At least since Philip K. Dick pondered whether androids dream of electric sheep, writers have wrestled with the inevitable encroachment of artificially intelligent humanoids. Most of these speculations have dwelt in the darker corners of science fiction, with rogue robots developing beyond their programming, eclipsing the Singularity, and proceeding to terminate us. Luckily, we’re not there yet; these days, they only want to take our jobs, not our lives. A more recent spate of films and series has taken a more exploratory, compassionate look at relationships between humans and their AI counterparts, from “Ex Machina” to “Her” to “Westworld” to “Marjorie Prime” and, now, “I’m Your Man,” Germany’s Best International Film entry for next year’s Academy Awards. Of all of these forward-thinking projects, “I’m Your Man” is the one most tethered to the mechanics of a traditional romantic comedy. This shouldn’t scare away the cineastes and skeptics. To the contrary, “I’m Your Man” is a deeply intelligent consideration of a not-too-future world when the bespoke droid will be a viable option for courtship alongside bars and Tinder. It puts a rejuvenating defibrillator to the tired heart of the rom-com. First-time feature-film writer-director Maria Schrader (she also directed Netflix’s excellent miniseries “Unorthodox”) situates her prescient sci-fi in the earthbound here-and-now. Alma (Maren Eggert) is a scientist whose latest endeavor involves translating ancient Sumerian cuneiforms. As one of the few single people in her department, she agrees to beta-test, for three weeks, a promising new product: a humanoid companion named Tom (Dan Stevens) that has been algorithmically tailored to meet her desired specifications for a partner. She meets him in his factory, in a surreal, scarlet-lit ballroom patterned after a 1920s speakeasy. To a stranger, he is indistinguishable from a human, albeit one of the better-looking ambassadors of our species, though his flirting needs work: “Your eyes are like two mountain lakes I could sink into,” he offers, and it’s a miracle Schrader found a take in which Stevens gets through the line without breaking character. Soon afterward, Tom glitches, repeating the same sentence fragment like a stuck record-a minor growing pain that is swiftly mended. As Alma discovers, taking Tom home with her is akin to dating Data from “Star Trek: The Next Generation.” He’s a superior wealth of encyclopedic information who will gladly share his knowledge, whether or not he is asked to do so, but actual human emotions are a bridge too far. Yet the nuanced rate at which Tom gradually grows-or perhaps only appears to grow-is one of the mysteries and pleasures of “I’m Your Man.” Alma is a reticent roommate and a sour host who has neither a prurient nor scientific interest in Tom; she just wants to get the trial over with. Yet even a cold interaction is an interaction, and Tom’s nurture-over-nature accretion of general artificial intelligence-his ability to make a joke, to express disobedience, to show empathy-suggests a consciousness beyond the boundaries of his creators. Or are we just reading too much into the ones and zeroes? Schrader is a canny director to walk this line without overtly delineating it. Either way, Tom’s seeming elasticity increases his human traits, chiseling away at the affection that’s buried in Alma. Schrader, along with co-screenwriter Jan Schomburg, ultimately crafts two three-dimensional, charming, endearing leads-both of whom achieve these traits despite themselves, with Alma having to overcome her cynicism (and related, tragic backstory) and Tom his hardwiring. They’re not a match made in heaven, but a match made in a computer, and computers usually know us better than we do. At least for now, we have the ability to shut off the computer, to find our happiness in the flesh, with all its messiness, its frustrations, its unknowns. Whether we will want to, when given Tom-like upgrades, is another story. “I’m Your Man” is now playing at Living Room Theaters at FAU in Boca Raton, Movies of Delray, and the Gateway Cinema in Fort Lauderdale.