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Reinforcement learning-based estimation for spatio-temporal systems
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DOI：10.1038/s41598-024-72055-1.png)
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Abstract
En 中文
State estimators such as Kalman filters compute an estimate of the instantaneous state of a dynamical system from sparse sensor measurements. For spatio-temporal systems, whose dynamics are governed by partial differential equations (PDEs), state estimators are typically designed based on a reduced-order model (ROM) that projects the original high-dimensional PDE 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 with parametric uncertainties, we show that in the limit of very few sensors, the trained RL-ROE outperforms a Kalman filter designed using the same ROM and yields accurate instantaneous estimates of high-dimensional states corresponding to unknown initial conditions and physical parameter values. The RL-ROE opens the door to lightweight real-time sensing of systems governed by parametric PDEs.
Keywords:
Estimation
Filtering
Partial differential equations
Model reduction
Reinforcement learning
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