mlsanityData to 7 Oct 2026

Derivative-enhanced Deep Operator Network

arXiv 2402.19242 ↗First posted 29 Feb 2024cs.LG cs.CE cs.NAcited by 19

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Abstract (arXiv)

The deep operator networks (DeepONet), a class of neural operators that learn mappings between function spaces, have recently been developed as surrogate models for parametric partial differential equations (PDEs). In this work we propose a derivative-enhanced deep operator network (DE-DeepONet), which leverages derivative information to enhance the solution prediction accuracy and provides a more accurate approximation of solution-to-parameter derivatives, especially when training data are limited. DE-DeepONet explicitly incorporates linear dimension reduction of high dimensional parameter input into DeepONet to reduce training cost and adds derivative loss in the loss function to reduce the number of required parameter-solution pairs. We further demonstrate that the use of derivative loss can be extended to enhance other neural operators, such as the Fourier neural operator (FNO). Numerical experiments validate the effectiveness of our approach.

Key facts. Cited by 19 papers in the map (data through 7 Oct 2026). Builds on 15 of its 34 references that are in the map. First posted on arXiv 29 Feb 2024.

Builds on

15 of 34 references.

References · 15

  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. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 537
  4. 2020Multipole Graph Neural Operator for Parametric Partial Differential Equationscited by 343
  5. 2023GNOT: A General Neural Operator Transformer for Operator Learningcited by 321
  6. 2021Factorized Fourier Neural Operatorscited by 237
  7. 2017Sobolev Training for Neural Networkscited by 136
  8. 2023An Expert's Guide to Training Physics-informed Neural Networkscited by 119
  9. 2022Derivative-Informed Neural Operator: An Efficient Framework for High-Dimensional Parametric Derivative Learningcited by 43
  10. 2020Derivative-Informed Projected Neural Networks for High-Dimensional Parametric Maps Governed by PDEscited by 40
  11. 2022Neural Implicit Flow: a mesh-agnostic dimensionality reduction paradigm of spatio-temporal datacited by 37
  12. 2020Projected Stein Variational Gradient Descentcited by 33
3 more
  1. 2018Certified dimension reduction in nonlinear Bayesian inverse problemscited by 26
  2. 2022Residual-based error correction for neural operator accelerated infinite-dimensional Bayesian inverse problemscited by 21
  3. 2023Efficient PDE-Constrained optimization under high-dimensional uncertainty using derivative-informed neural operatorscited by 18

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 3; 2025: 6; 2026: 10.

19 papers.

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  1. 2024MODNO: Multi Operator Learning With Distributed Neural Operatorscited by 14
  2. 2025Fusion-DeepONet: A Data-Efficient Neural Operator for Geometry-Dependent Hypersonic and Supersonic Flowscited by 13
  3. 2024LD-EnSF: Synergizing Latent Dynamics with Ensemble Score Filters for Fast Data Assimilation with Sparse Observationscited by 10
  4. 2025Enabling Local Neural Operators to perform Equation-Free System-Level Analysiscited by 10
  5. 2024LazyDINO: Fast, scalable, and efficiently amortized Bayesian inversion via structure-exploiting and surrogate-driven measure transportcited by 7
  6. 2025Variationally correct operator learning: Reduced basis neural operator with a posteriori error estimationcited by 5
  7. 2025FD-Bench: A Modular and Fair Benchmark for Data-driven Fluid Simulationcited by 4
  8. 20253D Neural Operator-Based Flow Surrogates around 3D geometries: Signed Distance Functions and Derivative Constraintscited by 2
  9. 2026Deep Hilbert--Galerkin Methods for Infinite-Dimensional PDEs and Optimal Controlcited by 2
  10. 2025PolyMicros: Bootstrapping a Foundation Model for Polycrystalline Material Structurecited by 1
  11. 2026Sequential Bayesian Optimal Experimental Design in Infinite Dimensions via Policy Gradient Reinforcement Learningcited by 1
  12. 2026Toward AI-Driven Digital Twins for Metropolitan Floods: A Conditional Latent Dynamics Network Surrogate of the Shallow Water Equationscited by 1
7 more
  1. 2026Universal Approximation of Nonlinear Operators and Their Derivativescited by 0
  2. 2026Smooth Piecewise Cutting for Neural Operator to Handle Discontinuities and Sharp Transitionscited by 0
  3. 2026APEX: Amplitude Anchors and Phase Priors for Target-Scarce Higher-Frequency Wave Predictioncited by 0
  4. 2026LEIA: Learned Environment for Interactive Architected Materialscited by 0
  5. 2026PGD-NO: A Neural Operator with Precomputed Geometry Decomposition for 3D Million-scale Physics Simulationscited by 0
  6. 2026Neural Networks with Local Converging Inputs for Efficient Options Pricing Modelscited by 0
  7. 2026FAST-DeepONet: Factor-Augmented Branch Representations for High-Dimensional PDE Inputs in the Small-Sample Regimecited by 0