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 extremely large mathematical calculations known as configurational 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 the framework with machine learning potentials that capture how atoms interact and move. This integration allows scientists to model materials accurately and efficiently across a wide range of physical environments.

For decades, researchers have depended on indirect computational techniques such as molecular dynamics and Monte Carlo simulations to estimate configurational integrals. These methods attempt to reproduce the movement of atoms by simulating enormous numbers of interactions over extended periods.

The main obstacle comes from what scientists call the "curse of dimensionality." As the number of variables grows, the complexity of the calculations increases exponentially. Even the most advanced supercomputers struggle with this challenge. As a result, simulations often run for weeks while still providing only approximate answers.

THOR AI converts this seemingly unmanageable problem into something that can be solved efficiently. It does this by expressing the massive high-dimensional dataset of the integrand as a sequence of smaller connected pieces. The framework relies on a mathematical strategy known as "tensor train cross interpolation" to achieve this compression.

Researchers also developed a specialized version of the method that detects key crystal symmetries within the material. By identifying these patterns, THOR AI dramatically reduces the amount of computation required. Calculations that once demanded thousands of hours can now be completed in seconds without sacrificing accuracy.

Source: Science Daily

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