Traditional electrostatic simulation are meshed-based methods which convert partial differential equations into an algebraic system of equations and their solutions are approximated through numerical methods. These methods are time consuming and any changes in their initial or boundary conditions will require solving the numerical problem again. Newer computational methods such as the physics informed neural net (PINN) similarly require re-training when boundary conditions changes. In this work, we propose an end-to-end deep learning approach to model parameter changes to the boundary conditions. The proposed method is demonstrated on the test problem of a long air-filled capacitor structure. The proposed approach is compared to plain vanilla deep learning (NN) and PINN. It is shown that our method can significantly outperform both NN and PINN under dynamic boundary condition as well as retaining its full capability as a forward model.

翻译：传统的静电仿真方法基于网格划分，将偏微分方程转化为代数方程组，并通过数值方法近似求解。这些方法耗时较长，且初始条件或边界条件的任何变化都需要重新求解数值问题。较新的计算方法如物理信息神经网络（PINN）在边界条件变化时同样需要重新训练。本研究提出一种端到端的深度学习方法，用于建模边界条件的参数变化。该方法在长型空气填充电容器结构的测试问题上得到验证。所提出的方法与普通深度学习（NN）及PINN进行了对比。结果表明，在动态边界条件下，我们的方法显著优于NN和PINN，同时完全保留了其作为正向模型的能力。