论文标题
对PDE的深度替代物的积极学习:应用到元图设计
Active learning of deep surrogates for PDEs: Application to metasurface design
论文作者
论文摘要
偏差方程的替代模型被广泛用于元材料的设计中,以快速评估可综合组件的行为。但是,机器学习的准确替代物的培训成本可以随变量的数量迅速增加。对于光子设备模型,我们发现随着设计区域的增长比光波长大,这种训练变得特别具有挑战性。我们提出了一种活跃的学习算法,该算法将训练点的数量减少了与随机样品相比的光学表面组件的神经网络替代模型的数量级以上。结果表明,替代评估比直接解决的速度要快两个数量级,我们证明了如何利用这一点以加速大规模的工程优化。
Surrogate models for partial-differential equations are widely used in the design of meta-materials to rapidly evaluate the behavior of composable components. However, the training cost of accurate surrogates by machine learning can rapidly increase with the number of variables. For photonic-device models, we find that this training becomes especially challenging as design regions grow larger than the optical wavelength. We present an active learning algorithm that reduces the number of training points by more than an order of magnitude for a neural-network surrogate model of optical-surface components compared to random samples. Results show that the surrogate evaluation is over two orders of magnitude faster than a direct solve, and we demonstrate how this can be exploited to accelerate large-scale engineering optimization.