February 28, 2016 07:40 PM

Elusive Hollywood couple Alicia Vikander and Michael Fassbender are sharing their awards season success with each other.

The Danish Girl star, who is nominated for best actress in a supporting role, and the Steve Jobs actor, who is nominated for best actor, had dinner at Sunset Tower restaurant with their parents on Saturday, a source tells PEOPLE.

Alicia Vikander
David Fisher/REX/Shutterstock

Vikander, 27, and Fassbender, 38, started dating after meeting on the set of their 2014 film The Light Between Oceans, but have rarely stepped out together at public events.

Check out PEOPLE’s full Academy Awards 2016 coverage and complete winners list!

The pair made their awards show debut at the Golden Globes in January.

Michael Fassbender
David Fisher/REX/Shutterstock

Vikander arrived on the Oscars red carpet solo, and she revealed that she’s nervous to be at the Academy Awards as a first-time nominee.

“I’m at the Oscars, it’s crazy,” Vikander said on the red carpet. “Being here is so surreal, I have butterflies in my tummy! Being here is extraordinary.”

The actress looked stunning in a Louis Vuitton gown which she described is in a “dusty yellow” hue. “I love the color. It spices it up a bit,” Vikander said.

As for what she’s going to be doing after her whirlwind awards season, she may be packing her bags.

“I just finished a film last week and I’m going to go for at least 4 or 5 days,” she said when asked during the PEOPLE preshow if she will be taking a break. Perhaps with Fassbender?

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