In 2016, an earthquake reduced the Church of San Salvatore in Campi in central Italy mostly to rubble, destroying its 15th-century frescoes. What remained were fragments, a complex puzzle that conservators at the Ministry of Culture have been working to reassemble ever since.

But the pieces are few and far between, “isolated islands within vast areas of loss,” Serena Di Gaetano and Federica Giacomini, senior conservator-restorers at the ministry’s restoration institute, said in a joint emailed response to questions. Their work, they said, is to somehow “bridge the gaps between what remains and what has been irretrievably lost.”

Enter Alex Kachkine, 25, a graduate researcher in mechanical engineering at M.I.T. who improbably rocked the art world in June with a paper in the scientific journal Nature describing a new way to restore paintings with the help of artificial intelligence.

A hobbyist restorer, he wrote a program that analyzes damage and prints the fixes on a super thin mask. The mask can be laid over the painting, making it appear fully restored, but can also be removed to reveal the original. To create the mask, the program used over 55,000 hues in several hours, and worked about 65 times as fast as traditional restoration, Mr. Kachkine estimated.

The study was a side project, but it generated buzz among conservators around the world, including at the Ministry of Culture in Italy — to Mr. Kachkine’s surprise.

At his day job, he researches the electron beam sources that create the intricate circuitry on microchips, which are then placed into phones or other devices. “Those require very high degrees of precision,” he said. “And it turns out a lot of the techniques we use to achieve that level of precision are applicable to art restoration.”

The Conservator’s Dilemma

Conservators have long debated just how heavy-handed to be about keeping works in viewing shape.

“Conservation is divided between preservation and restoration,” said Ann Shaftel, a conservator in Canada who specializes in preserving thangkas, Tibetan Buddhist fabric paintings used to guide meditation. In her work, the seeming grime that accumulates as a thangka hangs in an incense-filled monastery has spiritual value, and she favors a very light touch when it comes to preservation.

A similar perspective is increasingly shared by conservators of art of all kinds, though there is no universally accepted approach. “There is a dilemma about retouching a painting or not,” said Hartmut Kutzke, a chemist at the Museum of Cultural History at the University of Oslo. “It differs a little bit from country to country.”

Some favor maximalist interventions that restore a work to its former glory. Many prefer a minimally invasive approach that avoids irreversible changes. Mr. Kachkine’s method could resolve the tensions between the two camps, according to Mr. Kutzke, who wrote an article reviewing the study.

Since the digitally printed mask can create a removable full restoration, it is “a good bridge between the two worlds,” Mr. Kutzke said in an interview.

But the chemist noted that some of his colleagues who are conservators had nonetheless objected to the method. “They were actually quite skeptical because they said it’s too much change,” he said. “They were saying we have to accept that artworks age, and this is part of the artwork.”

Coding for Culture

In Italy, official conservators follow strict principles. Their interventions must be reversible and visible so as not to permanently alter originals or mislead future observers. But Ms. Di Gaetano and Ms. Giacomini say the ministry’s Central Institute for Restoration, known as I.C.R., also embraces cutting-edge technologies that can help preserve the past, like Mr. Kachkine’s.

Relying on A.I. for analytic help is not new. But Mr. Kachkine’s work caught the team’s eye because it goes a step further, they said. “It demonstrates how artificial intelligence algorithms, when correctly oriented and developed, can become concrete support tools not only in the study and documentation phase, but also during actual restoration operations,” Ms. Di Gaetano and Ms. Giacomini said.

Once the super thin mask is created, it’s attached to the original artwork with conservation varnish. “The mask can be peeled off with very minimal force, but the bond is there, and the bond is transparent, so it doesn’t affect the way that you see the underlying painting,” Mr. Kachkine said.

For conservators facing big-scale projects that defy traditional methods, like the frescoes of the Church of San Salvatore, this innovation offers hope. With the help of a program — and a printed screen — filling in the missing pieces of a huge puzzle could become less daunting. And ultimately, it could mean more cultural heritage is saved.

The restoration institute enlisted Mr. Kachkine seeking to develop a systematic approach to big projects that can be adapted to specific cases.

Now he is writing code to conform with Italy’s official conservation principles. The fixes must be done in a painting style called tratteggio, developed by the restoration institute’s founding director, where restored sections are painted in thin parallel lines to ensure additions are visibly distinct up-close but from afar allow the work to be appreciated as a whole.

“There’s going to be a lot more cases like this where the technique needs to be adapted to a particular circumstance,” Mr. Kachkine said.

From Innovative Technology to Usable Tool

Mr. Kachkine doesn’t plan to patent his method. Instead, by publishing his work, he hopes that conservators will be able to “leverage the benefits” of the techniques he gleaned from engineering to preserve “really valuable cultural heritage.”

Still, his approach is currently too complex for most conservators to use independently. “Many conservators have lamented to me that even though my methods are published and free to use, they would like to be able to buy masks without worrying about all the steps involved in fabricating them,” he said.

He is considering starting a business to develop the tool for commercial purposes, but for now is more focused on improving the technology.

Last month, he gave a talk at the de Young Museum in San Francisco and came back with additional programming tasks based on challenges faced by the conservators and curators he met there.

Experts say that the work has only just begun if he is to build a truly transformative tool.

Marc Melich-Mautner, an art and antiquities dealer in Austria, believes the method could revolutionize restoration, making it faster and less expensive, eventually making more art accessible. But accomplishing that goal will also require much more continued input from art professionals, in addition to tech development.

“It’s still a lot of Alex behind it,” he said of the program. “It has to be fed with information from the restoration world, with the techniques.”