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

• URL: http://arxiv.org/abs/2406.04626v2
• Date: Mon, 10 Jun 2024 16:28:15 GMT
• Title: Adaptive Interface-PINNs (AdaI-PINNs): An Efficient Physics-informed Neural Networks Framework for Interface Problems
• Authors: Sumanta Roy, Chandrasekhar Annavarapu, Pratanu Roy, Antareep Kumar Sarma,
• Abstract summary: We present an efficient physics-informed neural networks (PINNs) framework, termed Adaptive Interface-PINNs (AdaI-PINNs) This framework is an enhanced version of its predecessor, Interface PINNs or I-PINNs. In AdaI-PINNs, the activation functions vary solely in their slopes, which are trained along with the other parameters of the neural networks.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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://dx.doi.org/10.2139/ssrn.4766623), 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.

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