Competition and consensus for the scientific mach

AMHERST, Mass. – Thanks to a $ 1.95 million grant from the Air Force Office of Scientific Research, Markos Katsoulakis and Luc Rey-Bellet, both professors in the Department of Mathematics and Statistics at the University of Massachusetts Amherst, and Paul Dupuis, at Brown University, will spend the next four years developing a new approach to machine learning that goes beyond traditional reliance on big data.

Traditional machine learning relies on huge caches of data that an algorithm can sift through in order to “train” to accomplish a task, resulting in a mathematical model based on the data. But what about situations where there is very little data, or when generating enough data is prohibitive? One possible emerging remedy, often referred to as scientific machine learning, is to incorporate into algorithms expert knowledge gained through years of scientific research into the development of physical principles and rules.

Scientific machine learning is attracting great interest in a wide variety of applied fields and industries, including medicine, engineering, manufacturing and the sciences, but one of the main challenges is to ensure the reliability of algorithmic predictions. .

This is where Katsoulakis and Rey-Bellet come in, who together bring a new perspective to scientific machine learning, one focused on “divergences”. “The mathematical concept of ‘divergence’,” explains Rey-Bellet, “is a way to quantify the gap between what the machine learning algorithm predicts and actual experimental data.” He adds that “the discrepancies allow researchers to test different machine learning algorithms and find the ones that give the best results.”

The team proposes a new class of discrepancies, which involve two fictitious and competing agents, the “players”, playing a “game” against each other. The first player offers a new machine learning model, which simulates a real scenario; the other player can reject the proposition if the model predictions do not sufficiently match the actual experimental data available. The game continues until the players find an algorithm that satisfies them both. But these players have a trick up their sleeve: “A key new mathematical feature in our differences allows players to ‘know their physique’,” says Katsoulakis. “Smarter players compete more effectively, learn from each other faster, and need less data to train, but still remain open to learning new physics.”

Katsoulakis states that “it is an exciting time to be a mathematician” and adds that “applied mathematics, statistics, computer science and disciplinary research can complement each other and solve these fundamental problems of scientific machine learning in the years to come. to come “. Rey-Bellet adds a final thought: “For centuries, physics has been the main source of inspiration for all the mathematical sciences. In recent years, machine learning has started to play a similar role and brings a remarkable influx of new ideas into the world of mathematics.

Contacts: Markos Katsoulakis, [email protected]

Daegan Miller, [email protected]

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