Looking for Elegant Solutions

 

Senior STEM-SI student Sophia Martino is using SINDy to discover fundamental equations 

 

While explaining her summer research project, Sophia Martino, a computer engineering major with a minor in business at Lehigh University, pauses to reference a quote often attributed to Albert Einstein: “Make everything as simple as possible, but not simpler.” For a researcher like Sophia, who handles a lot of data using equations, this advice is both a goal and a challenge. 

The Bucks County resident is spending the summer working in Lehigh’s INTEGRITY (INTEGrated, Resilient, and Intelligent EnergY Systems) lab, headed by Electrical and Computer Engineering Department Assistant Professor Javad Khazaei. According to Dr. Khazaei, Sophia “is working on identifying nonlinear models of energy resources in smart grids using statistical machine-learning methods.” Sophia’s explanation is a little more detailed. 

As Sophia describes it, her research relies on a modeling procedure called SINDy. The acronym stands for “sparse identification of non-linear dynamics,” and it generates equations to uncover how a system works, essentially deriving physical laws from data with a time element. The equations SINDy uncovers explain and predict how the variables behave; for example, they might indicate changing climate patterns or show the spread of disease. 

Sophia’s research process begins with a set of variables, such as x, y, and z. Then she mathematically combines these original elements in various ways to generate a library of potential candidates that might belong in the final equation. Sophia says, “You know all the candidates are related, but you don’t know how. But after you run a regression algorithm, you might be left with a set of nonlinear terms that are most impactful to your system.” These SINDy-generated equations are the ones that can explain, predict, or perfect a system. Sophia can “check” her final equations and see if they are correct by running the process backward, as if she’s translating one language into another and then back to the original. If the reverse translation works, her calculations are correct.

While there are other ways to uncover governing equations via machine learning or neural networks, those methods can be limited to one scenario or can be a “black box,” as Sophia says: the method generates inputs and outputs with no transparency about how it works. SINDY’s advantage is in the nature of the results it generates. Its equations are interpretable, generalizable, and easy to use to train new models, and it is notable for being “sparse”: As Einstein advised, the model generates equations with the fewest number of terms that can explain the phenomenon being studied. This is, in part, what attracts Sophia to SINDy. She says, “I think there’s beauty in uncovering what’s naturally there. Using these super powerful tools like our computers and these algorithms to uncover something that is part of how things are created—that’s cool.” 

The eventual results of Sophia’s work can contribute to making systems more efficient. She could use SINDy to help solar-electric systems run more efficiently, which could lead to the creation of more efficient solar cells for solar panels, less wasteful solar-energy transmission, or simply lower costs for consumers and energy retailers. 

Sophia joined STEM-SI this summer because a previous project, researching how wi-fi waves change as a body moves through them, showed her how much she enjoys the research process, and STEM-SI offered her the chance to do it again, this time with an eye on future graduate studies. She started the summer by reading from a list Dr. Khazaei suggested, and she is following those with readings derived from the originals plus others she finds on her own, paired with videos about how SINDy works. From there, she’ll compile data, work with the model, and test (and re-test) her results.

After she graduates, Sophia hopes to either earn a master’s degree in electrical engineering or to spend some time traveling around Europe. Her long-term goals might involve taking her SINDy research into the solar-photovoltaic field or finding a way to apply her engineering knowledge to music—she’s part of an a cappella group at Lehigh and arranges music for it. But no matter which path she takes, she’ll be keeping it simple and meaningful.