Incorporating established physics into neural network algorithms helps them
to uncover new insights into material properties
According to researchers at Duke University, incorporating known physics
into machine learning algorithms can help the enigmatic black boxes attain
new levels of transparency and insight into the characteristics of
materials.
Researchers used a sophisticated machine learning algorithm in one of the
first efforts of its type to identify the characteristics of a class of
engineered materials known as metamaterials and to predict how they interact
with electromagnetic fields.
The algorithm was essentially forced to show its work since it first had to
take into account the known physical restrictions of the metamaterial. The
method not only enabled the algorithm to predict the properties of the
metamaterial with high accuracy, but it also did it more quickly and with
additional insights than earlier approaches.
The results were published in the journal Advanced Optical Materials on May
13th, 2022.
“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 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 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 to artificial intelligence
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 exactly 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.”
Reference:
Learning the Physics of All-Dielectric Metamaterials with Deep Lorentz
Neural Networks - by Omar Khatib, Simiao Ren, Jordan Malof and Willie J.
Padilla, 13 May 2022, Advanced Optical Materials.
DOI: 10.1002/adom.202200097
Tags:
Physics