Reinforcement learning-based estimation for partial differential equations
arxiv(2023)
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.
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