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Emanuele Zappala, an assistant professor of mathematics at ISU, and his colleagues at Yale have developed the Attentional Neural Integral Equations algorithm, or ANIE for short. Their work was  and describes how ANIE can model large, complex systems using data alone.

“Natural phenomena–everything from plasma physics to how viruses spread–are all governed by equations which we do not fully understand,” explains Zappala. “One of the main complexities lies in long-distance relations between different data points in the systems over space and time. What ANIE does is it allows us to learn these complex systems using just those known data points.” 

For example, says Zappala, the brain is one of the systems ANIE can model. “In the brain, one neuron is not only affected by nearby neurons but also by others that are further away since connections between neurons can be very long. Also, the brain does not work only in the present but also uses memory and information from the past. ANIE functions similarly to the brain itself, in that predictions are made by gathering information from all space and time data points.”

Currently, running ANIE requires a lot of processing power, and training ANIE on a system can take up to 10 hours on a typical laptop. Zappala says one research track he may follow for ANIE Is to make the algorithm “more computationally efficient,” allowing it to be run on an off-the-shelf consumer computer. Another could be exploring its applications for nuclear fusion and studying the universe’s smallest particles. To start, however, Zappala has received a nearly $700,000 grant from the National Institutes of Health to explore how ANIE can help diagnose the severity of neurological diseases in the brain over the next four years. Zappala and his collaborators will train ANIE using recordings of brain activity to determine the “dynamic fingerprints” of different brain activities and then be able to decode the results and provide a severity score for various disorders such as depression, dementia, anxiety, and more. 

“Beyond the brain, ANIE could be used by an engineer to design a new type of reactor, a doctor to diagnose a patient’s disease, and a physicist to study the properties of plasma,” said Zappala. “While ANIE itself is not of immediate use to most people, its applications may reverberate in the lives of everyone.”