Neural Parameter Regression for Explicit Representations of PDE Solution Operators
Not on the map. Why?
Abstract (arXiv)
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.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 23 of its 32 references that are in the map. First posted on arXiv 19 Mar 2024.
Builds on
23 of 32 references.
References · 23
- 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,597
- 2020Implicit Neural Representations with Periodic Activation Functionscited by 2,214
- 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
- 2016HyperNetworkscited by 1,003
- 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 629
- 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 537
- 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 516
- 2021Physics-informed neural networks with hard constraints for inverse designcited by 277
- 2021Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equationscited by 142
- 2016Identity Matters in Deep Learningcited by 107
- 2023A Brief Review of Hypernetworks in Deep Learningcited by 102
- 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 88
11 more
- 2021Long-time integration of parametric evolution equations with physics-informed DeepONetscited by 87
- 2021Improved architectures and training algorithms for deep operator networkscited by 85
- 2022Generic bounds on the approximation error for physics-informed (and) operator learningcited by 65
- 2022Reliable extrapolation of deep neural operators informed by physics or sparse observationscited by 62
- 2023Hypernetwork-based Meta-Learning for Low-Rank Physics-Informed Neural Networkscited by 42
- 2021HyperPINN: Learning parameterized differential equations with physics-informed hypernetworkscited by 38
- 2023PERP: Rethinking the Prune-Retrain Paradigm in the Era of LLMscited by 14
- 2021How I Learned to Stop Worrying and Love Retrainingcited by 12
- 2024Generating synthetic data for neural operatorscited by 11
- 2023Improving physics-informed DeepONets with hard constraintscited by 9
- 2022Adaptive physics-informed neural operator for coarse-grained non-equilibrium flowscited by 6
Built on by
Citing papers per year: 2025: 1.
1 paper.