论文标题
部分可观测时空混沌系统的无模型预测
Online bin stretching lower bounds: Improved search of computational proofs
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。
Computing lower and upper bounds on the competitive ratio of online algorithms is a challenging question: For a minimization combinatorial problem, proving a competitive ratio for a given algorithm leads to an upper bound. However computing lower bounds requires a proof on all algorithms. This can be modeled as a 2-player game where a strategy for one of the players is a proof for the lower bound. The tree representing the proof can can be found computationally. This method has been used with success on the online bin stretching problem where a set of items must be packed online in $m$ bins. The items are guaranteed to fit into the $m$ bins. However, the online procedure might require to stretch the bins to a larger capacity in order to be able to pack all the items. This stretching factor is the objective to be minimized. We propose original ideas to strongly improve the speed of computer searches for lower bound: propagate the game states that can be pruned from the search and improve the speed and memory usage in the dynamic program which is used in the search. These improvements allowed to increase significantly the speed of the search and hence to prove new lower bounds for the bin stretching problem for 6, 7 and 8 bins.
