Researchers at Duke University have demonstrated that incorporating known physics into machine learning algorithms can help impenetrable black boxes achieve new levels of transparency and understanding of material properties.
In one of the first such projects, researchers built a modern machine learning algorithm to determine the properties of a class of engineering materials known as metamaterials and to predict how they interact with fields. electromagnetic.
Because it had to consider the known physical constraints of the metamaterial first, the program was essentially forced to show its work. Not only did the approach allow the algorithm to accurately predict the properties of the metamaterial, but it did so more efficiently than previous methods while providing new insights.
The results appear online the week of May 9 in the newspaper Advanced optical materials.
“By incorporating known physics directly into 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 primarily a demonstration showing that the approach could recreate known solutions, it also revealed insights into the inner workings of non-metallic metamaterials that no one knew before.”
Metamaterials are synthetic materials composed of many individual technical characteristics, 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 different ways, such as absorbing, emitting, or deflecting specific wavelengths. In the new paper, the researchers set out to build a type of machine learning model called a neural network to find out how a range of heights and widths of a single cylinder affects these interactions. But they also wanted his answers to make sense.
“Neural networks try to find patterns in data, but sometimes the patterns they find don’t obey the laws of physics, which makes the pattern they create 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 might match the data but aren’t actually true.”
The physics the research team imposed on the neural network is 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 directly to predicting a cylinder’s response, the model had to learn to predict Lorentz parameters which it then used to calculate the cylinder’s response.
Incorporating this extra step, however, is much easier said than done.
“When you make a neural network more interpretable, which is sort of what we’ve done here, it can be harder to tweak it,” said Omar Khatib, a postdoctoral researcher working in Padilla’s lab. “We certainly struggled to optimize the training to learn the patterns.”
Once the model worked, however, it proved to be more efficient than previous neural networks the group had created for the same tasks. In particular, the group found that this approach can significantly reduce the number of model parameters needed to determine metamaterial properties.
They also discovered that this physics-based approach is capable of making discoveries on its own.
When an electromagnetic wave passes through an object, it does not necessarily interact with it in exactly the same way at the start of its journey as it does at the end. This phenomenon is known as spatial dispersion. Because the researchers had to change the spatial dispersion parameters for the model to work accurately, they discovered insights into the physics of the process that they hadn’t known before.
“Now that we’ve demonstrated that it can be done, we want to apply this approach to systems where the physics are unknown,” Padilla said.
“Many people use neural networks to predict material properties, but getting enough training data from simulations is a daunting task,” Malof added. “This work also shows a path to building models that don’t need as much data, which is useful across the board.”
This research was supported by the Ministry of Energy (DESC0014372).
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