New machine learning method turbocharges heat transfer simulations

For nearly a decade, Xiulin Ruan and his research group have been at the forefront of how phonons interact with each other in materials. Now his team has worked with machine learning expert Guang Lin to develop a new computing method for predicting and modeling four-phonon scattering more quickly.

Their journey began with Tianli Feng's theory and computational method of four-phonon scattering, paving the way for a practical tool developed by Zherui Han called “FourPhonon” that is now used by hundreds of researchers worldwide. The latest advancement, led by PhD student Ziqi Guo (co-advised by Ruan and Lin and supported by their joint National Science Foundation award), makes running these simulations much quicker and more accessible than ever. This leap forward in efficiency opens vast possibilities for discovering new materials, significantly impacting fields ranging from thermal management, energy conservation to the development of new technologies and marks a major milestone in the field of materials informatics.

"Material simulation is like a high-tech shortcut that lets scientists understand how materials will behave without having to grow materials and do measurements in a lab, saving both time and money," said Guo. "It's especially useful for figuring out how materials conduct heat, which involves understanding how heat carriers called phonons scatter inside materials. This scattering event usually takes a supercomputer ages to calculate."

Guo and co-authors have found a way to make these predictions faster and cheaper using machine learning and statistical techniques, making it much easier to find new materials with unique thermal properties for everything from smartphones to solar panels. This is achieved by representing the entire calculation with a small portion of them, reducing the computational cost by orders of magnitudes while maintaining accuracy.

“This concept is simple but clever,” said Ruan, “It works surprisingly well.”

“This study has demonstrated that our machine learning and sampling-accelerated method removes the computational barrier associated with phonon scattering calculations,” said Lin.

Their research has been published in NPJ Computational Materials, and they have open-sourced their code at

"The new method significantly cuts down the time and computing power needed, making it faster and easier to identify materials that could be used for everything from electronics to energy-efficient buildings," said Guo. "It also enables us to study new physics phenomenon with unprecedented accuracy, which was inaccessible due to the high computational cost."

The thermal radiative properties portion of the work was supported by National Science Foundation (Award No. 2102645). The thermal conductivity portion was supported by National Science Foundation (Award No. 2321301), and the methodology is implemented into an open-source code FourPhonon and that effort was supported by National Science Foundation (Award No. 2311848). Simulations were performed at the Rosen Center for Advanced Computing (RCAC) of Purdue University.

Source: Guang Lin,

Xiulin Ruan,


Sampling-accelerated prediction of phonon scattering rates for converged thermal conductivity and radiative properties
Ziqi Guo, Zherui Han, Dudong Feng, Guang Lin, Xiulin Ruan
ABSTRACT: The prediction of thermal conductivity and radiative properties is crucial. However, computing phonon scattering, especially for four-phonon scattering, could be prohibitively expensive, and the thermal conductivity for silicon after considering four-phonon scattering is significantly under-predicted and not converged in the literature. Here we propose a method to estimate scattering rates from a small sample of scattering processes using maximum likelihood estimation. The calculation of scattering rates and associated thermal conductivity and radiative properties are dramatically accelerated by three to four orders of magnitude. This allows us to use an unprecedented q-mesh (discretized grid in the reciprocal space) of 32 × 32 × 32 for calculating four-phonon scattering of silicon and achieve a converged thermal conductivity value that agrees much better with experiments. The accuracy and efficiency of our approach make it ideal for the high-throughput screening of materials for thermal and optical applications.