Interface PINNs (I-PINNs): A physics-informed neural networks framework for interface problems

Here, 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.. Authors: Sarma, Antareep Kumar [Indian Inst. of Technology (IIT), Madras (India)] (ORCID:0000000210042787); Roy, Sumanta [Indian Inst. of Technology (IIT), Madras (India)] (ORCID:0000000314416624); Annavarapu, Chandrasekhar [Indian Inst. of Technology (IIT), Madras (India)] (ORCID:0000000336080500); Roy, Pratanu [Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)] (ORCID:0000000194680999); Jagannathan, Shriram [Nvidia Corporation, Santa Clara, CA (United States)]. DOE Contract: AC52-07NA27344. Subjects: 42 ENGINEERING; 58 GEOSCIENCES; 97 MATHEMATICS AND COMPUTING; Deep learning; Discontinuous fields; Heterogeneous materials; Interface problems; Physics-informed machine learning; Physics-informed neural networks