论文标题
部分可观测时空混沌系统的无模型预测
On the use of hybrid coarse-level models in multilevel minimization methods
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。
Solving large-scale nonlinear minimization problems is computationally demanding. Nonlinear multilevel minimization (NMM) methods explore the structure of the underlying minimization problem to solve such problems in a computationally efficient and scalable manner. The efficiency of the NMM methods relies on the quality of the coarse-level models. Traditionally, coarse-level models are constructed using the additive approach, where the so-called $τ$-correction enforces a local coherence between the fine-level and coarse-level objective functions. In this work, we extend this methodology and discuss how to enforce local coherence between the objective functions using a multiplicative approach. Moreover, we also present a hybrid approach, which takes advantage of both, additive and multiplicative, approaches. Using numerical experiments from the field of deep learning, we show that employing a hybrid approach can greatly improve the convergence speed of NMM methods and therefore it provides an attractive alternative to the almost universally used additive approach.
