截断Burgers-Hopf动力系统对非平衡扰动的最优响应
Optimal response to non-equilibrium disturbances under truncated Burgers-Hopf dynamics
摘要：
我们的模型和计算截断Burgers-Hopf动力学的平均响应有限扰动远离吉布斯均分能谱使用一个动态优化框架最近概念化的一系列文件。非平衡平均有近似的测地线路径在概率空间中，最适合的Liouvillean动态在一个家庭的准平衡试验密度。通过重铸的测地线原则作为一个最优控制问题，我们解决了数值的非平衡响应使用增广拉格朗日，非线性共轭梯度下降法。对于中等扰动，我们发现一个很好的协议之间的最佳预测和截断Burgers-Hopf动力学的直接数值模拟。在这个接近平衡的制度，我们认为，最优响应理论提供了一个近似的，但预测对应的波动耗散身份。
英文摘要：
We model and compute the average response of truncated Burgers-Hopf dynamics to finite perturbations away from the Gibbs equipartition energy spectrum using a dynamical optimization framework recently conceptualized in a series of papers. Non-equilibrium averages are there approximated in terms of geodesic paths in probability space that best-fit the Liouvillean dynamics over a family of quasi-equilibrium trial densities. By recasting the geodesic principle as an optimal control problem, we solve numerically for the non-equilibrium responses using an augmented Lagrangian, non-linear conjugate gradient descent method. For moderate perturbations, we find an excellent agreement between the optimal predictions and the direct numerical simulations of the truncated Burgers-Hopf dynamics. In this near-equilibrium regime, we argue that the optimal response theory provides an approximate yet predictive counterpart to fluctuation-dissipation identities.
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