We propose a new weak-form Physics-Informed Neural Network approach (named INI-VPINN). INI-VPINN naturally incorporates Neumann boundary and interface conditions into the variational formulation. It removes the need for additional loss terms or multiple subdomain networks. This framework employs compact support weighting functions and integration by parts to implicitly impose flux and continuity constraints. In this way, it implicitly ensures physical consistency across material boundaries. The proposed method is tested on Poisson and Laplace problems with sharp interfaces and complex geometries. Results show that, compared with several other Physics Informed Neural Networks-based formulations, the INI-VPINN consistently achieves higher accuracy, smoother and faster convergence. The proposed framework provides a general approach for solving multimaterial problems with complex geometries and mixed Neumann-Dirichlet boundary conditions using neural networks. The implementation is publicly available in a GitHub repository.

翻译：我们提出了一种新的弱形式物理信息神经网络方法（命名为INI-VPINN）。INI-VPINN将Neumann边界条件和界面条件自然地纳入变分公式中，消除了对额外损失项或多个子域网络的需求。该框架采用紧支撑加权函数和分部积分来隐式施加通量和连续性约束，从而在材料边界处隐式保证物理一致性。所提出的方法在具有尖锐界面和复杂几何的Poisson及Laplace问题上进行了测试。结果表明，与多种其他基于物理信息神经网络的公式相比，INI-VPINN始终能实现更高的精度、更平滑且更快的收敛。该框架提供了一种通用方法，可利用神经网络求解具有复杂几何和混合Neumann-Dirichlet边界条件的多材料问题。相关实现已在GitHub仓库中公开提供。