A systematic approach is developed for constructing proper trial solutions to Partial Differential Equations (PDEs) of up to second order, using neural forms that satisfy prescribed initial, boundary and interface conditions. The spatial domain considered is of the rectangular hyper-box type. On each face either Dirichlet or Neumann conditions may apply. Robin conditions may be accommodated as well. Interface conditions that induce discontinuities, have not been treated to date in the relevant neural network literature. As an illustration a common problem of heat conduction through a system of two rods in thermal contact is considered.

中文翻译：

---

求解矩形域内偏微分方程的神经形式的系统构造，受初始、边界和界面条件的影响

开发了一种系统方法，使用满足规定的初始、边界和界面条件的神经形式，为高达二阶的偏微分方程 (PDE) 构建适当的试验解。考虑的空间域是矩形超框类型。在每个面上，Dirichlet 或 Neumann 条件都可能适用。也可以适应罗宾条件。迄今为止，相关神经网络文献中尚未处理导致不连续性的界面条件。作为说明，我们考虑了通过热接触的两个棒的系统进行热传导的常见问题。