New AI cracks complex engineering problems faster than supercomputers

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"... 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. ...

In addition to demonstrating the applicability of DIMON in solving other engineering problems, ... 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 prognostic accuracy. ...

to study cardiac arrhythmia, which is 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. ..."

From the abstract:

"Solving partial differential equations (PDEs) using numerical methods is a ubiquitous task in engineering and medicine. However, the computational costs can be prohibitively high when many-query evaluations of PDE solutions on multiple geometries are needed. Here we aim to address this challenge by introducing Diffeomorphic Mapping Operator Learning (DIMON), a generic artificial intelligence framework that learns geometry-dependent solution operators of different types of PDE on a variety of geometries.

We present several examples to demonstrate the performance, efficiency and scalability of the framework in learning both static and time-dependent PDEs on parameterized and non-parameterized domains; these include solving the Laplace equations, reaction–diffusion equations and a system of multiscale PDEs that characterize the electrical propagation on thousands of personalized heart digital twins. DIMON can reduce the computational costs of solution approximations on multiple geometries from hours to seconds with substantially less computational resources."

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A scalable framework for learning the geometry-dependent solution operators of partial differential equations (open access)

Fig. 1: Learning geometry-dependent solution operator of PDEs on a family of diffeomorphic domains with DIMON.