Stochastic collocation (SC) is a well-known non-intrusive method of constructing surrogate models for uncertainty quantification. In dynamical systems, SC is especially suited for full-field uncertainty propagation that characterizes the distributions of the high-dimensional primary solution fields of a model with stochastic input parameters. However, due to the highly nonlinear nature of the parameter-to-solution map in even the simplest dynamical systems, the constructed SC surrogates are often inaccurate. This work presents an alternative approach, where we apply the SC approximation over the dynamics of the model, rather than the solution. By combining the data-driven sparse identification of nonlinear dynamics (SINDy) framework with SC, we construct dynamics surrogates and integrate them through time to construct the surrogate solutions. We demonstrate that the SC-over-dynamics framework leads to smaller errors, both in terms of the approximated system trajectories as well as the model state distributions, when compared against full-field SC applied to the solutions directly. We present numerical evidence of this improvement using three test problems: a chaotic ordinary differential equation, and two partial differential equations from solid mechanics.

尝试应用数据驱动的非线性动力学稀疏辨识（SINDy）框架与随机插值（Stochastic Collocation，SC）相结合，构建动力学代理，并通过时间积分来构建代理解决方案。通过将SC应用于模型动力学而不是解决方案，我们证明了SC过动力学框架在近似系统轨迹和模型状态分布方面相较于直接应用于解决方案的全场SC方法都具有更小的误差。我们通过三个测试问题，包括一个混沌常微分方程和两个固体力学方程，提供了这种改进的数值证据。

基于准确数据驱动的动力系统代理模型用于不确定性的正向传播