用物理方程增强稀疏观测，让机器人在复杂流体中更准更快地控制。

Control in fluid environments is an important research area with numerous applications across various domains, including underwater robotics, aerospace engineering, and biomedical systems. However, in practice, control methods often face challenges due to sparse or missing observations, stemming from sensor limitations and faults. These issues result in observations that are not only sparse but also inconsistent in their number and modalities (e.g., velocity and pressure sensors). In this work, we propose a Physics-Informed Representation (PIR) algorithm for multi-modal policies of control to leverage the sparse and random observations in complex fluid environments. PIR integrates sparse observational data with the Partial Differential Equation (PDE) information to distill a unified representation of fluid systems. The main idea is that PDE solutions are determined by three elements: the equation, initial conditions, and boundary conditions. Given the equation, we only need to learn the representation of the initial and boundary conditions, which define a trajectory of a specific fluid system. Specifically, it leverages PDE loss to fit the neural network and data loss calculated on the observations with random quantities and multi-modalities to propagate the information with initial and boundary conditions into the representations. The representations are the learnable parameters or the output of the encoder. In the experiments, the PIR illustrates the superior consistency with the features of the ground truth compared with baselines, even when there are missing modalities. Furthermore, PIR combined with Reinforcement Learning has been successfully applied in control tasks where the robot leverages the learned state by PIR faster and more accurately, passing through the complex vortex street from a random starting location to reach a random target.