low_e1_d-1_HJ_Lagrange_long.mat from Observation-based correction of dynamical models using thermostats

Models used in simulation may give accurate short-term trajectories but distort long-term (statistical) properties. In this work, we augment a given approximate model with a control law (a ‘thermostat’) that gently perturbs the dynamical system to target a thermodynamic state consistent with a set of prescribed (possibly evolving) observations. As proof of concept, we provide an example involving a point vortex fluid model on the sphere, for which we show convergence of equilibrium quantities (in the stationary case) and the ability of the thermostat to dynamically track a transient state.

仿真中使用的模型虽可生成准确的短期轨迹，却会扭曲长期（统计）特性。本研究为给定的近似模型添加了一种控制律（control law，即‘恒温器’），该控制律可对动力系统（dynamical system）进行轻柔扰动，使其目标热力学状态（thermodynamic state）与一组预设（可能随时间演化的）观测结果保持一致。作为概念验证，我们给出了一个涉及球面点涡流体模型（point vortex fluid model）的示例，在此示例中我们证明了平稳情形下平衡量（equilibrium quantities）的收敛性，以及该恒温器动态追踪瞬态（transient state）的能力。