Researchers at Duke University have demonstrated that incorporating known physics into machine learning algorithms can help the inscrutable black boxes attain new levels of transparency and insight into material properties. 

In one of the first projects of its kind, researchers constructed a modern machine learning algorithm to determine the properties of a class of engineered materials known as metamaterials and to predict how they interact with electromagnetic fields. 

Because it first had to consider the metamaterial’s known physical constraints, the program was essentially forced to show its work. Not only did the approach allow the algorithm to accurately predict the metamaterial’s properties, but it also did so more efficiently than previous methods while providing new insights.

The results appear online the week of May 9 in the journal Advanced Optical Materials.

“By incorporating known physics directly into the machine learning, the algorithm can find solutions with less training data and in less time,” said Willie Padilla, professor of electrical and computer engineering at Duke. “While this study was mainly a demonstration showing that the approach could recreate known solutions, it also revealed some insights into the inner workings of non-metallic metamaterials that nobody knew before.”

Metamaterials are synthetic materials composed of many individual engineered features, which together produce properties not found in nature through their structure rather than their chemistry. In this case, the metamaterial consists of a large grid of silicon cylinders that resemble a Lego baseplate.

Depending on the size and spacing of the cylinders, the metamaterial interacts with electromagnetic waves in various ways, such as absorbing, emitting, or deflecting specific wavelengths. In the new paper, the researchers sought to build a type of machine learning model called a neural network to discover how a range of heights and widths of a single-cylinder affects these interactions. But they also wanted its answers to make sense.

“Neural networks try to find patterns in the data, but sometimes the patterns they find don’t obey the laws of physics, making the model it creates unreliable,” said Jordan Malof, assistant research professor of electrical and computer engineering at Duke. “By forcing the neural network to obey the laws of physics, we prevented it from finding relationships that may fit the data but aren’t actually true.”

The physics that the research team imposed upon the neural network are called a Lorentz model — a set of equations that describe how the intrinsic properties of a material resonate with an electromagnetic field. Rather than jumping straight to predicting a cylinder’s response, the model had to learn to predict the Lorentz parameters that it then used to calculate the cylinder’s response.

Incorporating that extra step, however, is much easier said than done.

“When you make a neural network more interpretable, which is in some sense what we’ve done here, it can be more challenging to fine-tune,” said Omar Khatib, a postdoctoral researcher working in Padilla’s laboratory. “We definitely had a difficult time optimizing the training to learn the patterns.”

Once the model was working, however, it proved to be more efficient than previous neural networks the group had created for the same tasks. In particular, the group found this approach can dramatically reduce the number of parameters needed for the model to determine the metamaterial properties.

They also found that this physics-based approach is capable of making discoveries all on its own.

As an electromagnetic wave travels through an object, it doesn’t necessarily interact with it in the same way at the beginning of its journey as it does at its end. This phenomenon is known as spatial dispersion. Because the researchers had to tweak the spatial dispersion parameters to get the model to work accurately, they discovered insights into the physics of the process that they hadn’t previously known.

“Now that we’ve demonstrated that this can be done, we want to apply this approach to systems where the physics is unknown,” Padilla said.

“Lots of people are using neural networks to predict material properties, but getting enough training data from simulations is a giant pain,” Malof added. “This work also shows a path toward creating models that don’t need as much data, which is useful across the board.”

Researchers have discovered that light, in the form of a laser, can trigger a form of magnetism in a normally nonmagnetic material. This magnetism centers on the behavior of electrons. These subatomic particles have an electronic property called “spin,” which has a potential application in quantum supercomputing. The researchers found that electrons within the material became oriented in the same direction when illuminated by photons from a laser.

The experiment was led by scientists at the University of Washington and the University of Hong Kong. 

By controlling and aligning electron spins at this level of detail and accuracy, this platform could have applications in the field of quantum simulation, according to co-senior author Xiaodong Xu, a Boeing Distinguished Professor at the UW in the Department of Physics and the Department of Materials Science and Engineering.

“In this system, we can use photons essentially to control the ‘ground state’ properties — such as magnetism — of charges trapped within the semiconductor material,” said Xu, who is also a faculty researcher with the UW’s Clean Energy Institute and the Molecular Engineering & Sciences Institute. “This is a necessary level of control for developing certain types of qubits — or ‘quantum bits’ — for quantum computing and other applications.”

Xu, whose research team spearheaded the experiments, led the study with co-senior author Wang Yao, professor of physics at the University of Hong Kong, whose team worked on the theory underpinning the results. Other UW faculty members involved in this study are co-authors Di Xiao, a UW professor of physics and materials science and engineering who also holds a joint appointment at the Pacific Northwest National Laboratory, and Daniel Gamelin, a UW professor of chemistry and director of the Molecular Engineering Materials Center.

The team worked with ultrathin sheets — each just three layers of atoms thick — of tungsten diselenide and tungsten disulfide. Both are semiconductor materials, so named because electrons move through them at a rate between that of a fully conducting metal and an insulator, with potential uses in photonics and solar cells. Researchers stacked the two sheets to form a “moiré superlattice,” a stacked structure made up of repeating units.

Stacked sheets like these are powerful platforms for quantum physics and materials research because the superlattice structure can hold excitons in place. Excitons are bound pairs of “excited” electrons and their associated positive charges, and scientists can measure how their properties and behavior change in different superlattice configurations.

The researchers were studying the exciton properties within the material when they made the surprising discovery that light triggers a key magnetic property within the normally nonmagnetic material. Photons provided by the laser “excited” excitons within the laser beam’s path, and these excitons induced a type of long-range correlation among other electrons, with their spins all orienting in the same direction.

“It’s as if the excitons within the superlattice had started to ‘talk’ to spatially separated electrons,” said Xu. “Then, via excitons, the electrons established exchange interactions, forming what’s known as an ‘ordered state’ with aligned spins.”  

The spin alignment that the researchers witnessed within the superlattice is a characteristic of ferromagnetism, the form of magnetism intrinsic to materials like iron. It is normally absent from tungsten diselenide and tungsten disulfide. Each repeating unit within the moiré superlattice is essentially acting as a quantum dot to “trap” an electron spin, said Xu. Trapped electron spins that can “talk” to each other, as these can, have been suggested as the basis for a type of qubit, the basic unit for quantum computers that could harness the unique properties of quantum mechanics for computation.

In a separate paper published Nov. 25 in Science, Xu and his collaborators found new magnetic properties in moiré superlattices formed by ultrathin sheets of chromium triiodide. Unlike the tungsten diselenide and tungsten disulfide, chromium triiodide harbors intrinsic magnetic properties, even as a single atomic sheet. Stacked chromium triiodide layers formed alternating magnetic domains: ferromagnetic one — with spins all aligned in the same direction — and another that is “antiferromagnetic,” where spins point in opposite directions between adjacent layers of the superlattice and essentially “cancel each other out,” according to Xu. That discovery also illuminates relationships between a material’s structure and its magnetism that could propel future advances in supercomputing, data storage, and other fields.  

“It shows you the magnetic ‘surprises’ that can be hiding within moiré superlattices formed by 2D quantum materials,” said Xu. “You can never be sure what you’ll find unless you look.”