Neural Parameter Regression for Explicit Representations of PDE Solution Operators

• URL: http://arxiv.org/abs/2403.12764v1
• Date: Tue, 19 Mar 2024 14:30:56 GMT
• Title: Neural Parameter Regression for Explicit Representations of PDE Solution Operators
• Authors: Konrad Mundinger, Max Zimmer, Sebastian Pokutta,
• Abstract summary: We introduce Neural Regression (NPR), a novel framework specifically developed for learning solution operators in Partial Differential Equations (PDEs) NPR employs Physics-Informed Neural Network (PINN, Raissi et al., 2021) techniques to regress Neural Network (NN) parameters. The framework shows remarkable adaptability to new initial and boundary conditions, allowing for rapid fine-tuning and inference.
• Score: 22.355460388065964
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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