论文标题
关于通过分析函数参数参数的边界条件
On boundary conditions parametrized by analytic functions
论文作者
论文摘要
计算机代数可以使用符号算法回答有关部分微分方程的各种问题。但是，在计算机代数中将数据包含在方程中很少。因此，最近，计算机代数模型与高斯流程（机器学习中的回归模型）相结合，以描述数据下某些微分方程的行为。尽管可以在这种情况下描述多项式边界条件，但我们将这些模型扩展到分析边界条件。此外，我们描述了具有某些分析系数的Weyl代数的Gröbner和Janet碱基的必要算法。使用这些算法，我们提供了由分析功能界定并适应观测的域中无差流的示例。
Computer algebra can answer various questions about partial differential equations using symbolic algorithms. However, the inclusion of data into equations is rare in computer algebra. Therefore, recently, computer algebra models have been combined with Gaussian processes, a regression model in machine learning, to describe the behavior of certain differential equations under data. While it was possible to describe polynomial boundary conditions in this context, we extend these models to analytic boundary conditions. Additionally, we describe the necessary algorithms for Gröbner and Janet bases of Weyl algebras with certain analytic coefficients. Using these algorithms, we provide examples of divergence-free flow in domains bounded by analytic functions and adapted to observations.
