论文标题
将高斯流程限制为线性普通微分方程的系统
Constraining Gaussian Processes to Systems of Linear Ordinary Differential Equations
论文作者
论文摘要
许多应用程序中的数据遵循普通微分方程（ODE）的系统。本文提出了一种新型的算法和符号结构，用于高斯过程的协方差函数（GPS），并严格遵循具有恒定系数的线性均匀ode系统，我们称之为lode-gps。将这种强的感应偏置引入GP，可以改善此类数据的建模。使用史密斯正常形式算法，一种符号技术，我们克服了当前在艺术状态下的当前限制：（1）需要在一组解决方案中对某些独特性条件的需求，通常在经典ode求解器及其概率求解器及其概率对应物中假定，（2）限制对可控系统的限制，通常是在covariancience in Covariancience in covariancience in covariancience中的典型假设。我们显示了Lode-GP在许多实验中的有效性，例如通过最大化的可能性来学习物理解释的参数。
Data in many applications follows systems of Ordinary Differential Equations (ODEs). This paper presents a novel algorithmic and symbolic construction for covariance functions of Gaussian Processes (GPs) with realizations strictly following a system of linear homogeneous ODEs with constant coefficients, which we call LODE-GPs. Introducing this strong inductive bias into a GP improves modelling of such data. Using smith normal form algorithms, a symbolic technique, we overcome two current restrictions in the state of the art: (1) the need for certain uniqueness conditions in the set of solutions, typically assumed in classical ODE solvers and their probabilistic counterparts, and (2) the restriction to controllable systems, typically assumed when encoding differential equations in covariance functions. We show the effectiveness of LODE-GPs in a number of experiments, for example learning physically interpretable parameters by maximizing the likelihood.
