论文标题
逆问题：使用基于物理的简化模型的确定性方法
Inverse Problems: A Deterministic Approach using Physics-Based Reduced Models
论文作者
论文摘要
这些讲义说明了我通过结合最佳测量观测值和参数化的PDE模型，总结了我就解决反问题（状态和参数估计）主题提供的各种暑期学校。根据任何重建算法可以达到的最小重建误差定义了最佳性能概念之后，注释基于非线性还原模型的实践数值算法，这些算法可以证明它们可以证明它们可以提供接近最佳的性能。我们还讨论了使用该方法的传感器放置算法。拟议的概念可能被视为探索贝叶斯倒置的替代方案，而有利于更确定性的准确性量化概念。
These lecture notes summarize various summer schools that I have given on the topic of solving inverse problems (state and parameter estimation) by combining optimally measurement observations and parametrized PDE models. After defining a notion of optimal performance in terms of the smallest reconstruction error that any reconstruction algorithm can achieve, the notes present practical numerical algorithms based on nonlinear reduced models for which one can prove that they can deliver a performance close to optimal. We also discuss algorithms for sensor placement with the approach. The proposed concepts may be viewed as exploring alternatives to Bayesian inversion in favor of more deterministic notions of accuracy quantification.
