Local-gradient-based optimization approaches lack nonlocal exploration ability required for escaping from local minima in non-convex landscapes. A directional Gaussian smoothing (DGS) approach was recently proposed by the authors (Zhang et al., 2020) and used to define a truly nonlocal gradient, referred to as the DGS gradient, in order to enable nonlocal exploration in high-dimensional black-box optimization. Promising results show that replacing the traditional local gradient with the nonlocal DGS gradient can significantly improve the performance of gradient-based methods in optimizing highly multi-modal loss functions. However, the current DGS method is designed for unbounded and unconstrained optimization problems, making it inapplicable to real-world engineering design optimization problems where the tuning parameters are often bounded and the loss function is usually constrained by physical processes. In this work, we propose to extend the DGS approach to the constrained inverse design framework in order to find a better design. The proposed framework has its advantages in portability and flexibility to naturally incorporate the parameterization, physics simulation, and objective formulation together to build up an effective inverse design workflow. A series of adaptive strategies for smoothing radius and learning rate updating are developed to improve the computational efficiency and robustness. To enable a clear binarized design, a dynamic growth mechanism is imposed on the projection strength in parameterization. Our methodology is demonstrated by an example of designing a nanoscale wavelength demultiplexer and shows superior performance compared to the state-of-the-art approaches. By incorporating volume constraints, the optimized design achieves an equivalently high performance but significantly reduces the amount of material usage.
- Jiaxin Zhang, Sirui Bi, and Guannan Zhang, A directional Gaussian smoothing optimization method for computational inverse design in nanophotonics, Materials & Design, 197 (1), pp. 109213, 2021.
- Jiaxin Zhang, Sirui Bi, and Guannan Zhang, A nonlocal-gradient descent method for inverse design in nanophotonics, NeurIPS Workshop on Machine Learning for Engineering Modeling, Simulation and Design, Dec. 2020. [Download our poster] [A short video presentation]
Significance and Impact
Compared to the local gradient, the directional smoothing allows for a large smoothing radius to capture the global structure of loss landscapes and thus provide a strong nonlocal exploration capability for escaping from local minima in non-convex landscapes. Furthermore, our workflow does not rely on the sensitivity analysis with multiple assumptions, so that it has wider feasibility to nonlinear, dynamic, and non-isotropic materials under complex physical conditions. In the meantime, our method having the benefits of gradient-based optimization can be easily scaled to high-dimensional design space, which alleviates the challenges in derivative-free global optimization, such as Bayesian optimization.
Last Updated: January 14, 2021 - 11:02 am