mlsanityData to 7 Oct 2026

On Approximating the Dynamic Response of Synchronous Generators via Operator Learning: A Step Towards Building Deep Operator-based Power Grid Simulators

arXiv 2301.12538 ↗First posted 29 Jan 2023cs.LG cs.AI math.DScited by 13

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Abstract (arXiv)

This paper develops an Operator Learning framework for approximating the dynamic response of synchronous generators. The framework can be used to (i) build a neural network-based generator model that interacts with a power grid simulator or (ii) shadow the true generator's transient response. First, we develop a data-driven Deep Operator Network (DeepONet) to approximate the infinite-dimensional solution operator of the generators. Then, we design a numerical scheme based on DeepONet that simulates the generator's response over a given time horizon. The proposed scheme recursively employs the trained DeepONet to simulate the response for a given multi-dimensional input that describes the interaction between the generator and the power grid. In addition, we design a residual DeepONet numerical scheme that can incorporate information from existing mathematical models. We accompany this residual DeepONet scheme with an estimate for the prediction's cumulative error. Finally, we build a data aggregation (DAgger) strategy that allows fine-tuning of DeepONets using aggregated training data that the DeepONets will likely encounter during interactive simulations with other grid components. As a proof of concept, we demonstrate that the proposed frameworks can effectively approximate the transient model of a synchronous generator.

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Builds on 17 of its 54 references that are in the map. First posted on arXiv 29 Jan 2023.

Builds on

17 of 54 references.

References · 17

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  3. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  4. 2018Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Modelscited by 748
  5. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 537
  6. 2019Benchmarking Model-Based Reinforcement Learningcited by 158
  7. 2018Data Driven Governing Equations Approximation Using Deep Neural Networkscited by 94
  8. 2018Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systemscited by 88
  9. 2021Long-time integration of parametric evolution equations with physics-informed DeepONetscited by 87
  10. 2019Physics-Informed Neural Networks for Power Systemscited by 80
  11. 2022Scalable Uncertainty Quantification for Deep Operator Networks using Randomized Priorscited by 39
  12. 2020Learning Poisson systems and trajectories of autonomous systems via Poisson neural networkscited by 37
5 more
  1. 2022DeepONet-Grid-UQ: A Trustworthy Deep Operator Framework for Predicting the Power Grid's Post-Fault Trajectoriescited by 30
  2. 2021DAE-PINN: A Physics-Informed Neural Network Model for Simulating Differential-Algebraic Equations with Application to Power Networkscited by 28
  3. 2021Accelerated replica exchange stochastic gradient Langevin diffusion enhanced Bayesian DeepONet for solving noisy parametric PDEscited by 22
  4. 2020Accelerating Simulation of Stiff Nonlinear Systems using Continuous-Time Echo State Networkscited by 7
  5. 2020Multi-Fidelity Gaussian Process based Empirical Potential Development for Si:H Nanowirescited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 6; 2025: 2; 2026: 2.

13 papers.

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  1. 2024Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networkscited by 28
  2. 2024MODNO: Multi Operator Learning With Distributed Neural Operatorscited by 14
  3. 2024LeMON: Learning to Learn Multi-Operator Networkscited by 13
  4. 2024DeepONet as a Multi-Operator Extrapolation Model: Distributed Pretraining with Physics-Informed Fine-Tuningcited by 11
  5. 2023PINNSim: A Simulator for Power System Dynamics based on Physics-Informed Neural Networkscited by 8
  6. 2025A Deep Learning Framework for Multi-Operator Learning: Architectures and Approximation Theorycited by 6
  7. 2024Conformalized Prediction of Post-Fault Voltage Trajectories Using Pre-trained and Finetuned Attention-Driven Neural Operatorscited by 5
  8. 2023A Physics-Guided Bi-Fidelity Fourier-Featured Operator Learning Framework for Predicting Time Evolution of Drag and Lift Coefficientscited by 4
  9. 2023B-LSTM-MIONet: Bayesian LSTM-based Neural Operators for Learning the Response of Complex Dynamical Systems to Length-Variant Multiple Input Functionscited by 1
  10. 2026Generalization Bounds and Statistical Guarantees for Multi-Task and Multiple Operator Learning with MNO Networkscited by 1
  11. 2024A Unified Approach for Learning the Dynamics of Power System Generators and Inverter-based Resourcescited by 0
  12. 2025Physics-Informed Learning of Proprietary Inverter Models for Grid Dynamic Studiescited by 0
1 more
  1. 2026Neural Controlled Differential Equations for EMT-Level Surrogate Modeling of Grid-Forming Inverterscited by 0