论文标题
部分可观测时空混沌系统的无模型预测
ADMM based Fourier phase retrieval with untrained generative prior
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
Fourier phase retrieval (FPR) is an inverse problem that recovers the signal from its Fourier magnitude measurement, it's ill-posed especially when the sampling rates are low. In this paper, an untrained generative prior is introduced to attack the ill-posedness. Based on the alternating direction method of multipliers (ADMM), an algorithm utilizing the untrained generative network called Net-ADM is proposed to solve the FPR problem. Firstly, the objective function is smoothed and the dimension of the variable is raised to facilitate calculation. Then an untrained generative network is embedded in the iterative process of ADMM to project an estimated signal into the generative space, and the projected signal is applied to next iteration of ADMM. We theoretically analyzed the two projections included in the algorithm, one makes the objective function descent, and the other gets the estimation closer to the optimal solution. Numerical experiments show that the reconstruction performance and robustness of the proposed algorithm are superior to prior works, especially when the sampling rates are low.
