Adaptive Semiparametric Bayesian Differential Equations Via Sequential Monte Carlo
提出一种贝叶斯框架，用灵活的非参数函数表示动态过程以避免数值求解器，并通过退火框架下的序贯蒙特卡洛算法推断非线性微分方程中的未知参数，适用于常微分和时滞微分方程。
Nonlinear differential equations (DEs) are used in a wide range of scientific problems to model complex dynamic systems. The differential equations often contain unknown parameters that are of scientific interest, which have to be estimated from noisy measurements of the dynamic system. Generally, there is no closed-form solution for nonlinear DEs, and the likelihood surface for the parameter of interest is multi-modal and very sensitive to different parameter values. We propose a Bayesian framework for nonlinear DE systems. A flexible nonparametric function is used to represent the dynamic process such that expensive numerical solvers can be avoided. A sequential Monte Carlo algorithm in the annealing framework is proposed to conduct Bayesian inference for parameters in DEs. In our numerical experiments, we use examples of ordinary differential equations and delay differential equations to demonstrate the effectiveness of the proposed algorithm. We developed an R package that is available at https://github.com/shijiaw/smcDE. Supplementary files for this article are available online.