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Caltech researchers have devised an artificial intelligence (AI)–driven approach that significantly accelerates computations of the quantum interactions occurring within materials. In recent work, the team concentrates on interactions among atomic vibrations, known as phonons—interactions that influence a broad spectrum of material characteristics, encompassing heat transfer, thermal expansion, and phase changes. This innovative machine learning method could be adapted to calculate all quantum interactions, possibly providing comprehensive insights into how particles and excitations behave in substances.

Researchers including Marco Bernardi, a professor of applied physics, physics, and materials science at Caltech, along with his graduate student Yao Luo (MS ’24), have been exploring methods to expedite the enormous calculations needed to comprehend such particle interactions from fundamental principles in actual materials—that is, starting solely with a material’s atomic arrangement and the principles of quantum mechanics. Last year, Bernardi and Luo developed a data-driven technique based on a method known as singular value decomposition (SVD) to streamline the vast mathematical matrices that scientists utilize to depict the interactions between electrons and phonons in a material.

The situation concerning phonon interactions is even more intricate. These interactions are represented in multidimensional entities called tensors, which are generalizations of vectors and matrices in higher dimensions. The intricacy of these tensors escalates exponentially with the number of particles involved, constraining scientists’ understanding of interactions involving three or more phonons.

Now, motivated by recent progress in machine learning, Bernardi and Luo have designed an AI-based technique that examines the high-order tensors encoding phonon interactions in a material and retrieves only the essential components required to finalize the calculations that elucidate thermal transport. They detail their findings in a publication featured in the journal Physical Review Letters.

Employing the latest cutting-edge techniques, a supercomputer requires hours or even days to compute the interactions between three or four phonons in a material. The new approach facilitates computers to accomplish the same thermal transport and phonon dynamics computations 1,000 to 10,000 times quicker, all while preserving accuracy.

“The computations for four-phonon interactions are a nightmare,” Bernardi states. “For intricate materials, this task could entail weeklong calculations. Now we can conduct them in 10 seconds.”

Bernardi elaborates further about the method:

“We utilize a machine learning technique known as CANDECOMP/PARAFAC tensor decomposition, but we had to modify it to conform to the symmetry of this particular physical challenge. Initially, we establish a neural network and then execute it on GPUs, questioning: ‘What are the optimal functions to approximate the actual tensor that represents these phonon interactions?’ Once we determine the number of product terms we wish to retain, the machine learning process provides the best functions to estimate the complete tensor. We generally only require a few of these products, achieving substantial reductions in computational complexity compared to using the entire tensor. This technique allows us to learn the compressed version of phonon interactions, and we can still utilize these highly compressed tensors to compute all relevant observables with equivalent accuracy.”

Bernardi notes that the innovative method is particularly suitable for high-throughput screening of thermal physics and heat transport across extensive material databases, a significant initiative within the materials community. Regarding future endeavors, he adds, “My current vision is to compress all varieties of quantum interactions and higher-order processes in materials with comparable techniques. The essential strategy will be to avoid the creation of large tensors altogether and to learn the interactions directly in compressed form.”

The publication is titled “Tensor Learning and Compression of N-phonon Interactions.” Additional contributors include Dhruv Mangtani, who participated in 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. This work was supported by funding from the National Science Foundation and an Eddleman Fellowship. The research employed resources from the National Energy Research Scientific Computing Center, a Department of Energy Office of Science user facility.

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