Neural Operator-enabled Topology-informed Evolutionary Strategy for PDE-Constrained Optimization

• URL: http://arxiv.org/abs/2607.07682v1
• Date: Wed, 08 Jul 2026 17:41:56 GMT
• Title: Neural Operator-enabled Topology-informed Evolutionary Strategy for PDE-Constrained Optimization
• Abstract summary: Notes integrates dimensionality reduction, representation learning, and optimization for efficient transferable inverse design.<n> Applied to nanophotonic beam-deflector inverse design governed by Maxwell Neurals equations, Notes consistently achieves 95 percent efficiency.
• Score: 8.562789153023688
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The inverse design of physical systems governed by partial differential equations is computationally demanding due to the high dimensionality and non-convexity of design spaces. Generative models for inverse design often lack robustness and transferability, whereas evolutionary strategies are robust but struggle in high-dimensional spaces. This paper introduces a Neural Operator-enabled Topology-informed Evolutionary Strategy (NOTES) that integrates dimensionality reduction, representation learning, and evolutionary optimization for efficient and transferable inverse design. NOTES couples a DeepONet-based neural operator with the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) to perform global optimization in a compact latent space that encodes topology-aware priors while discovering high-performance designs for unseen operating conditions. Applied to nanophotonic beam-deflector inverse design governed by Maxwell's equations, NOTES reduces the design dimensionality from 256 to 25 and consistently achieves over 95 percent efficiency, outperforming CMA-ES, topology optimization, and other baselines. Applied to structural optimization, NOTES discovers designs that achieve compliance down to 246. By decoupling topology learning of a DeepONet from the governing physics in a PDE solver, NOTES provides a flexible and transferable framework for the inverse design of physical systems.

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