Researchers have developed a novel artificial intelligence framework that solves a fundamental challenge in statistical physics, potentially revolutionizing materials science. The new method provides a direct and exact calculation for a century-old problem that was previously considered unsolvable, offering a tool to accelerate the discovery and design of new materials. The work was a collaboration between scientists at the University of New Mexico and Los Alamos National Laboratory.
The AI framework, named Tensors for High-dimensional Object Representation (THOR), computes the configurational integral, a complex mathematical quantity that describes the thermodynamic and mechanical properties of materials by accounting for the interactions of all their particles. Previously, scientists relied on computationally expensive and time-consuming simulations that provided only approximations. THOR, however, can compute this integral in seconds, a task that would take even the most powerful supercomputers weeks or longer using conventional methods, and in some cases, would require computational times exceeding the age of the universe.
Overcoming the Curse of Dimensionality
The central challenge in calculating the configurational integral is a phenomenon known as the “curse of dimensionality.” This term describes the exponential increase in complexity that arises when dealing with high-dimensional problems. In materials science, the number of possible configurations of particles in a system can be immense, making a direct calculation of the configurational integral practically impossible with traditional methods. These methods, such as molecular dynamics and Monte Carlo simulations, attempt to bypass this problem by simulating the movement of atoms over time to estimate the integral. While these techniques have been invaluable, they are indirect and face limitations in accuracy and scalability, especially when dealing with materials under extreme conditions like high pressures or during phase transitions.
A New Computational Approach
The THOR framework employs a mathematical technique called tensor networks to transform the high-dimensional problem into a more manageable one. It represents the vast amount of data in the integral as a chain of smaller, interconnected components using a method known as “tensor train cross interpolation.” This approach allows the framework to efficiently compress and evaluate the complex integrals and partial differential equations that are key to understanding a material’s properties. A customized version of this method also identifies important crystal symmetries, which further simplifies the calculation without sacrificing accuracy. This innovative use of tensor networks is what enables THOR to achieve its remarkable speed and precision.
The Power of Tensor Networks
Tensor networks are a powerful tool with applications across various scientific fields, including quantum physics, machine learning, and statistical mechanics. They provide a way to represent and compute with complex, high-dimensional data by breaking it down into a network of smaller, lower-rank tensors. This decomposition makes calculations that would otherwise be intractable, feasible. In the context of the THOR framework, tensor networks allow for a direct, first-principles calculation of the configurational integral, a feat that was long thought to be impossible. This represents a paradigm shift from the approximate methods that have been the standard for decades.
Demonstrated Success and Future Applications
The researchers have successfully applied the THOR framework to several real-world materials, including copper, argon under high pressure, and tin undergoing a phase transition. The results from THOR matched the best available simulations from Los Alamos but were achieved more than 400 times faster. This leap in computational efficiency opens the door to a deeper understanding of material behavior and could significantly accelerate the development of new materials with desired properties. The framework is designed to work seamlessly with modern machine learning models of atomic interactions, making it a versatile tool for materials science, physics, and chemistry.
Open-Source for Broader Impact
To encourage further research and application, the THOR project has been made available as an open-source tool on GitHub. This will allow scientists worldwide to use and build upon the framework, potentially leading to breakthroughs in a wide range of fields that rely on understanding the behavior of complex systems. The team behind THOR includes project lead Boian Alexandrov, a senior AI scientist at Los Alamos, and Duc Truong, the lead author of the study published in Physical Review Materials. Their work provides a powerful new tool for the scientific community and marks a significant step forward in our ability to model and predict the properties of matter.
The Researchers Behind the Breakthrough
The development of the THOR framework was led by a team of researchers from the University of New Mexico and Los Alamos National Laboratory. Boian Alexandrov, a senior scientist at the Theoretical Division at Los Alamos, led the project. He holds PhDs in both Nuclear Engineering and Computational Biophysics. The lead author of the study is Duc Truong, a scientist at Los Alamos specializing in computational and applied mathematics. Dimiter Petsev, a professor in the UNM Department of Chemical and Biological Engineering, was also part of the team.
