论文标题
部分可观测时空混沌系统的无模型预测
Smart: A program to automatically compute accelerations and variational equations
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。
Modern astronomical potentials modeling galaxies or stellar systems can be rather involved, and deriving their first derivatives (accelerations) and second derivatives (variational equations) in order to compute orbits and their chaoticity may be a formidable task. We present here a fully automated routine, dubbed Smart, with which the accelerations and the variational equations of an arbitrary potential that has been written in the Fortran 77 language can be computed. Almost any Fortran 77 statement is admitted in the potential, and the output are standard Fortran 77 routines ready to use. We validate our algorithm with a set of potentials including time-dependent, velocity-dependent and very complex potentials that even involve auxiliary routines. We also describe with some detail a realistic seven-component Galactic potential, MilkyWayHydra, which yields very involved derivatives, thus being a good test bed for Smart.
