AI Breakthrough Finally Cracks Century-Old Physics Problem

An AI framework now computes once-impossible physics equations within seconds. The breakthrough redefines how scientists study the behavior of materials.

Researchers at the University of New Mexico and Los Alamos National Laboratory have created an advanced computational framework that solves a major problem that has challenged statistical physicists for decades.

Known as the Tensors for High-dimensional Object Representation (THOR) AI framework, the system uses tensor network algorithms to efficiently compress and analyze vast configurational integrals and partial differential equations. These equations are fundamental for determining how materials behave under different thermodynamic and mechanical conditions. By combining tensor networks with machine learning potentials, which represent interatomic forces and atomic motion, the researchers achieved accurate, scalable simulations of materials 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.”

Overcoming the limits of classical simulations

Historically, scientists have depended on approximate methods like molecular dynamics and Monte Carlo simulations to estimate the configurational integral. These techniques indirectly mimic atomic motion over long time scales to work around the “curse of dimensionality,” where computational complexity increases exponentially with each added variable, even overwhelming the world’s fastest supercomputers. Despite requiring weeks of intensive processing, such simulations still produce limited results.

Dimiter Petsev, a professor in the UNM Department of Chemical and Biological Engineering, frequently collaborates with Alexandrov on research in materials science. After learning about the new computational strategies Alexandrov’s team had developed, Petsev realized they could be applied to directly solving the configurational integral—a task previously regarded as impossible 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.”

Fast and accurate computation with THOR AI

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.

Reference: “Breaking the curse of dimensionality: Solving configurational integrals for crystalline solids by tensor networks” by Duc P. Truong, Benjamin Nebgen, Derek DeSantis, Dimiter N. Petsev, Kim Ø. Rasmussen and Boian S. Alexandrov, 27 August 2025, Physical Review Materials.
DOI: 10.1103/xrbw-xr49

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