论文标题
贝叶斯颂滤器的傅立叶状态空间模型
A Fourier State Space Model for Bayesian ODE Filters
论文作者
论文摘要
高斯ode滤波是一种求解普通微分方程（ODE）的概率数值方法。它从定义ode的矢量场的评估中计算出贝叶斯后验。其最受欢迎的版本采用了集成的布朗运动先验，它使用了泰勒的均值扩展来推断向前，并且具有与经典数值方法相同的收敛速率。由于许多重要ODE的解决方案是周期性功能（振荡器），因此我们提出了一个问题，是否也可以在高斯ode滤波的框架内将傅立叶扩展带来。为此，我们为ODES构建了一个傅立叶状态空间模型，并结合了泰勒（Brownian Motion）和傅立叶状态空间模型的“混合”模型。我们通过实验证明，混合模型如何在廉价预测到时域结束时变得有用。
Gaussian ODE filtering is a probabilistic numerical method to solve ordinary differential equations (ODEs). It computes a Bayesian posterior over the solution from evaluations of the vector field defining the ODE. Its most popular version, which employs an integrated Brownian motion prior, uses Taylor expansions of the mean to extrapolate forward and has the same convergence rates as classical numerical methods. As the solution of many important ODEs are periodic functions (oscillators), we raise the question whether Fourier expansions can also be brought to bear within the framework of Gaussian ODE filtering. To this end, we construct a Fourier state space model for ODEs and a `hybrid' model that combines a Taylor (Brownian motion) and Fourier state space model. We show by experiments how the hybrid model might become useful in cheaply predicting until the end of the time domain.
