Mezic Recognized for Groundbreaking Mathematical Theory

MixMode CTO and Chief Scientist, Igor Mezić, has received the prestigious J.D. Crawford Prize from the Society for Industrial and Applied Mathematics (SIAM). The prize is awarded every two years to one individual for a significant accomplishment in the area of nonlinear science. Dr. Mezic received the award for his mathematical theory that makes it easier to understand and speed up an array of previously unsolvable computations in a wide range of applications, including fluid dynamics, energy-efficient design, network security and operations, and complex systems dynamics. 

UC Santa Barbara recently reported on Mezić’s accomplishment in the article, “Igor Mezić Earns Major SIAM Award for Development of Koopman Operator Theory.” The article explains that the Crawford Prize recognizes contributions from a paper addressing fundamental issues in the field of dynamical-systems. 

Mezić’s single-author paper, titled “Spectrum of the Koopman Operator, Spectral Expansions in Functional Spaces, and State-Space Geometry,” published in the journal Nonlinear Science in 2019 develops a mathematical theory for complex systems such as networks, power grids and the human brain.

“It’s wonderful to me that the dynamical systems community deems my work worthy of the Crawford Prize,” said Mezić, who is also director of UCSB’s Center for Energy Efficient Design and head of the Buildings and Design Solutions Group at the CoE’s Institute for Energy Efficiency. 

Mezić realized that a different mathematical framework was needed to model complex systems. He began working on the problem for his PhD dissertation, which he received in 1994, by incorporating Koopman operator theory, which had been developed in the 1930s but was never used on a large scale because the geometric point of view was so popular. Mezić, however, realized that it could be useful.

“I wanted to preserve the power to describe geometrical objects — because humans think geometrically — but work it so that you could understand a dynamical system that has many dimensions,” he says. “I’ve ported geometric concepts of dynamical systems into an operator theoretical context so that they can be turned into algorithms, artificial intelligence, etc. It is adding to geometry that Crawford utilized by setting them up in a different, more easily utilized domain.”

“Whereas a car has a hundred or a thousand dimensions to its dynamical system, artificial intelligence and deep-learning systems have hundreds of thousands or even millions of dimensions. Mezić’s theory not only has the mathematical power to resolve such complex systems, but also avoids abstraction,” he says, so that “it is very cleanly and clearly understandable what the objects are.”

The U.S. Army reported that the Department of Defense Multidisciplinary University Research Initiative, known as MURI, and managed by the Army Research Office, supported the prize-winning paper. 

“The thing that excites me most about Dr. Mezić’s work is the emerging ability to tackle perennially difficult technical challenges,” said Dr. Matthew Munson , program manager for fluid dynamics Army Research Office, an element of the U.S. Army Combat Capabilities Development Command, known as DEVCOM, Army Research Laboratory. “The future Army will operate in an environment that is hugely complex and uncertain, which requires the ability to solve hard problems quickly. The theoretical frameworks and computational tools that he and his team have developed, along with his continuing discoveries, are poised to make a major impact on how the Army solves these future challenges.”

The awards are typically funded at $1.25 million per year for three years with an option for two additional years for research teams whose efforts intersect more than one traditional scientific and engineering discipline.

“This new approach will change the world,” Munson said. “In the future, I think it will be the standard theory used for analysis and prediction of many dynamic systems. The potential applications are numerous, and the potential impacts are enormous.”

John Keister, CEO of MixMode, added: “Over the years, Dr. Mezic’s research and accomplishments have had a massive impact on a variety of industries and government entities. We at MixMode are fortunate to be working with Dr. Mezic on applying his algorithm and his theories to the realm of Cybersecurity where groundbreaking approaches are very much needed to combat the ever-increasing capabilities of the adversaries.”

Read more on this award and Mezic’s accomplishments:

Igor Mezić Earns Major SIAM Award for Development of Koopman Operator Theory

Army-Funded Researcher Receives Award for Mathematical Theory

Solving the Unsolvable – Igor Mezić Earns Major Award for His Advancement of Koopman Operator Theory

About MixMode:

MixMode is a next-generation, AI-powered cybersecurity platform focused on solving three primary issues for the Security Operations Center: providing next-generation threat detection, surfacing zero-day attacks and improving false-positive alert fatigue. MixMode allows security teams to dramatically increase productivity and efficiency while significantly decreasing the wasted time, effort, and resources associated with legacy cybersecurity tools. 

MixMode’s AI intelligently creates and updates the network baseline, then provides security teams with sophisticated functionality like predictive attack detection, 95% false-positive alert reduction, and all the tools necessary to investigate a threat. SOC teams can easily integrate MixMode into their security stack to dramatically reduce the investigation time, cost, and expertise required to respond to persistent threats, malware, insider attacks, and nation-state espionage efforts. MixMode’s core AI algorithm is patented and was utilized over the past 20 years on projects for DARPA and the DoD. MixMode is headquartered in Santa Barbara, CA.

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