论文标题
迭代替代模型优化（ISMO）：一种用于PDE的主动学习算法，用于PDE的限制优化，深层神经网络
Iterative Surrogate Model Optimization (ISMO): An active learning algorithm for PDE constrained optimization with deep neural networks
论文作者
论文摘要
我们提出了一种新型的主动学习算法，称为迭代替代模型优化（ISMO），以实现PDE约束优化问题的稳健有效的数值近似。该算法基于深度神经网络，其关键特征是通过深神经网络与任何基本标准优化算法之间的反馈回路进行迭代选择训练数据。在合适的假设下，我们表明，随着训练样本数量的增加，所得的优化器会呈指数速度（并且具有指数衰减的差异）。为PDE提供了最佳控制，参数识别和形状优化问题的数值示例，以验证提出的理论，并说明ISMO显着优于标准的基于基于Deep Deep News网络的替代替代算法。
We present a novel active learning algorithm, termed as iterative surrogate model optimization (ISMO), for robust and efficient numerical approximation of PDE constrained optimization problems. This algorithm is based on deep neural networks and its key feature is the iterative selection of training data through a feedback loop between deep neural networks and any underlying standard optimization algorithm. Under suitable hypotheses, we show that the resulting optimizers converge exponentially fast (and with exponentially decaying variance), with respect to increasing number of training samples. Numerical examples for optimal control, parameter identification and shape optimization problems for PDEs are provided to validate the proposed theory and to illustrate that ISMO significantly outperforms a standard deep neural network based surrogate optimization algorithm.
