Stellarator coils must produce magnetic fields that confine plasma along twisted, three-dimensional paths. The design space is enormous: each coil's shape is a curve in three dimensions, and a stellarator has dozens of coils, each interacting with every other through the magnetic field they jointly produce. The optimization must satisfy physics constraints (quasisymmetry for confinement), engineering constraints (structural stresses, manufacturing tolerances), and geometric constraints (coils can't intersect each other or the vacuum vessel).
Traditional optimization uses gradient-based methods on a surrogate model: compute the magnetic field from a candidate coil set, evaluate the physics objectives, adjust the coil shapes, repeat. The finite-element stress analysis — which determines whether the coils will physically survive the electromagnetic forces — is typically done after the optimization, as a post-hoc check. If the stresses exceed limits, the optimization is rerun with tighter geometric constraints, hoping to converge on a buildable design.
Kaptanoglu and Gil put the finite-element calculation inside the loop.
At each optimization step, the AI evaluates not just the magnetic field quality but the structural stresses in the coils under the self-generated electromagnetic loads. Coil shapes that produce good magnetic fields but fail structurally are penalized immediately, steering the optimization away from mechanically impossible designs before they dominate the search.
The result is designs that are simultaneously optimized for physics and engineering, rather than sequentially optimized for physics and then checked for engineering. The designs that emerge from the coupled loop are different — not just refined versions of physics-first designs, but qualitatively different coil topologies that trade small physics performance for large structural margin.
The brute-force search can't find these designs because the coupled objective landscape has a different structure from the physics-only landscape. The AI navigates the coupled landscape directly.