Researchers have developed a computational framework capable of solving a mathematical problem in statistical physics that has challenged scientists for nearly a century. The system, known as THOR AI, enables direct calculation of configurational integrals, complex equations that describe how particles interact within materials.
The method was created by scientists from the University of New Mexico and Los Alamos National Laboratory. By combining tensor network algorithms with machine learning models that describe atomic interactions, the framework allows researchers to analyze the thermodynamic behavior of materials far more efficiently than traditional simulation methods, according to ScienceDaily.
Configurational integrals are central to statistical mechanics because they describe how particles interact across a system and determine key physical properties such as temperature dependent stability, phase transitions, and mechanical behavior. However, calculating these integrals directly has historically been considered impractical due to the enormous number of variables involved.
The difficulty arises from what scientists call the “curse of dimensionality.” In systems containing many atoms, the number of interacting variables grows exponentially, making direct mathematical integration extremely computationally expensive. For decades, researchers have relied on indirect approaches such as molecular dynamics and Monte Carlo simulations to approximate the result.
These simulation techniques model atomic motion by calculating vast numbers of particle interactions over time. While effective, they can require weeks of computing time on powerful supercomputers and often produce approximate results rather than exact solutions.
The THOR AI framework addresses this challenge by restructuring the high dimensional mathematical problem into a compressed representation using tensor networks. Tensor networks are mathematical structures that break large datasets into smaller connected components, making them easier to process computationally.
A key component of the approach is a technique called tensor train cross interpolation, which allows the system to compress the multidimensional data describing atomic interactions into a series of smaller calculations. By identifying patterns and symmetries in the material’s crystal structure, the framework further reduces the amount of computation required.
This compression enables THOR AI to perform calculations that would previously have required extremely long simulation times. Researchers report that tasks once requiring thousands of computing hours can now be completed in seconds while maintaining comparable accuracy.
To test the framework, scientists applied it to several materials systems, including copper, crystalline argon under high pressure, and phase transitions in tin. In these tests, the THOR AI calculations reproduced results obtained from traditional high performance simulations while running more than 400 times faster.
The framework also integrates with modern machine learning potentials used in materials science to model atomic interactions. These models allow the system to simulate how materials behave under a wide range of conditions, including extreme pressure and temperature environments.
Researchers say the new method could accelerate discoveries across several scientific fields. Accurate modeling of particle interactions is important in metallurgy, condensed matter physics, and chemical engineering, where understanding material behavior is essential for designing new alloys, semiconductors, and energy technologies.
The study describing the system was published in the journal Physical Review Materials. Scientists involved in the project say the framework may serve as a new benchmark method for high dimensional calculations in statistical physics.
By enabling faster and more direct solutions to previously intractable equations, the THOR AI framework could expand the range of physical systems that researchers can analyze using computational techniques.
