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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

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