NOTES enables efficient PDE-constrained inverse design via neural operator and evolutionary strategy

The paper introduces Neural Operator-enabled Topology-informed Evolutionary Strategy (NOTES), a method that integrates dimensionality reduction, representation learning, and evolutionary optimization for inverse design of physical systems governed by partial differential equations.

• NOTES couples a DeepONet-based neural operator with Covariance Matrix Adaptation Evolution Strategy (CMA-ES) to perform global optimization in a compact latent space encoding topology-aware priors.
• Applied to nanophotonic beam-deflector inverse design, NOTES reduces design dimensionality from 256 to 25 and consistently achieves over 95 percent efficiency.
• In structural optimization tasks, the method discovers designs achieving compliance down to 246.
• The approach outperforms CMA-ES, topology optimization, and other baselines while decoupling topology learning from the governing physics in a PDE solver.

By providing a flexible and transferable framework, NOTES addresses the computational demands of high-dimensional and non-convex design spaces where generative models often lack robustness.