Adaptive Interface-PINNs (AdaI-PINNs): An Efficient Physics-informed Neural Networks Framework for Interface Problems
<|reference_start|>Adaptive Interface-PINNs (AdaI-PINNs): An Efficient Physics-informed Neural Networks Framework for Interface Problems: 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.<|reference_end|>
@article{roy2024adaptive,
    title={Adaptive Interface-PINNs (AdaI-PINNs): An Efficient Physics-informed
  Neural Networks Framework for Interface Problems},
    author={Sumanta Roy, Chandrasekhar Annavarapu, Pratanu Roy, Antareep Kumar
  Sarma},
    journal={arXiv preprint arXiv:2406.04626},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.04626},
    primaryClass={cs.LG}
}