New AI Framework Solves Century-Old Physics Calculation

A team of researchers from the University of New Mexico and Los Alamos National Laboratory has developed a new artificial intelligence framework that solves a fundamental problem in statistical physics that has challenged scientists for a century. The system, called THOR, dramatically accelerates calculations essential for understanding the properties of materials.

The breakthrough addresses the calculation of the configurational integral, a complex mathematical problem that describes particle interactions within a material. By using a novel approach based on tensor networks, the THOR AI can perform these calculations more than 400 times faster than previous state-of-the-art methods, reducing computation time from weeks to mere seconds.

A Longstanding Computational Challenge

For decades, determining the thermodynamic and mechanical properties of materials has relied on understanding how atoms and particles interact. This behavior is captured by a mathematical concept known as the configurational integral. However, calculating it directly has been a significant obstacle in statistical physics.

The primary difficulty lies in the sheer complexity of the problem. For a typical material, the integral involves thousands of dimensions, one for each particle's coordinates. This leads to a problem that computer scientists call the "curse of dimensionality," where the computational complexity grows exponentially with the number of dimensions.

Previously, scientists used approximation methods like molecular dynamics and Monte Carlo simulations. These techniques simulate the movements of countless atoms over extended periods to estimate the material's properties. While useful, these simulations often require weeks of processing time on supercomputers and still face significant limitations.

"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," explained Dimiter Petsev, a professor at the UNM Department of Chemical and Biological Engineering.

The THOR AI Solution

The new framework, named THOR for Tensors for High-dimensional Object Representation, sidesteps these limitations. It was developed by a team led by Boian Alexandrov, a senior AI scientist at Los Alamos National Laboratory. The system employs tensor network algorithms, a mathematical tool originally from quantum physics, to simplify the high-dimensional problem.

Instead of trying to compute the entire massive integral at once, THOR uses a technique called "tensor train cross interpolation." This method breaks down the complex, high-dimensional data into a chain of smaller, interconnected components called tensors. This process effectively compresses the problem into a manageable form without losing critical information.

The framework is also designed to recognize important symmetries within the material's crystal structure, further simplifying the calculation. This combination of data compression and symmetry recognition is what allows THOR to achieve its remarkable speed.

Demonstrated Performance and Applications

To validate its effectiveness, the research team tested THOR on several challenging problems in materials science. The framework was used to model the properties of different materials under various physical conditions.

Key Test Cases:

• Metals at High Pressure: The system accurately calculated the properties of metals like copper under extreme pressure.
• Crystalline Noble Gases: It successfully modeled argon in its crystalline state, another complex scenario.
• Phase Transitions: THOR was used to calculate the solid-solid phase transition of tin, a process where the material changes its crystal structure while remaining solid.

In all test cases, THOR successfully reproduced the results from the most advanced supercomputer simulations but did so in a fraction of the time. The framework also integrates seamlessly with modern machine learning potentials, which are AI models that describe the interactions between atoms. This compatibility makes THOR a versatile and powerful tool for a wide range of applications in physics, chemistry, and materials science.

A New Era for Materials Science

The development of THOR AI represents a significant shift in how scientists can approach fundamental problems in statistical mechanics. By providing a method for direct, first-principles calculation, it moves beyond the approximations that have been standard for nearly a century.

"This breakthrough replaces century-old simulations and approximations of configurational integral with a first-principles calculation," said Duc Truong, a 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 ability to quickly and accurately determine thermodynamic behavior can inform research in critical areas such as metallurgy and the development of new materials. As a testament to its collaborative and open-science approach, the team has made the THOR Project available on GitHub for other researchers to use and build upon.