than 400 times faster. It also works seamlessly with modern machine learning-based atomic models, making it a versatile tool for 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.
