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Abstract Nanophotonic freeform design has the potential to push the performance of optical components to new limits, but there remains a challenge to effectively perform optimization while reliably enforcing design and manufacturing constraints. We present Neuroshaper, a framework for freeform geometric parameterization in which nanophotonic device layouts are defined using an analytic neural network representation. Neuroshaper serves as a qualitatively new way to perform shape optimization by capturing multi-scalar, freeform geometries in an overparameterized representation scheme, enabling effective optimization in a smoothened, high dimensional geometric design space. We show that Neuroshaper can enforce constraints and topology manipulation in a manner where local constraints lead to global changes in device morphology. We further show numerically and experimentally that Neuroshaper can apply to a diversity of nanophotonic devices. The versatility and capabilities of Neuroshaper reflect the ability of neural representation to augment concepts in topological design. 

Surrogate neural network-based partial differential equation (PDE) solvers have the potential to solve PDEs in an accelerated manner, but they are largely limited to systems featuring fixed domain sizes, geometric layouts, and boundary conditions. We propose Specialized Neural Accelerator-Powered Domain Decomposition Methods (SNAP-DDM), a DDM-based approach to PDE solving in which subdomain problems containing arbitrary boundary conditions and geometric parameters are accurately solved using an ensemble of specialized neural operators. We tailor SNAP-DDM to 2D electromagnetics and fluidic flow problems and show how innovations in network architecture and loss function engineering can produce specialized surrogate subdomain solvers with near unity accuracy. We utilize these solvers with standard DDM algorithms to accurately solve freeform electromagnetics and fluids problems featuring a wide range of domain sizes.