We present a novel physics-informed neural networks (PINNs) framework for modeling interface problems, termed Interface PINNs (I-PINNs). I-PINNs uses different neural networks for any two subdomains separated by a sharp interface such that the neural networks differ only through their activation functions while the other parameters remain identical. The performance of I-PINNs, conventional PINNs, and other existing domain-decomposition PINNs methods such as extended PINNs (XPINNs) and multi-domain PINN (M-PINN) is compared through several one-dimensional, two-dimensional, and three-dimensional benchmark elliptic interface problems. The results demonstrate that I-PINNs provides a root-mean-square-error accuracy, at least two orders of magnitude better than conventional PINNs and XPINNs at approximately one-tenth of the computational cost of conventional PINNs and half the cost of XPINNs. Additionally, while I-PINNs and M-PINN provide comparable accuracies, M-PINN is found to be approximately 50% more expensive.

中文翻译：

---

接口 PINN (I-PINN)：用于解决接口问题的物理信息神经网络框架


我们提出了一种新颖的物理信息神经网络 (PINN) 框架，用于建模接口问题，称为接口 PINN (I-PINN)。 I-PINN 对由尖锐界面分隔的任意两个子域使用不同的神经网络，使得神经网络仅通过其激活函数而有所不同，而其他参数保持相同。通过几个一维、二维和三维模型对 I-PINN、传统 PINN 以及其他现有的域分解 PINN 方法（例如扩展 PINN（XPINN）和多域 PINN（M-PINN））的性能进行了比较。维度基准椭圆界面问题。结果表明，I-PINN 的均方根误差精度比传统 PINN 和 XPINN 至少高出两个数量级，而计算成本约为传统 PINN 的十分之一和 XPINN 的一半。此外，虽然 I-PINN 和 M-PINN 的精度相当，但 M-PINN 的成本要高出大约 50%。