Adaptive Interface-PINNs (AdaI-PINNs): An Efficient Physics-Informed Neural Networks Framework for Interface Problems

Journal Article · Sat Mar 01 00:00:00 EST 2025 · Communications in Computational Physics

DOI:https://doi.org/10.4208/cicp.OA-2024-0131· OSTI ID:2571702

Roy, Sumanta ^[1]; Annavarapu, Chandrasekhar ^[1]; Roy, Pratanu ^[2]; Sarma, Antareep Kumar ^[3]

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1. Indian Inst. of Technology (IIT), Madras (India)
2. Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
3. Ecole Polytechnique Federale Lausanne (EPFL) (Switzerland)

Here, we present an efficient physics-informed neural networks (PINNs) framework, termed Adaptive Interface-PINNs (AdaI-PINNs), to improve the modeling of interface problems with discontinuous coefficients and/or interfacial jumps. This framework is an enhanced version of its predecessor, Interface PINNs or I-PINNs (Sarma et al.; https://doi.org/10.1016/j.cma.2024.117135), which involves domain decomposition and assignment of different predefined activation functions to the neural networks in each subdomain across a sharp interface, while keeping all other parameters of the neural networks identical. In AdaI-PINNs, the activation functions vary solely in their slopes, which are trained along with the other parameters of the neural networks. This makes the AdaI-PINNs framework fully automated without requiring preset activation functions. Comparative studies on one-dimensional, two-dimensional, and three-dimensional benchmark elliptic interface problems reveal that AdaI-PINNs outperform I-PINNs, reducing computational costs by 2-6 times while producing similar or better accuracy.

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
• Sponsoring Organization: Exxon Mobil Corporation; Ministry of Education (MoE); USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: AC52-07NA27344
• OSTI ID: 2571702
• Report Number(s): LLNL--JRNL-865210
• Journal Information: Communications in Computational Physics, Journal Name: Communications in Computational Physics Journal Issue: 3 Vol. 37; ISSN 1815-2406; ISSN 1991-7120
• Publisher: Global Science Press
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
AdaI-PINNs
Deep learning
Domain decomposition
I-PINNs
Interface problems
PINN
Physics-informed machine learning
adaptive activation function