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In the hot summer,Smartphones, tablets and other electronic devices often have performance and safety issues due to "overheating"How to design electronic products with better heat dissipation, materials are the key.

One of the key links is:Accurately predict the thermal properties of materials。

The main carrier for transporting heat in materials is phonons, and the transport and scattering mechanism of phonons at the interface determines the thermal conductivity of the material. Therefore, accurately modeling the phonon scattering relationship becomes the key to predicting the thermal properties of materials.

Nowadays, aNew AI methodsGreatly speeds up the prediction of thermal properties of materials compared to traditional machine learning modelsIncreased by hundreds to thousands of times。

Recently, a research team from the Massachusetts Institute of Technology (MIT) and its collaborators have made an important breakthrough in this field. They designed a new machine learning model called "Virtual Node Graph Neural Network" (VGNN).VGNN can calculate the phonon dispersion relations of thousands of materials in just a few seconds on a single PC.。

The related research paper, titled “Virtual node graph neural network for full phonon prediction”, has been published in the scientific journal Nature Computational Science.

The study found that VGNN was not only successful in phonon prediction, but also inPredict electronic band structure, optical absorption peaks, magnetic properties and other complex material propertiesIt also shows certain potential.

Prediction speed increased by 100 or 1,000 times

It is estimated that about70%Eventually it all becomes waste heat.

If scientists could better predict how heat moves through semiconductors and insulators, they could design more efficient power generation systems. However, the thermal properties of materials are extremely difficult to model.

The thermal properties of materials are affected by many complex factors such as the material's microstructure, atomic arrangement, and chemical bonding, and their thermal properties are highly nonlinear and multi-scale.

The prediction of thermal properties of materials mainly depends on the measurement of phonon scattering relationships. Traditional experimental measurement and theoretical calculation methods have high requirements for experimental equipment and operations, are time-consuming and costly, and cannot meet the needs of rapid prediction and large-scale screening.

When using machine learning to predict material properties, the measurement and modeling process of phonon scattering relationships is extremely complex due to factors such as experimental measurement and computational modeling, and it is currently difficult to accurately predict.

In this work, VGNN can handle output characteristics of variable or even arbitrary dimensions by introducing virtual nodes, thereby directly calculating the regional center phonon energy and the full phonon band structure from the atomic structure in complex materials, and realizing phonon property optimization in a larger structural design space.

Figure | Overview of the VGNN method as a general method for enhancing graph neural networks

Specifically, the research team proposed three different virtual node enhancement schemes, namely vector virtual node (VVN), matrix virtual node (MVN) and momentum-correlated matrix virtual node (k-MVN).

The VVN scheme directly obtains the phonon spectrum from the virtual node, but there is a bottleneck in information transmission; the MVN scheme predicts the phonon energy by constructing a virtual dynamic matrix, which can robustly predict the thermal properties of complex materials; the k-MVN scheme uses unit cell translation to generate momentum dependence and obtain the complete phonon band structure.

The results show that these methods all successfully predict phonon scattering relationships in complex materials.

To test the performance of the VGNN model, the research team designed a series of experiments that used 8 GPUs to generate more than 146,000 predictions in less than 5 hours, involving materials with up to 400 atoms in a single unit cell.

Currently, MLIP is the main method for phonon prediction in the field of machine learning, so the researchers compared the performance of VGNN and MLIP in terms of accuracy and efficiency in the experiment.

Figure｜Comparison of computation time and running time of VGNN and MLIP

The experimental results show that VGNN systematically speeds up the prediction of phonon diffusion relations by hundreds to thousands of times. The researchers said that VGNN uses a unique method of directly inferring the elements of the dynamical matrix, bypassing the calculation of force, second-order derivatives of interatomic potentials, and Fourier transforms used in the MLIP calculation process, significantly improving the prediction efficiency.

In addition, the VGNN model not only surpasses the traditional GNN method in the accuracy of predicting complex material properties, but also significantly improves the computational efficiency. All three models show strong performance in predicting heat capacity, and the k-MVN model has the smallest error.

The research team also pointed out that by adopting a virtual node addition scheme based on the physical model, the model's extrapolation ability when dealing with complex materials has been significantly improved.

Figure｜k-MVN predicts the full acoustic subband structure

The MVN and k-MVN schemes show excellent generalization capabilities in complex materials with hundreds of atomic unit cells, which also shows that careful consideration of the physical basis of the problem when designing the virtual node addition scheme can enhance the extrapolation ability of the model.

The study shows that despite the general complexity of the phonon band structure, the k-MVN model can still predict the location and shape of the phonon bands, such as the gaps between different optical branches.

The research team also used the virtual node GNN to calculate the phonon properties of high entropy alloys and established a phonon scattering database for more than 100,000 materials. This breakthrough not only significantly improved the efficiency and accuracy of phonon predictions, but also provided a powerful tool for future material design and optimization.

Shortcomings and Prospects

Although the VGNN model has shown great potential in predicting the thermal properties of materials, the research team also stated that the k-MVN model still has difficulty capturing the effects of long-range interactions when predicting electronic band structures.

To address these issues, the research team plans to further improve model performance by optimizing the design of virtual nodes and increasing the diversity of training data sets.

In the future, the VGNN method is expected to be applied to a wider range of material prediction fields, including the optimization design of alloys, interfaces, and amorphous solid materials.This technology will not only help accelerate the discovery and application of new materials, but will also promote the development of high-tech fields such as energy conversion, thermal energy storage and superconducting materials.。

https://www.nature.com/articles/s43588-024-00661-0

https://www.nature.com/articles/s43588-024-00665-w

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