mlsanityData to 14 Oct 2026

D2NO: Efficient Handling of Heterogeneous Input Function Spaces with Distributed Deep Neural Operators

arXiv 2310.18888 ↗First posted 29 Oct 2023math.NA cs.LG cs.NAcited by 18

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Abstract (arXiv)

Neural operators have been applied in various scientific fields, such as solving parametric partial differential equations, dynamical systems with control, and inverse problems. However, challenges arise when dealing with input functions that exhibit heterogeneous properties, requiring multiple sensors to handle functions with minimal regularity. To address this issue, discretization-invariant neural operators have been used, allowing the sampling of diverse input functions with different sensor locations. However, existing frameworks still require an equal number of sensors for all functions. In our study, we propose a novel distributed approach to further relax the discretization requirements and solve the heterogeneous dataset challenges. Our method involves partitioning the input function space and processing individual input functions using independent and separate neural networks. A centralized neural network is used to handle shared information across all output functions. This distributed methodology reduces the number of gradient descent back-propagation steps, improving efficiency while maintaining accuracy. We demonstrate that the corresponding neural network is a universal approximator of continuous nonlinear operators and present four numerical examples to validate its performance.

Key facts. Cited by 18 papers in the map (data through 14 Oct 2026). Builds on 25 of its 52 references that are in the map. First posted on arXiv 29 Oct 2023.

Builds on

25 of 52 references.

References · 25

  1. 2016Communication-Efficient Learning of Deep Networks from Decentralized Datacited by 7,669
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  3. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  4. 2019Federated Learning: Challenges, Methods, and Future Directionscited by 1,538
  5. 2019On the Convergence of FedAvg on Non-IID Datacited by 1,229
  6. 2022FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operatorscited by 776
  7. 2021FedBN: Federated Learning on Non-IID Features via Local Batch Normalizationcited by 571
  8. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 540
  9. 2022MIONet: Learning multiple-input operators via tensor productcited by 181
  10. 2022Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisonscited by 170
  11. 2022Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transportcited by 92
  12. 2019First Analysis of Local GD on Heterogeneous Datacited by 81
13 more
  1. 2022Reliable extrapolation of deep neural operators informed by physics or sparse observationscited by 62
  2. 2023Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustnesscited by 60
  3. 2023Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestrationcited by 46
  4. 2022Scalable Uncertainty Quantification for Deep Operator Networks using Randomized Priorscited by 39
  5. 2022DeepONet-Grid-UQ: A Trustworthy Deep Operator Framework for Predicting the Power Grid's Post-Fault Trajectoriescited by 30
  6. 2021Accelerated replica exchange stochastic gradient Langevin diffusion enhanced Bayesian DeepONet for solving noisy parametric PDEscited by 22
  7. 2021Reduced operator inference for nonlinear partial differential equationscited by 21
  8. 2022Residual-based error correction for neural operator accelerated infinite-dimensional Bayesian inverse problemscited by 21
  9. 2023PPDONet: Deep Operator Networks for Fast Prediction of Steady-State Solutions in Disk-Planet Systemscited by 19
  10. 2023PROSE: Predicting Operators and Symbolic Expressions using Multimodal Transformerscited by 16
  11. 2021On Convergence of Federated Averaging Langevin Dynamicscited by 14
  12. 2022DeepGraphONet: A Deep Graph Operator Network to Learn and Zero-shot Transfer the Dynamic Response of Networked Systemscited by 14
  13. 2023Deep Operator Learning-based Surrogate Models with Uncertainty Quantification for Optimizing Internal Cooling Channel Rib Profilescited by 10

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 10; 2025: 4; 2026: 4.

18 papers.

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  1. 2024Towards a Foundation Model for Partial Differential Equations: Multi-Operator Learning and Extrapolationcited by 46
  2. 2024Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networkscited by 28
  3. 2024VICON: Vision In-Context Operator Networks for Multi-Physics Fluid Dynamics Predictioncited by 25
  4. 2024Basis-to-Basis Operator Learning Using Function Encoderscited by 17
  5. 2024MODNO: Multi Operator Learning With Distributed Neural Operatorscited by 14
  6. 2024LeMON: Learning to Learn Multi-Operator Networkscited by 14
  7. 2025Active operator learning with predictive uncertainty quantification for partial differential equationscited by 12
  8. 2024Efficient and generalizable nested Fourier-DeepONet for three-dimensional geological carbon sequestrationcited by 11
  9. 2025A Deep Learning Framework for Multi-Operator Learning: Architectures and Approximation Theorycited by 9
  10. 2024Federated scientific machine learning for approximating functions and solving differential equations with data heterogeneitycited by 8
  11. 2024Time-Series Forecasting, Knowledge Distillation, and Refinement within a Multimodal PDE Foundation Modelcited by 7
  12. 2024Conformalized Prediction of Post-Fault Voltage Trajectories Using Pre-trained and Finetuned Attention-Driven Neural Operatorscited by 5
6 more
  1. 2026Multiple Neural Operators Achieve Near-Optimal Rates for Multi-Task Learningcited by 4
  2. 2025Coefficient-to-Basis Network: A Fine-Tunable Operator Learning Framework for Inverse Problems with Adaptive Discretizations and Theoretical Guaranteescited by 3
  3. 2026Graph In-Context Operator Networks for Generalizable Spatiotemporal Predictioncited by 3
  4. 2026Generalization Bounds and Statistical Guarantees for Multi-Task and Multiple Operator Learning with MNO Networkscited by 3
  5. 2025Single vs. Multiple Branches in DeepONet and S-DeepONet: Network Architecture Follows Coupling in Multiphysics Systemscited by 2
  6. 2026Neural Operators for Multi-Task Control and Adaptationcited by 1