论文标题
部分可观测时空混沌系统的无模型预测
A Discipline of Programming with Quantities
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。
In scientific and engineering applications, physical quantities embodied as units of measurement (UoM) are frequently used. The loss of the Mars climate orbiter, attributed to a confusion between the metric and imperial unit systems, popularised the disastrous consequences of incorrectly handling measurement values. Dimensional analysis can be used to ensure expressions containing annotated values are evaluated correctly. This has led to the development of a large number of libraries, languages and validators to ensure developers can specify and verify UoM information in their designs and codes. Many tools can also automatically convert values between commensurable UoM, such as yards and metres. However these systems do not differentiate between quantities and dimensions. For instance torque and work, which share the same UoM, can not be interchanged because they do not represent the same entity. We present a named quantity layer that complements dimensional analysis by ensuring that values of different quantities are safely managed. Our technique is a mixture of analysis and discipline, where expressions involving multiplications are relegated to functions, in order to ensure that named quantities are handled soundly.