Scientists at the California Institute of Technology have devised an AI-based approach to accelerate computations of quantum interactions in materials. The findings appeared in the journal Physical Review Letters.
Inspired by recent advances in machine learning, Caltech scientists 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. Image Credit: Rosa Romano, EAS Communications/Caltech
In the new study, the group focuses on interactions between atomic vibrations, or phonons, which influence a variety of material characteristics such as heat transmission, thermal expansion, and phase transitions.
The new machine learning technique might be expanded to calculate all quantum interactions, possibly allowing for encyclopedic knowledge of how particles and excitations behave in materials.
Scientists like Marco Bernardi, a professor of applied physics, physics, and materials science at Caltech, along with his graduate student Yao Luo (MS '24), are working to accelerate the complex calculations needed to understand particle interactions in real materials from first principles, which means starting with only a material's atomic structure and the laws of quantum mechanics.
Bernardi and Luo created a data-driven approach last year that simplifies the massive mathematical matrices scientists use to depict the interactions between electrons and phonons in a material. This method is based on a technique known as singular value decomposition (SVD).
The situation becomes even more complex when it comes to phonon interactions. Tensors are multidimensional objects, extensions of vectors and matrices into higher dimensions, that capture complex relationships. Scientists’ understanding of interactions involving three or more phonons is limited by the exponential increase in tensor complexity as the number of particles grows.
Bernardi and Luo have now created an AI-based method that sorts through the high-order tensors that represent phonon interactions in a material and extracts only the essential bits required to finish the calculations that explain heat transport, motivated by current developments in machine learning.
Using cutting-edge techniques, a supercomputer can calculate the interactions of three or four phonons in a material in hours or even days. The new technique allows computers to do the same thermal transport and phonon dynamics calculations 1,000 to 10,000 times quicker while remaining accurate.
The calculations for four-phonon interactions are a nightmare. For complex materials, this task would involve weekslong calculations. Now we can do them in 10 seconds.
Marco Bernardi, Professor, Applied Physics, Physics, and Materials Science, California Institute of Technology
Bernardi provides further information regarding the method:
He added, “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.”
He further stated, “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 further notes that the novel approach is particularly suited for high-throughput screening of thermal physics and heat transport in large material databases, which is a significant effort in the materials community.
As for future work, he added, “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.”
Additional contributors are Dhruv Mangtani, a SURF student in Bernardi's lab; Shiyu Peng, a postdoctoral scholar and research associate; and Caltech graduate students Jia Yao (MS ‘25) and Sergei Kliavinek.
The National Science Foundation provided funding for the study, as did the Eddleman Fellowship. The National Energy Research Scientific Computing Center, a user facility of the Department of Energy Office of Science, was used for this study.
Journal Reference:
Luo, Y., et al. (2025) Tensor Learning and Compression of N-Phonon Interactions. Physical Review Letters. doi.org/10.1103/nmgj-yq1g.