论文标题
部分可观测时空混沌系统的无模型预测
A generalized Hamiltonian formulation of the principle of virtual work
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。
The authors previous derivation of a variational principle from the total work functional, as a generalization of the first variation of an action functional, is extended by deriving a corresponding generalization of the Hamiltonian formulation of that action functional. Some consequences of it are that one can decompose the Lie brackets of arbitrary vector fields on symplectic mechanics into a sum of terms that involve the Poisson brackets of the functions that appear in the normal form of the Pfaffian that is symplectic-dual to the vector field and that one can also generalize the Hamilton-Jacobi equation to a system of nonlinear first-order partial differential equations for the contact field that one uses in order to obtain them.
