Machine learning unravels quantum atomic vibrations in materials

Caltech scientists have developed an artificial intelligence (AI)–based method that dramatically speeds up calculations of the quantum interactions that take place in materials. In new work, the group focuses on interactions among atomic vibrations, or phonons—interactions that govern a wide range of material properties, including heat transport, thermal expansion, and phase transitions. The new machine learning approach could be extended to compute all quantum interactions, potentially enabling encyclopedic knowledge about how particles and excitations behave in materials.

Scientists like Marco Bernardi, professor of applied physics, physics, and materials science at Caltech, and his graduate student Yao Luo (MS '24) have been trying to find ways to speed up the gargantuan calculations required to understand such particle interactions from first principles in real materials—that is, beginning with only a material's atomic structure and the laws of quantum mechanics.

Last year, Bernardi and Luo developed a data-driven method based on a technique called singular value decomposition (SVD) to simplify the enormous mathematical matrices scientists use to represent the interactions between electrons and phonons in a material.

The case of phonon interactions is even more complex. These interactions are encoded in multidimensional objects called tensors, generalizations of vectors and matrices in higher dimensions. 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 technique that sifts through the high-order tensors that encode phonon interactions in a material and extracts only the crucial bits needed to complete the calculations that explain thermal transport. They describe the work in a paper that appears in the journal Physical Review Letters.

Using current state-of-the-art techniques, a supercomputer takes hours or days to calculate the interactions between three or four phonons in a material. The new method enables computers to complete the same thermal transport and phonon dynamics calculations 1,000 to 10,000 times faster, all while maintaining accuracy.

"The calculations for four-phonon interactions are a nightmare," Bernardi says. "For complex materials, this task would involve weekslong calculations. Now we can do them in 10 seconds."

Bernardi explains more about the method:

"We use a machine learning technique called CANDECOMP/PARAFAC tensor decomposition, but we had to adapt it to satisfy the symmetry of this specific physical problem. We first set up a neural network and then run it on GPUs and ask: 'What are the best functions to approximate the actual tensor that describes these phonon interactions?'

"Once we fix the number of product terms we want to keep, the machine learning process returns the best functions to approximate the full tensor. We typically only need a few of these products, saving orders of magnitude in computational complexity compared to using the full tensor. This method allows us to learn the compressed form of phonon interactions, and we can still use these highly compressed tensors to compute all the observables of interest with the same accuracy."

Bernardi adds that the new method is well suited for high-throughput screening of thermal physics and heat transport in large material databases, a major effort in the materials community. As for future work, he says, "My vision right now is to compress all different types of quantum interactions and high-order processes in materials with similar techniques. The key will be to bypass the formation of large tensors altogether and to learn the interactions directly in compressed form."

The paper is titled "Tensor Learning and Compression of N-phonon Interactions." Additional authors are Dhruv Mangtani, who worked on the project as a SURF student in Bernardi's lab; Shiyu Peng, a postdoctoral scholar research associate; and Caltech graduate students Jia Yao (MS '25) and Sergei Kliavinek.