论文标题
通过顺序的蒙特卡洛自适应半参数贝叶斯微分方程
Adaptive semiparametric Bayesian differential equations via sequential Monte Carlo
论文作者
论文摘要
非线性微分方程（DES）在广泛的科学问题中使用来对复杂的动态系统进行建模。微分方程通常包含具有科学意义的未知参数，必须从动态系统的嘈杂测量中估算。通常，非线性DES没有封闭形式的解决方案，而感兴趣的参数的可能性表面是多模式的，并且对不同的参数值非常敏感。我们为非线性DE系统提出了一个贝叶斯框架。灵活的非参数函数用于表示动态过程，从而可以避免昂贵的数值求解器。提出了退火框架中的顺序蒙特卡洛算法，以对DES中的参数进行贝叶斯推断。在我们的数值实验中，我们使用普通微分方程的示例并延迟微分方程来证明所提出算法的有效性。我们开发了一个可在\ url {https://github.com/shijiaw/smcde}上获得的R软件包。
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 \url{https://github.com/shijiaw/smcDE}.
