arXivDaily arXiv每日学术速递 周一至周五更新
北美退伍军人节(Veterans Day),12 日无更新
arXiv 2302.01189cs.LGcs.SYeess.SY
收藏

基于强化学习的偏微分方程估计

Reinforcement learning-based estimation for partial differential equations

Mitsubishi Electric Research Laboratories(三菱电机研究院)

Saviz Mowlavi, Mouhacine Benosman

AI总结:

针对非线性偏微分方程系统中ROM误差影响状态估计的问题,提出强化学习降阶估计器RL-ROE,用强化学习训练的非线性策略校正测量信息,并在Burgers和Navier-Stokes方程中验证其少传感器优势。

摘要:

在由流体流动等非线性偏微分方程控制的系统中,卡尔曼滤波器等状态估计器的设计依赖于降阶模型(ROM),该模型将原始高维动力学投影到计算上可处理的低维空间。然而,ROM容易出现较大误差,这会对估计器的性能产生负面影响。在此,我们介绍强化学习降阶估计器(RL-ROE),这是一种基于ROM的估计器,其中接收测量值的校正项由通过强化学习训练的非线性策略给出。策略的非线性使RL-ROE能够有效补偿ROM的误差,同时仍利用不完美的动力学知识。通过涉及Burgers方程和Navier-Stokes方程的示例,我们表明在传感器极少的极限情况下,经过训练的RL-ROE优于使用相同ROM设计的卡尔曼滤波器。此外,它能为对应于各种物理参数值的轨迹生成准确的高维状态估计,而无需直接知道这些参数值。

英文摘要:

In systems governed by nonlinear partial differential equations such as fluid flows, the design of state estimators such as Kalman filters relies on a reduced-order model (ROM) that projects the original high-dimensional dynamics onto a computationally tractable low-dimensional space. However, ROMs are prone to large errors, which negatively affects the performance of the estimator. Here, we introduce the reinforcement learning reduced-order estimator (RL-ROE), a ROM-based estimator in which the correction term that takes in the measurements is given by a nonlinear policy trained through reinforcement learning. The nonlinearity of the policy enables the RL-ROE to compensate efficiently for errors of the ROM, while still taking advantage of the imperfect knowledge of the dynamics. Using examples involving the Burgers and Navier-Stokes equations, we show that in the limit of very few sensors, the trained RL-ROE outperforms a Kalman filter designed using the same ROM. Moreover, it yields accurate high-dimensional state estimates for trajectories corresponding to various physical parameter values, without direct knowledge of the latter.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑