mlsanityData to 7 Oct 2026

DeepONet-Grid-UQ: A Trustworthy Deep Operator Framework for Predicting the Power Grid's Post-Fault Trajectories

arXiv 2202.07176 ↗First posted 15 Feb 2022math.NA cs.LG cs.NAcited by 30

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Abstract (arXiv)

This paper proposes a new data-driven method for the reliable prediction of power system post-fault trajectories. The proposed method is based on the fundamentally new concept of Deep Operator Networks (DeepONets). Compared to traditional neural networks that learn to approximate functions, DeepONets are designed to approximate nonlinear operators. Under this operator framework, we design a DeepONet to (1) take as inputs the fault-on trajectories collected, for example, via simulation or phasor measurement units, and (2) provide as outputs the predicted post-fault trajectories. In addition, we endow our method with a much-needed ability to balance efficiency with reliable/trustworthy predictions via uncertainty quantification. To this end, we propose and compare two methods that enable quantifying the predictive uncertainty. First, we propose a textitBayesian DeepONet (B-DeepONet) that uses stochastic gradient Hamiltonian Monte-Carlo to sample from the posterior distribution of the DeepONet parameters. Then, we propose a textitProbabilistic DeepONet (Prob-DeepONet) that uses a probabilistic training strategy to equip DeepONets with a form of automated uncertainty quantification, at virtually no extra computational cost. Finally, we validate the predictive power and uncertainty quantification capability of the proposed B-DeepONet and Prob-DeepONet using the IEEE 16-machine 68-bus system.

Key facts. Cited by 30 papers in the map (data through 7 Oct 2026). Builds on 18 of its 70 references that are in the map. First posted on arXiv 15 Feb 2022.

Builds on

18 of 70 references.

References · 18

  1. 2017Attention Is All You Needcited by 59,932
  2. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  3. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  4. 2020A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challengescited by 813
  5. 2018Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Modelscited by 748
  6. 2015Deep Speech 2: End-to-End Speech Recognition in English and Mandarincited by 449
  7. 2014Stochastic Gradient Hamiltonian Monte Carlocited by 341
  8. 2021Choose a Transformer: Fourier or Galerkincited by 333
  9. 2020B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Datacited by 329
  10. 2020Understanding and mitigating gradient pathologies in physics-informed neural networkscited by 134
  11. 2018Data Driven Governing Equations Approximation Using Deep Neural Networkscited by 94
  12. 2021Physics-informed neural networks for solving Reynolds-averaged Navierunicodex2013Stokes equationscited by 68
6 more
  1. 2021DAE-PINN: A Physics-Informed Neural Network Model for Simulating Differential-Algebraic Equations with Application to Power Networkscited by 28
  2. 2016Intelligent Time-Adaptive Transient Stability Assessment Systemcited by 12
  3. 2021Machine Learning-Driven Virtual Bidding with Electricity Market Efficiency Analysiscited by 7
  4. 2021Learning and Fast Adaptation for Grid Emergency Control via Deep Meta Reinforcement Learningcited by 6
  5. 2017Developing a Correlation Indices to Identify Coordinated Cyber-Attacks on Power Gridscited by 2
  6. 2021Adaptive Load Shedding for Grid Emergency Control via Deep Reinforcement Learningcited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 6; 2023: 8; 2024: 6; 2025: 6; 2026: 4.

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  1. 2022Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transportcited by 92
  2. 2023A Mathematical Guide to Operator Learningcited by 74
  3. 2022Reliable extrapolation of deep neural operators informed by physics or sparse observationscited by 62
  4. 2022Scalable Uncertainty Quantification for Deep Operator Networks using Randomized Priorscited by 39
  5. 2022Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problemscited by 34
  6. 2023Uncertainty quantification for noisy inputs-outputs in physics-informed neural networks and neural operatorscited by 28
  7. 2024RiemannONets: Interpretable Neural Operators for Riemann Problemscited by 28
  8. 2024Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networkscited by 28
  9. 2023IB-UQ: Information bottleneck based uncertainty quantification for neural function regression and neural operator learningcited by 18
  10. 2023D2NO: Efficient Handling of Heterogeneous Input Function Spaces with Distributed Deep Neural Operatorscited by 18
  11. 2022DeepGraphONet: A Deep Graph Operator Network to Learn and Zero-shot Transfer the Dynamic Response of Networked Systemscited by 14
  12. 2023On Approximating the Dynamic Response of Synchronous Generators via Operator Learning: A Step Towards Building Deep Operator-based Power Grid Simulatorscited by 13
18 more
  1. 2025Active operator learning with predictive uncertainty quantification for partial differential equationscited by 12
  2. 2022Variational Bayes Deep Operator Network: A data-driven Bayesian solver for parametric differential equationscited by 11
  3. 2023Deep Operator Learning-based Surrogate Models with Uncertainty Quantification for Optimizing Internal Cooling Channel Rib Profilescited by 10
  4. 2024Conformalized Prediction of Post-Fault Voltage Trajectories Using Pre-trained and Finetuned Attention-Driven Neural Operatorscited by 5
  5. 2025A Conformal Prediction Framework for Uncertainty Quantification in Physics-Informed Neural Networkscited by 5
  6. 2023A Physics-Guided Bi-Fidelity Fourier-Featured Operator Learning Framework for Predicting Time Evolution of Drag and Lift Coefficientscited by 4
  7. 2024Uncertainty quantification for deeponets with ensemble kalman inversioncited by 4
  8. 2024Physics and geometry informed neural operator network with application to acoustic scatteringcited by 3
  9. 2025Conformalized-KANs: Uncertainty Quantification with Coverage Guarantees for Kolmogorov-Arnold Networks (KANs) in Scientific Machine Learningcited by 3
  10. 2023B-LSTM-MIONet: Bayesian LSTM-based Neural Operators for Learning the Response of Complex Dynamical Systems to Length-Variant Multiple Input Functionscited by 1
  11. 2025ON-Traffic: An Operator Learning Framework for Online Traffic Flow Estimation and Uncertainty Quantification from Lagrangian Sensorscited by 1
  12. 2025Deep set based operator learning with uncertainty quantificationcited by 1
  13. 2026Physics-Guided Dimension Reduction for Simulation-Free Operator Learning of Stiff Differential-Algebraic Systemscited by 1
  14. 2024A Unified Approach for Learning the Dynamics of Power System Generators and Inverter-based Resourcescited by 0
  15. 2025Operator Learning for Power Systems Simulationcited by 0
  16. 2026Conformalized Quantum DeepONet Ensembles: Towards Scalable Operator Learning with Distribution-Free Guaranteescited by 0
  17. 2026Two-Step MV-DeepONet: Probabilistic Operator Learning for Uncertainty Propagation Driven by Random Input Fieldscited by 0
  18. 2026A Unified Mamba--MoE Surrogate for Closed-Loop Simulation and Measurement-Window Forecasting of Inverter Transientscited by 0