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Shape optimization has been playing an important role in a large variety ofengineering applications. Existing shape optimization methods are generallymesh-dependent and therefore encounter challenges due to mesh deformation. Toovercome this limitation, we present a new adjoint-oriented neural networkmethod, AONN-2, for PDE-constrained shape optimization problems. This methodextends the capabilities of the original AONN method [1], which is developedfor efficiently solving parametric optimal control problems. AONN-2 inheritsthe direct-adjoint looping (DAL) framework for computing the extremum of anobjective functional and the neural network methods for solving complicatedPDEs from AONN. Furthermore, AONN-2 expands the application scope to shapeoptimization by taking advantage of the shape derivatives to optimize the shaperepresented by discrete boundary points. AONN-2 is a fully mesh-free shapeoptimization approach, naturally sidestepping issues related to meshdeformation, with no need for maintaining mesh quality and additional meshcorrections. A series of experimental results are presented, highlighting theflexibility, robustness, and accuracy of AONN-2.

AONN-2: An adjoint-oriented neural network method for PDE-constrained shape optimization