Meta-neural Topology Optimization: Knowledge Infusion with Meta-learning

When faced with novel design problems, traditional topology optimization methods discard all prior design experience and start from a uniform initial guess. While this avoids biasing the optimizer towards any particular solution, it also means that many computationally expensive iterations are needed to converge. Existing machine learning approaches address this through data-driven design prediction, but require large datasets of pre-optimized structures and often struggle to generalize across boundary conditions and mesh resolutions. We propose a new method, termed meta-neural topology optimization, which uses a meta-learning algorithm to learn effective initial designs for topology optimization with neural field parameterizations -- continuous, mesh-independent representations that encode material distributions in the weights of a neural network. Through bilevel optimization, our method distills reusable design knowledge from partial optimization trajectories, eliminating the need for pre-optimized training data. By conditioning the neural field on strain energy fields of reference designs, a single set of learned parameters encodes problem-specific initial structures for diverse boundary conditions. We evaluate our approach on 3000 compliance minimization tasks across in-distribution, out-of-distribution, and cross-resolution scenarios. Our method converges in fewer iterations in 57.6% of in-distribution and 74.1% of cross-resolution tasks, while maintaining design quality competitive with standard density-based topology optimization. Notably, initializations learned on coarse meshes transfer successfully to discretizations four times finer. Code is available at https://github.com/bessagroup/metatopia.