AI vs. supercomputers: New AI-based method solves complex equations faster and uses less computing power

A new artificial intelligence-based method quickly solves complex math equations used broadly across many industries - and it's faster running on a personal computer than traditional methods using supercomputers. The research was funded by multiple grants from the U.S. National Science Foundation and published in Nature Computational Science.

Engineers, scientists and others use partial differential equations to create complex models that can predict how fluids, electrical currents or other forces move through or impact various materials or shapes. These equation-based models can predict anything from how air moves around an airplane wing to how a building buckles under stress or what shape a metal car frame takes in a collision. This computationally heavy modeling work is time-consuming and generally requires a supercomputer to solve the many differential equations involved.

But now, a new AI-based framework - dubbed Diffeomorphic Mapping Operator Learning (DIMON) - is able to solve these equations much faster than other methods that use a supercomputer, and it can do so using just a regular personal computer.

"This is a solution that we think will have generally a massive impact on various fields of engineering because it's very generic and scalable," said Natalia Trayanova, a Johns Hopkins University biomedical engineering and medicine professor who co-led the research. "It can work basically on any problem, in any domain of science or engineering, to solve partial differential equations on multiple geometries, like in crash testing, orthopedics research or other complex problems where shapes, forces and materials change."

In addition to demonstrating the applicability of DIMON in solving engineering problems, Trayanova's team tested the new AI using 1,000 digital models of real human hearts, or "digital twins." DIMON was able to predict how electrical signals propagated through each unique heart shape, including cardiac arrhythmia.

"We're bringing novel technology into the clinic, but a lot of our solutions are so slow it takes us about a week from when we scan a patient's heart and solve the partial differential equations to predict if the patient is at high risk for sudden cardiac death and what is the best treatment plan," said Trayanova, who directs the Johns Hopkins Alliance for Cardiovascular Diagnostic and Treatment Innovation.

"With this new AI approach, the speed at which we can have a solution is unbelievable. The time to calculate the prediction of a heart digital twin is going to decrease from many hours to 30 seconds, and it will be done on a desktop computer rather than on a supercomputer, allowing us to make it part of the daily clinical workflow."

Adds Yulia Gel, program director in the NSF Division of Mathematical Sciences, "This approach has a potential to be particularly useful for uncertainty quantification of digital twins based on smaller datasets, which remain one of the primary roadblocks for wider adoption of digital twins in healthcare."

"Great work like this shows the incredible promise of digital twins and AI to revolutionize healthcare and many other areas through the application of the mathematical sciences," adds NSF Mathematical Sciences Division Director David Manderscheid.

Postdoctoral fellow and study co-author Minglang Yin also explains the key to AI speeding past supercomputers, and it's all about pattern learning. "For each problem, DIMON first solves the partial differential equations on a single shape and then maps the solution to multiple new shapes," describes Yin.

"We are very excited to put it to work on many problems, as well as to provide it to the broader community to accelerate their engineering design solutions."