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

arXiv:2607.07682v2 Announce Type: replace 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.

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.

Machine Learning (cs.LG)

arXiv:2607.07682 [cs.LG]

(or arXiv:2607.07682v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.07682 Focus to learn more arXiv-issued DOI via DataCite

https://doi.org/10.1109/TEVC.2026.3708401 Focus to learn more DOI(s) linking to related resources

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

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