The present disclosure is directed to a system for reparameterizing of a neural network to optimize structural designs. The system can obtain data descriptive of a design space for a physical design problem. The design space is parameterized by a first set of parameters. The system can reparameterize the design space with a machine-learned model that comprises a second set of parameters. For a plurality of iterations, the system can provide an input to the machine-learned model to produce a proposed solution. The system can apply one or more design constraints to the solution to create a constrained solution. The system can generate a physical outcome associated with the constrained solution using a physical model. The system can evaluate the physical outcome using an objective function and update at least one of the second set of parameters. After the plurality of iterations, the system can output a solution.