It is estimated that about 70 percent of the energy generated worldwide finally ends up as waste heat.
If scientists could higher predict how heat moves through semiconductors and insulators, they might develop more efficient power generation systems. But the thermal properties of materials could be extremely difficult to model.
The problem is phonons, subatomic particles that transport heat. Some of the thermal properties of a cloth rely upon a measurement called the phonon dispersion relation, which could be incredibly difficult to acquire, let alone use when designing a system.
A team of researchers from MIT and elsewhere has taken on this challenge by rethinking the issue from the bottom up. The results of their work is a brand new machine learning framework that may predict phonon dispersion relations as much as 1,000 times faster than other AI-based techniques—with comparable and even higher accuracy. Compared to more traditional, non-AI-based approaches, it may very well be 1 million times faster.
This method could help engineers design power generation systems that produce more electricity more efficiently. It may be used to design more efficient microelectronics, as heat management stays a significant obstacle to speeding up electronic devices.
“Phonons are chargeable for the warmth loss, but determining their properties is amazingly difficult, each computationally and experimentally,” says Mingda Li, associate professor of nuclear science and engineering and lead writer of a paper on the technique.
In addition to Li, the study's co-authors are Ryotaro Okabe, a chemistry graduate student, and Abhijatmedhi Chotrattanapituk, a student of electrical engineering and computer science, in addition to Tommi Jaakkola, Thomas Siebel Professor of Electrical Engineering and Computer Science at MIT, and others from MIT, Argonne National Laboratory, Harvard University, the University of South Carolina, Emory University, the University of California at Santa Barbara, and Oak Ridge National Laboratory. The research appears in
Predicting phonons
Heat-carrying phonons are difficult to predict because they’ve a particularly wide frequency range and the particles interact and move at different speeds.
The phonon dispersion relation of a cloth is the connection between the energy and momentum of phonons in its crystal structure. For years, researchers have tried to predict phonon dispersion relations using machine learning, but it surely requires so many high-precision calculations that the models falter.
“If you had 100 CPUs and a couple of weeks, you can probably calculate the phonon dispersion relation for a cloth. The whole community really wants a more efficient method for this,” says Okabe.
The machine learning models that scientists often use to perform these calculations are often known as graph neural networks (GNN). A GNN transforms the atomic structure of a cloth right into a crystal graph consisting of several nodes representing atoms connected by edges that represent the interatomic bonds between atoms.
While GNNs are well suited to calculate many quantities, equivalent to magnetization or electric polarization, they should not flexible enough to efficiently predict a particularly high-dimensional quantity equivalent to the phonon dispersion relation. Since phonons can move around atoms on the X, Y, and Z axes, their momentum space is difficult to model with a set graph structure.
To achieve the mandatory flexibility, Li and his colleagues developed virtual nodes.
They create what is known as a Virtual Node Graph Neural Network (VGNN) by adding a set of flexible virtual nodes to the fixed crystal structure to represent phonons. The virtual nodes allow the scale of the neural network's output to differ in order that it shouldn’t be constrained by the fixed crystal structure.
Virtual nodes are connected to the graph in such a way that they will only receive messages from real nodes. Although virtual nodes are updated when the model updates real nodes during computation, they don’t affect the accuracy of the model.
“The way we do it is vitally efficient in coding. You just generate a couple of more nodes in your GNN. The physical location doesn't matter, and the actual nodes don't even know the virtual nodes are there,” says Chotrattanapituk.
Reduce complexity
Because it has virtual nodes to represent phonons, the VGNN can skip many complex calculations when estimating phonon dispersion relationships, making the tactic more efficient than an ordinary GNN.
The researchers proposed three different versions of VGNNs with increasing complexity. Each of them could be used to predict phonons directly from the atomic coordinates of a cloth.
Because their approach offers the flexibleness to rapidly model high-dimensional properties, they will use it to estimate phonon dispersion relationships in alloy systems. These complex mixtures of metals and nonmetals pose a selected challenge for traditional modeling approaches.
The researchers also found that VGNNs offered barely higher accuracy in predicting the warmth capability of a cloth. In some cases, prediction errors were two orders of magnitude lower using their technique.
Using a VGNN, phonon dispersion relationships for several thousand materials could be calculated in only a couple of seconds using a PC, says Li.
This efficiency could allow scientists to look a bigger space when searching for materials with certain thermal properties, equivalent to superior heat storage, energy conversion or superconductivity.
Furthermore, the virtual knot technique shouldn’t be limited to phonons and may be used to predict sophisticated optical and magnetic properties.
In the long run, researchers hope to refine the technique in order that virtual nodes turn out to be more sensitive and may detect small changes that may affect the phonon structure.
“Researchers have been too focused on using graph nodes to represent atoms, but we will rethink that. Graph nodes could be anything. And virtual nodes are a really general approach that may very well be used to predict many high-dimensional quantities,” says Li.
“The authors' modern approach greatly extends the outline of solids by graph neural networks by incorporating essential physics-based elements through virtual nodes, equivalent to wave-vector-dependent band structures and dynamic matrices,” says Olivier Delaire, associate professor in Duke University's Thomas Lord Department of Mechanical Engineering and Materials Science, who was not involved on this work. “I find the acceleration in predicting complex phonon properties to be astonishing, several orders of magnitude faster than a state-of-the-art universal machine learning of interatomic potentials. Impressively, the advanced neural network captures positive features and obeys physical rules. There is great potential to increase the model to explain other essential material properties: electronic, optical and magnetic spectra and band structures come to mind.”
This work is supported by the U.S. Department of Energy, the National Science Foundation, a Mathworks Fellowship, a Sow-Hsin Chen Fellowship, the Harvard Quantum Initiative, and Oak Ridge National Laboratory.
