A superconductor is a material that, at very low temperatures, conducts electricity without losses: electrons move without bumping into each other, like a crowd walking down a perfectly smooth corridor. But turn on a strong magnetic field, and vortices appear inside the superconductor — tiny regions where superconductivity vanishes. If these vortices are not pinned, they start to move and create resistance, destroying the material's main advantage.

To hold the vortices, defects are deliberately added to the superconductor — irregularities, pores, or inserts of another material. They work like potholes on a road: a wheel (the vortex) falls into a pothole and stays put instead of rolling on. The better these potholes are placed, the more current the superconductor can handle. Usually, engineers find the defect arrangement by hand, through trial and error. The authors proposed an automatic method: the computer itself iterates through options and finds the best shape and placement of defects, as if optimizing a maze for maximum delay of runners.

The method is based on the Ginzburg–Landau equations, which describe how superconductivity changes in space and time. The computer program gradually alters the geometry of the defects until it obtains a configuration where vortices are pinned as firmly as possible. This is like a sculptor chipping away excess material to reveal the form, but here the material is virtual. Such an approach is already used in aviation and construction, and now it is coming to superconductor technology.

In the future, this could enable superconducting magnets for MRI machines, particle accelerators, and fusion reactors that operate with lower energy costs. And also — lossless power transmission lines, which energy engineers around the world dream of.