Shape optimization using a neural implicit geometry representation

Abstract

A fundamental aspect of shape optimization is the geometry representation, since it determines the design space explored by the optimizer. Established approaches such as CAD-based parameterizations, free-form deformation, and node-based methods are widely used, but often require a manual, problem-specific setup, restrict the design space, or introduce many variables that require smoothing or filtering. This work presents a neural implicit geometry representation framework for gradient-based shape optimization. Geometries are described by a signed distance function represented by a neural decoder and controlled by a continuous latent field. The decoder is trained once on simple geometric primitives and then kept fixed, so new geometries are reconstructed and optimized by updating only latent control variables. The approach avoids problem-specific retraining and manual definition of design variables, provides local geometric control in a flexible design space, and yields a differentiable path to the extracted surface mesh. Reconstruction experiments show that geometrically diverse shapes can be represented without retraining. In three-dimensional drag-minimization problems, the method produces smooth shape evolutions, outperforms a comparable free-form deformation parameterization, and realizes topological changes. These results indicate that neural implicit geometry representations are a flexible and largely automated alternative to classical shape parameterizations.