SpSIR: a spatially-dependent sequential importance resampling for high dimensional spatial temporal system simulation

For a high dimensional spatial temporal system, data assimilation is introduced to dynamically adjust the simulation result when the model is imperfect or the parameters are imprecise. Sequential Monte Carlo (SMC) methods or particle filters (PFs) are popular data assimilation scheme. However, in a high dimensional spatial temporal system where observations and state are spatially distributed, directly applying SMC method may lead to poor prediction result or high computational cost because of the sample size. In this paper, we break a full state and observations into spatial regions and propose a new resampling algorithm: SpSIR. This algorithm exploits the spatial locality property and employs a divide and conquer strategy to reduce state dimension and data complexity. A case study in wildfire simulation demonstrates that the proposed SpSIR algorithm improves the performance of prediction even when sample size is not quite large.

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