In various embodiments, a topology optimization application solves a topology optimization problem associated with designing a three-dimensional (“3D”) object. The topology optimization application coverts a first shape having a first resolution and representing the 3D object to a coarse shape having a second resolution that is lower than the first resolution. Subsequently, the topology optimization application computes coarse structural analysis data based on the coarse shape. The topology optimization application then uses a trained machine learning model to generate a second shape having the first resolution and representing the 3D object based on the first shape and the coarse structural analysis data. The trained machine learning model modifies a portion of a shape having the first resolution based on structural analysis data having the second resolution. Advantageously, generating the second shape based on structural analysis data having a lower resolution reduces computational complexity relative to prior art techniques.