论文标题
通过学习知觉的微分方程约束及其应用的优化
Optimization with learning-informed differential equation constraints and its applications
论文作者
论文摘要
灵感来自于对半线性椭圆形偏微分方程和物理集成成像的最佳控制应用程序的启发，并且研究了仅通过数据驱动技术才能访问的成分的微分方程约束优化问题。特别的重点是分析和数值方法，用于机器学习组件的问题。对于相当一般的上下文，提供了错误分析，并解决了基于人工神经网络近似产生的特定属性。此外，为两个启发性应用程序中的每个应用程序进行了分析细节，并提供了数值结果。
Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through data-driven techniques are studied. A particular focus is on the analysis and on numerical methods for problems with machine-learned components. For a rather general context, an error analysis is provided, and particular properties resulting from artificial neural network based approximations are addressed. Moreover, for each of the two inspiring applications analytical details are presented and numerical results are provided.
