Particle filtering is a popular class of methods to estimate the state of non-linear non-Gaussian state-space models in an online manner. However, in practice, their application to systems described by partial differential equations is limited due to issues of particle degeneracy in arbitrarily high dimension spaces and the prohibitively high computational cost of evaluating posteriors with direct numerical solvers. Here we use smooth transformation of prior particles into posterior, localization in which spurious correlations over large distances are suppressed, marginalize out conditionally linear-Gaussian state variables, employ a Physics-informed neural network to predict PDE solution over large time steps, and implement a cheap operator for recursive projection onto affine subspace of physical constraints. Through hardware-in-the-loop simulation testing on benchmark problem of a one-way coupled PDE system, it is validated that such an integrated framework maintains higher accuracy of the state estimates over existing methods when degree of non-linearity is increased. The efficiency and scalability of proposed framework paves way for state estimation of coupled PDE systems on embedded systems and mobile platforms.

中文翻译：

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可扩展的边缘化粒子滤波器，用于改进单向耦合 PDE 系统的状态估计


粒子过滤是一类流行的方法，用于在线估计非线性非高斯状态空间模型的状态。然而，在实践中，由于任意高维空间中的粒子简并问题以及使用直接数值求解器评估后验的高计算成本，它们在偏微分方程描述的系统中的应用受到限制。在这里，我们使用先验粒子到后验粒子的平滑变换，其中抑制了长距离上的虚假相关性，边缘化了条件线性高斯状态变量，使用物理信息神经网络来预测大时间步长的偏微分方程解，并实现了一个廉价的运算符，用于递归投影到物理约束的仿射子空间。通过对单向耦合偏微分方程系统基准问题的硬件在环仿真测试，验证了当非线性度增加时，这种集成框架比现有方法保持了更高的状态估计精度。所提出的框架的效率和可扩展性为嵌入式系统和移动平台上耦合 PDE 系统的状态估计铺平了道路。