mlsanityData to 7 Oct 2026

Nonlinear model reduction for operator learning

arXiv 2403.18735 ↗First posted 27 Mar 2024cs.LG cs.NA math.NAcited by 8

Not on the map. Why?

Abstract (arXiv)

Operator learning provides methods to approximate mappings between infinite-dimensional function spaces. Deep operator networks (DeepONets) are a notable architecture in this field. Recently, an extension of DeepONet based on model reduction and neural networks, proper orthogonal decomposition (POD)-DeepONet, has been able to outperform other architectures in terms of accuracy for several benchmark tests. We extend this idea towards nonlinear model order reduction by proposing an efficient framework that combines neural networks with kernel principal component analysis (KPCA) for operator learning. Our results demonstrate the superior performance of KPCA-DeepONet over POD-DeepONet.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 5 of its 10 references that are in the map. First posted on arXiv 27 Mar 2024.

Builds on

5 of 10 references.

References · 5

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  3. 2021Neural Operator: Learning Maps Between Function Spacescited by 413
  4. 2020Model Reduction and Neural Networks for Parametric PDEscited by 257
  5. 2023Machine Learning for Partial Differential Equationscited by 20

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 3; 2025: 2; 2026: 3.

8 papers.

  1. 2024Spatio-spectral graph neural operator for solving computational mechanics problems on irregular domain and unstructured gridcited by 6
  2. 2024A general reduced-order neural operator for spatio-temporal predictive learning on complex spatial domainscited by 3
  3. 2025A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materialscited by 1
  4. 2025Variational Rank Reduction Autoencoders for Generative Thermal Designcited by 1
  5. 2024Enhancing Multiscale Simulations with Constitutive Relations-Aware Deep Operator Networkscited by 0
  6. 2026The Error of Deep Operator Networks Is the Sum of Its Parts: Branch-Trunk and Mode Error Decompositionscited by 0
  7. 2026Physics-Informed Reduced-Order Operator Learning for Hyperelasticity in Continuum Micromechanicscited by 0
  8. 2026NOFE - Neural Operator Function Embeddingcited by 0