Machine learning unleashes quantum atomic vibrations of materials

Caltech scientists have developed an artificial intelligence (AI)-based method that dramatically accelerates the calculation of quantum interactions that occur in materials. In the new work, the group focuses on atomic oscillations, or interactions between phonons. This is an interaction that governs a wide range of material properties, including heat transport, thermal expansion, and phase transition. It could potentially extend the new machine learning approach to calculate all quantum interactions and allow for encyclopedia knowledge of how particles and excitation work in materials.

Scientists like Marco Bernardi, a professor of applied physics, physics and materials science in California, and his graduate student Yao Luo (MS '24), are trying to find ways to speed up the huge interactions needed to understand such particle interactions from the first principles of actual materials.

Last year, Bernardi and Luo developed a data-driven method based on a technique called Singular Value Decomposition (SVD) to simplify the huge mathematical matrix scientists use to represent the interaction between electrons and phonons in materials.

The case of phonon interactions is even more complicated. These interactions are encoded in multidimensional objects called tensors, vector generalizations, and higher dimension matrices. The complexity of these tensors grows exponentially with the number of particles involved, limiting scientists' understanding of interactions involving three or more phonons.

Now inspired by recent advances in machine learning, Bernardi and Luo have developed an AI-based method of encoding phonon interactions in materials and sifting through higher order tensors that extract only the critical bits needed to complete the calculations that explain heat transport. They describe their works in papers published in journals. Physical Review Letter.

Using current cutting-edge techniques, a supercomputer takes hours or days to calculate the interaction between three or four phonons in a material. This new method allows computers to complete the same heat transport and phonon dynamics calculations 1,000-10,000 times faster, maintaining accuracy.

“Calculating the 4-phonon interaction is a nightmare,” says Bernardi. “For complex materials, this task involves calculations for several weeks. This can be done in 10 seconds.”

Bernardi explains this in detail.

“We're using a machine learning technique called CandeComp/Parafac tensor decomposition, but we had to adapt to meet the symmetry of this particular physical problem. We need to first set up a neural network and run it on the GPU and ask.

“If you modify the number of product terms you want to keep, the machine learning process will return the best features to approximate the perfect tensor. Usually, only a few of these products are needed, saving several orders of magnitude in computational complexity compared to using a full tensor.

Bernardi adds that the new method is suitable for high-throughput screening of thermophysics and heat transport in large-scale materials databases, a major initiative in the materials community. Regarding future work, he said, “My vision now is to compress all different types of quantum interactions and higher order processes of materials with similar techniques. The key is to completely bypass the formation of large tensors and learn direct interactions in compressed forms.”

The title of this paper is “Tensor Learning and Compression of N-Phonon Interactions.” The other author is Dhruv Mangtani, who worked on the project as a surf student in Bernardi's lab. Shiyu Peng, a scholarly scholar of the Bible. Caltech graduate students Jia Yao (MS '25) and Sergei Kliavinek.