Transforming engineering and healthcare, DIMON makes solving complex equations faster and accessible, replacing supercomputers with desktop solutions.
DIMON revolutionizes modeling by eliminating the need for recalculating grids with every shape change. Instead of breaking complex forms into small elements, it predicts how physical factors like heat, stress, and motion behave across various shapes, dramatically speeding up simulations and optimizing designs. Image: Minglang Yin / Johns Hopkins University
DIMON revolutionizes modeling by eliminating the need for recalculating grids with every shape change. Instead of breaking complex forms into small elements, it predicts how physical factors like heat, stress, and motion behave across various shapes, dramatically speeding up simulations and optimizing designs. Image: Minglang Yin / Johns Hopkins University
Modeling how cars deform in a crash, how spacecraft respond to extreme environments, or how bridges resist stress could be made thousands of times faster thanks to new artificial intelligence that enables personal computers to solve massive math problems that generally require supercomputers.
The new AI framework is a generic approach that can quickly predict solutions to pervasive and time-consuming math equations needed to create models of how fluids or electrical currents propagate through different geometries, like those involved in standard engineering testing.
Details about the research appear in the journal Nature Computational Science.
Introducing DIMON: Solving Complex Equations with Speed and Precision
Called DIMON (Diffeomorphic Mapping Operator Learning), the framework solves ubiquitous math problems known as partial differential equations that are present in nearly all scientific and engineering research. Using these equations, researchers can translate real-world systems or processes into mathematical representations of how objects or environments will change over time and space.
"While the motivation to develop it came from our own work, 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."
"DIMON is particularly unique because it learns how physical systems behave across different shapes, eliminating the need to recalculate equations from scratch when geometries change," Trayanova added.
Transforming Cardiac Research with Heart Digital Twins
In addition to demonstrating DIMON's applicability to solving other engineering problems, Trayanova's team tested the new AI on over 1,000 heart "digital twins," highly detailed computer models of real patients' hearts. The platform was able to predict how electrical signals propagated through each unique heart shape, achieving high predictive accuracy.
Trayanova's team relies on solving partial differential equations to study cardiac arrhythmia, an electrical impulse misbehavior in the heart that causes irregular beating. With their heart digital twins, researchers can diagnose whether patients might develop the often fatal condition and recommend ways to treat it.
"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 just 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."
A Game-Changer for Engineering and Design
Partial differential equations are generally solved by breaking complex shapes like airplane wings or body organs into grids or meshes made of small elements. The problem is then solved on each simple piece and recombined. But if these shapes change—like in crashes or deformations—the grids must be updated, and the solutions recalculated, which can be computationally slow and expensive.
DIMON solves that problem by using AI to understand how physical systems behave across different shapes without needing to recalculate everything from scratch for each new shape. Instead of dividing shapes into grids and solving equations over and over, the AI predicts how factors such as heat, stress, or motion will behave based on patterns it has learned, making it much faster and more efficient in tasks like optimizing designs or modeling shape-specific scenarios. For instance, DIMON has been shown to achieve accuracy rates within 0.02 of standard numerical solutions while speeding up computations by a factor of up to 10,000, even on complex, realistic 3D geometries.
The research also provides insights into training efficiencies. DIMON uses advanced techniques like Principal Component Analysis (PCA) to parameterize shape variations, dramatically reducing computational memory requirements and making the model scalable for high-resolution applications.
Future Directions and Broader Applications
The team is incorporating cardiac pathology that leads to arrhythmia into the DIMON framework. Because of its versatility, the technology can be applied to shape optimization and many other engineering tasks where solving partial differential equations on new shapes is repeatedly needed, said Minglang Yin, a Johns Hopkins Biomedical Engineering Postdoctoral Fellow who developed the platform.
"For each problem, DIMON first solves the partial differential equations on a single shape and then maps the solution to multiple new shapes. This process ensures predictions are both fast and reliable across a diverse range of scenarios, from engineering prototypes to clinical applications," Yin said. "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."
Collaborative Efforts and Funding
Other authors are Nicolas Charon of the University of Houston, Ryan Brody and Mauro Maggioni (co-lead) of Johns Hopkins, and Lu Lu of Yale University.
This work is supported by NIH grants R01HL166759 and R01HL174440; a grant from the Leducq Foundations; the Heart Rhythm Society Fellowship; U.S. Department of Energy grants DE-SC0025592 and DE-SC0025593; NSF grants DMS-2347833, DMS-1945224, and DMS-2436738; and Air Force Research Laboratory awards FA9550-20-1-0288, FA9550-21-1-0317, and FA9550-23-1-0445.
Journal reference:
Yin, M., Charon, N., Brody, R., Lu, L., Trayanova, N., & Maggioni, M. (2024). A scalable framework for learning the geometry-dependent solution operators of partial differential equations. Nature Computational Science, 1-13. DOI:10.1038/s43588-024-00732-2, https://www.nature.com/articles/s43588-024-00732-2