Neural Parameter Regression for Explicit Representations of PDE Solution Operators
<|reference_start|>Neural Parameter Regression for Explicit Representations of PDE Solution Operators: We introduce Neural Parameter Regression (NPR), a novel framework specifically developed for learning solution operators in Partial Differential Equations (PDEs). Tailored for operator learning, this approach surpasses traditional DeepONets (Lu et al., 2021) by employing Physics-Informed Neural Network (PINN, Raissi et al., 2019) techniques to regress Neural Network (NN) parameters. By parametrizing each solution based on specific initial conditions, it effectively approximates a mapping between function spaces. Our method enhances parameter efficiency by incorporating low-rank matrices, thereby boosting computational efficiency and scalability. The framework shows remarkable adaptability to new initial and boundary conditions, allowing for rapid fine-tuning and inference, even in cases of out-of-distribution examples.<|reference_end|>
@article{mundinger2024neural,
    title={Neural Parameter Regression for Explicit Representations of PDE Solution
  Operators},
    author={Konrad Mundinger, Max Zimmer, Sebastian Pokutta},
    journal={arXiv preprint arXiv:2403.12764},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.12764},
    primaryClass={cs.LG cs.NA math.NA}
}