mlsanityData to 7 Oct 2026

HyperPINN: Learning parameterized differential equations with physics-informed hypernetworks

arXiv 2111.01008 ↗First posted 28 Oct 2021cs.LG physics.comp-phcited by 38

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Abstract (arXiv)

Many types of physics-informed neural network models have been proposed in recent years as approaches for learning solutions to differential equations. When a particular task requires solving a differential equation at multiple parameterizations, this requires either re-training the model, or expanding its representation capacity to include the parameterization -- both solution that increase its computational cost. We propose the HyperPINN, which uses hypernetworks to learn to generate neural networks that can solve a differential equation from a given parameterization. We demonstrate with experiments on both a PDE and an ODE that this type of model can lead to neural network solutions to differential equations that maintain a small size, even when learning a family of solutions over a parameter space.

Key facts. Cited by 38 papers in the map (data through 7 Oct 2026). Builds on 10 of its 12 references that are in the map. First posted on arXiv 28 Oct 2021.

Builds on

10 of 12 references.

References · 10

  1. 2018Neural Ordinary Differential Equationscited by 3,733
  2. 2016HyperNetworkscited by 1,003
  3. 2017DGM: A deep learning algorithm for solving partial differential equationscited by 674
  4. 2018Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equationscited by 233
  5. 2018Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systemscited by 88
  6. 2021Physics-informed neural networks for solving Reynolds-averaged Navierunicodex2013Stokes equationscited by 68
  7. 2018Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Datacited by 36
  8. 2020Active Training of Physics-Informed Neural Networks to Aggregate and Interpolate Parametric Solutions to the Navier-Stokes Equationscited by 24
  9. 2019A comparative study of physics-informed neural network models for learning unknown dynamics and constitutive relationscited by 9
  10. 2017Neural networks catching up with finite differences in solving partial differential equations in higher dimensionscited by 6

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 5; 2023: 8; 2024: 11; 2025: 7; 2026: 7.

38 papers.

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  1. 2022PDEBENCH: An Extensive Benchmark for Scientific Machine Learningcited by 396
  2. 2023A Brief Review of Hypernetworks in Deep Learningcited by 102
  3. 2023Hypernetwork-based Meta-Learning for Low-Rank Physics-Informed Neural Networkscited by 42
  4. 2023HyperDeepONet: learning operator with complex target function space using the limited resources via hypernetworkcited by 25
  5. 2022Deep Learning and Symbolic Regression for Discovering Parametric Equationscited by 22
  6. 2022Meta-PDE: Learning to Solve PDEs Quickly Without a Meshcited by 18
  7. 2023Evolve Smoothly, Fit Consistently: Learning Smooth Latent Dynamics For Advection-Dominated Systemscited by 14
  8. 2024CoLoRA: Continuous low-rank adaptation for reduced implicit neural modeling of parameterized partial differential equationscited by 12
  9. 2023Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrologycited by 11
  10. 2024Learning a Neural Solver for Parametric PDE to Enhance Physics-Informed Methodscited by 10
  11. 2025Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunitiescited by 10
  12. 2025HyPINO: Multi-Physics Neural Operators via HyperPINNs and the Method of Manufactured Solutionscited by 8
26 more
  1. 2024Learning Hamiltonian neural Koopman operator and simultaneously sustaining and discovering conservation lawcited by 7
  2. 2026Learning PDE Solvers with Physics and Data: A Unifying View of Physics-Informed Neural Networks and Neural Operatorscited by 6
  3. 2023Meta-learning of Physics-informed Neural Networks for Efficiently Solving Newly Given PDEscited by 5
  4. 2023Evolutionary Optimization of Physics-Informed Neural Networks: Advancing Generalizability by the Baldwin Effectcited by 5
  5. 2022Real-time Health Monitoring of Heat Exchangers using Hypernetworks and PINNscited by 3
  6. 2024Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks?cited by 3
  7. 2022Physics Informed Symbolic Networkscited by 2
  8. 2023Multiple Case Physics-Informed Neural Network for Biomedical Tube Flowscited by 2
  9. 2024Towards Automated Knowledge Integration From Human-Interpretable Representationscited by 2
  10. 2024Neural Parameter Regression for Explicit Representations of PDE Solution Operatorscited by 1
  11. 2024HyperSBINN: A Hypernetwork-Enhanced Systems Biology-Informed Neural Network for Efficient Drug Cardiosafety Assessmentcited by 1
  12. 2025Physics-Informed Deep B-Spline Networkscited by 1
  13. 2025A comprehensive analysis of PINNs: Variants, Applications, and Challengescited by 1
  14. 2026Nonlinear model reduction for transport-dominated problemscited by 1
  15. 2026Physics-Informed Chebyshev Polynomial Neural Operator for Parametric Partial Differential Equationscited by 1
  16. 2024D'OH: Decoder-Only Random Hypernetworks for Implicit Neural Representationscited by 0
  17. 2024Scalable physical source-to-field inference with hypernetworkscited by 0
  18. 2024Rational-WENO: A lightweight, physically-consistent three-point weighted essentially non-oscillatory schemecited by 0
  19. 2024jinns: a JAX Library for Physics-Informed Neural Networkscited by 0
  20. 2025LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEscited by 0
  21. 2025Beyond Static Models: Hypernetworks for Adaptive and Generalizable Forecasting in Complex Parametric Dynamical Systemscited by 0
  22. 2025Learning from Imperfect Data: Robust Inference of Dynamic Systems using Simulation-based Generative Modelcited by 0
  23. 2026Supervised Metric Regularization Through Alternating Optimization for Multi-Regime Physics-Informed Neural Networkscited by 0
  24. 2026HyperKKL: Enabling Non-Autonomous State Estimation through Dynamic Weight Conditioningcited by 0
  25. 2026Conflict-Aware Harmonized Rotational Gradient for Multiscale Kinetic Regimescited by 0
  26. 2026Amortizing Physics-Informed Neural Solvers via Graph Hypernetworkscited by 0