论文标题
对反问题的多级优化
Multilevel Optimization for Inverse Problems
论文作者
论文摘要
反问题发生在工程中的各种参数识别任务中。这些问题在实践中具有挑战性，因为它们需要重复评估计算昂贵的远期模型。我们引入了一个多级优化的统一框架，可以应用于广泛的基于优化的求解器。事实证明，我们的框架可以降低与评估各种物理模型所产生的昂贵前向图相关的计算成本。为了证明我们的分析的多功能性，我们讨论了它对包括多级（加速，随机）梯度下降，多级集合Kalman倒置和多级Langevin Sampler在内的各种方法的影响。我们还提供数值实验来验证我们的理论发现。
Inverse problems occur in a variety of parameter identification tasks in engineering. Such problems are challenging in practice, as they require repeated evaluation of computationally expensive forward models. We introduce a unifying framework of multilevel optimization that can be applied to a wide range of optimization-based solvers. Our framework provably reduces the computational cost associated with evaluating the expensive forward maps stemming from various physical models. To demonstrate the versatility of our analysis, we discuss its implications for various methodologies including multilevel (accelerated, stochastic) gradient descent, a multilevel ensemble Kalman inversion and a multilevel Langevin sampler. We also provide numerical experiments to verify our theoretical findings.
