论文标题
高斯过程回归受边界价值问题约束
Gaussian Process Regression constrained by Boundary Value Problems
论文作者
论文摘要
我们为高斯过程开发了一个受边界价值问题约束的回归框架。该框架可以应用于通过已知的二阶差异操作员和边界条件来推断良好的边界值问题的解决方案，但仅对源项的分散观测值可用。溶液的分散观察结果也可以用于回归中。该框架将高斯过程的线性转换与使用光谱膨胀在边界值问题的特征函数中给出的内核相结合。因此，它受益于减少协方差矩阵的属性。我们证明，与没有边界条件约束的物理学的高斯过程回归相比，所得框架可以产生更准确和稳定的解决方案推断。
We develop a framework for Gaussian processes regression constrained by boundary value problems. The framework may be applied to infer the solution of a well-posed boundary value problem with a known second-order differential operator and boundary conditions, but for which only scattered observations of the source term are available. Scattered observations of the solution may also be used in the regression. The framework combines co-kriging with the linear transformation of a Gaussian process together with the use of kernels given by spectral expansions in eigenfunctions of the boundary value problem. Thus, it benefits from a reduced-rank property of covariance matrices. We demonstrate that the resulting framework yields more accurate and stable solution inference as compared to physics-informed Gaussian process regression without boundary condition constraints.
