A paper coauthored by researchers at the University of Toronto’s Vector Institute and Google describes an AI technique called neural stochastic differential equations (SDEs) that’s tailored to health, science, and finance predictions.

It enables the modeling of random events that might affect people, prices, or the state of complex systems, like financial markets and health care networks. Market trades or hospital visits are examples of “random events” that could affect those systems. Unlike existing techniques, the authors say, neural SDEs can make predictions about these random events, like what the price of a stock might be in the next few days.

One of the most popular existing techniques — neural ordinary equations (ODEs) —  has an important limitation. It can’t account for random interactions, meaning the equations can’t update the state of a system as random events occur. (Think trades by other people that affect a company’s share price or a virus picked up at a hospital that changes a person’s health status.) The system has to be updated manually on some schedule to account for these, which means the model isn’t truly mapping to reality.

Neural SDEs have no such limitation because they represent continuous changes in state as they occur.

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As the coauthors of the paper explain, neural SDEs generalize ODEs by adding instantaneous noise to their dynamics. This, and other algorithmic tweaks, allows tens of thousands of variables (parameters) to be fitted to a neural SDE, allowing it to model things like the motion of molecules in a liquid, allele frequencies in a gene pool, or prices in a market.

In one experiment, the team trained ODE and neural SDE models on a real-world motion capture data set comprising 23 walking sequences partitioned into 15 training, three validation, and four test sequences. After 400 iterations, they observed improved predictive performance from the neural SDEs compared with the ODEs — the former had a mean squared error of 4.03% versus the ODE’s 5.98% (lower is better).

“Building on the early work of Einstein, these SDEs enable models to represent continuous changes in state as they occur and to do so at scale,” a Vector Institute spokesperson told VentureBeat via email. “Non-neural SDEs are used in finance and health today, but their scale is limited. As mentioned at the top, neural SDEs introduce the new chance to apply AI at scale to large complex financial systems without having to make the big … compromises that have typically been required.”