mlsanityData to 7 Oct 2026

HyperDeepONet: learning operator with complex target function space using the limited resources via hypernetwork

arXiv 2312.15949 ↗First posted 26 Dec 2023cs.LG cs.NA math.NAcited by 25

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Abstract (arXiv)

Fast and accurate predictions for complex physical dynamics are a significant challenge across various applications. Real-time prediction on resource-constrained hardware is even more crucial in real-world problems. The deep operator network (DeepONet) has recently been proposed as a framework for learning nonlinear mappings between function spaces. However, the DeepONet requires many parameters and has a high computational cost when learning operators, particularly those with complex (discontinuous or non-smooth) target functions. This study proposes HyperDeepONet, which uses the expressive power of the hypernetwork to enable the learning of a complex operator with a smaller set of parameters. The DeepONet and its variant models can be thought of as a method of injecting the input function information into the target function. From this perspective, these models can be viewed as a particular case of HyperDeepONet. We analyze the complexity of DeepONet and conclude that HyperDeepONet needs relatively lower complexity to obtain the desired accuracy for operator learning. HyperDeepONet successfully learned various operators with fewer computational resources compared to other benchmarks.

Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). Builds on 31 of its 47 references that are in the map. First posted on arXiv 26 Dec 2023.

Builds on

31 of 47 references.

References · 31

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19 more
  1. 2021Neural Operator: Learning Maps Between Function Spacescited by 413
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 14; 2025: 6; 2026: 5.

25 papers.

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  1. 2024Recent Advances on Machine Learning for Computational Fluid Dynamics: A Surveycited by 27
  2. 2024tLaSDI: Thermodynamics-informed latent space dynamics identificationcited by 23
  3. 2024Positional Knowledge is All You Need: Position-induced Transformer (PiT) for Operator Learningcited by 17
  4. 2025HyPINO: Multi-Physics Neural Operators via HyperPINNs and the Method of Manufactured Solutionscited by 8
  5. 2024Learning time-dependent PDE via graph neural networks and deep operator network for robust accuracy on irregular gridscited by 7
  6. 2024An Advanced Physics-Informed Neural Operator for Comprehensive Design Optimization of Highly-Nonlinear Systems: An Aerospace Composites Processing Case Studycited by 6
  7. 2024Neural Operators Can Play Dynamic Stackelberg Gamescited by 5
  8. 2025PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systemscited by 5
  9. 2024Separable Operator Networkscited by 4
  10. 2025FD-Bench: A Modular and Fair Benchmark for Data-driven Fluid Simulationcited by 4
  11. 2024Error analysis for finite element operator learning methods for solving parametric second-order elliptic PDEscited by 3
  12. 2024Neural Operators Learn the Local Physics of Magnetohydrodynamicscited by 2
13 more
  1. 2024Disentangled Representation Learning for Parametric Partial Differential Equationscited by 2
  2. 2024PinnDE: Physics-Informed Neural Networks for Solving Differential Equationscited by 1
  3. 2024Estimation of System Parameters Including Repeated Cross-Sectional Data through Emulator-Informed Deep Generative Modelcited by 1
  4. 2025Spectral-inspired Operator Learning with Limited Data and Unknown Physicscited by 1
  5. 2024Estimating the Distribution of Parameters in Differential Equations with Repeated Cross-Sectional Datacited by 0
  6. 2024FB-HyDON: Parameter-Efficient Physics-Informed Operator Learning of Complex PDEs via Hypernetwork and Finite Basis Domain Decompositioncited by 0
  7. 2025Learning from Imperfect Data: Robust Inference of Dynamic Systems using Simulation-based Generative Modelcited by 0
  8. 2025Low-rank adaptive physics-informed HyperDeepONets for solving differential equationscited by 0
  9. 2026Sparse FEONet: A Low-Cost, Memory-Efficient Operator Network via Finite-Element Local Sparsity for Parametric PDEscited by 0
  10. 2026Smooth Piecewise Cutting for Neural Operator to Handle Discontinuities and Sharp Transitionscited by 0
  11. 2026Hybrid Least Squares/Gradient Descent Methods for MIONetscited by 0
  12. 2026Feature Interaction Modeling for Neural Operatorscited by 0
  13. 2026Hypernetwork-Parameterized Spatially Adaptive Neural Operators for PDE Learningcited by 0