论文标题
部分可观测时空混沌系统的无模型预测
Physicality, Modeling and Making in a Computational Physics Class
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。
Computation is intertwined with essentially all aspects of physics research and is invaluable for physicists' careers. Despite its disciplinary importance, integration of computation into physics education remains a challenge and, moreover, has tended to be constructed narrowly as a route to solving physics problems. Here, we broaden Physics Education Research's conception of computation by constructing an epistemic \emph{metamodel} -- a model of modeling -- incorporating insights on computational modeling from the philosophy of science and prior work. The metamodel is formulated in terms of practices, things physicists do, and how these inform one another. We operationalize this metamodel in an educational environment that incorporates making, the creation of shared physical and digital artifacts, intended to promote students' agency, creativity and self-expression alongside doing physics. We present a content analysis of student work from initial implementations of this approach to illustrate the very complex epistemic maneuvers students make as they engaged in computational modeling. We demonstrate how our metamodel can be used to understand student practices, and conclude with implications of the metamodel for instruction and future research.