Identification of non-linear stochastic spatiotemporal dynamical systems

A systematic identification method for non-linear stochastic spatiotemproal (SST) systems described by non-linear stochastic partial differential equations (SPDEs) is investigated in this study based on pointwise observation data. A theoretical framework for a semi-finite element model approximating to an infinite-dimensional system is established, and several fundamental issues are discussed including the approximation error between the underlying infinite-dimensional dynamics and the model to be identified, and its rationality etc. Based on the proposed theoretical framework, a general identification method with irregular observation data is provided. These results not only provide an effective method for the identification of non-linear SST systems using measurement data (both offline and online), but also demonstrate a potential solution for the analysis, design and control of non-linear SST systems from a numerical point of view.