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

arXiv: https://arxiv.org/abs/2301.12538 · HTML: https://mlsanity.com/paper/2301.12538/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 54 references that are in the map.
- First posted on arXiv 29 Jan 2023.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Benchmarking Model-Based Reinforcement Learning](https://mlsanity.com/paper/1907.02057/) (2019)
- [Data Driven Governing Equations Approximation Using Deep Neural Networks](https://mlsanity.com/paper/1811.05537/) (2018)
- [Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems](https://mlsanity.com/paper/1801.01236/) (2018)
- [Long-time integration of parametric evolution equations with physics-informed DeepONets](https://mlsanity.com/paper/2106.05384/) (2021)
- [Physics-Informed Neural Networks for Power Systems](https://mlsanity.com/paper/1911.03737/) (2019)
- [Scalable Uncertainty Quantification for Deep Operator Networks using Randomized Priors](https://mlsanity.com/paper/2203.03048/) (2022)
- [Learning Poisson systems and trajectories of autonomous systems via Poisson neural networks](https://mlsanity.com/paper/2012.03133/) (2020)
- [DeepONet-Grid-UQ: A Trustworthy Deep Operator Framework for Predicting the Power Grid's Post-Fault Trajectories](https://mlsanity.com/paper/2202.07176/) (2022)
- [DAE-PINN: A Physics-Informed Neural Network Model for Simulating Differential-Algebraic Equations with Application to Power Networks](https://mlsanity.com/paper/2109.04304/) (2021)
- [Accelerated replica exchange stochastic gradient Langevin diffusion enhanced Bayesian DeepONet for solving noisy parametric PDEs](https://mlsanity.com/paper/2111.02484/) (2021)
- [Accelerating Simulation of Stiff Nonlinear Systems using Continuous-Time Echo State Networks](https://mlsanity.com/paper/2010.04004/) (2020)
- [Multi-Fidelity Gaussian Process based Empirical Potential Development for Si:H Nanowires](https://mlsanity.com/paper/2005.08638/) (2020)

## Built on by (most cited first, 13 of 13)

- [Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networks](https://mlsanity.com/paper/2402.15406/) (2024)
- [MODNO: Multi Operator Learning With Distributed Neural Operators](https://mlsanity.com/paper/2404.02892/) (2024)
- [LeMON: Learning to Learn Multi-Operator Networks](https://mlsanity.com/paper/2408.16168/) (2024)
- [DeepONet as a Multi-Operator Extrapolation Model: Distributed Pretraining with Physics-Informed Fine-Tuning](https://mlsanity.com/paper/2411.07239/) (2024)
- [PINNSim: A Simulator for Power System Dynamics based on Physics-Informed Neural Networks](https://mlsanity.com/paper/2303.10256/) (2023)
- [A Deep Learning Framework for Multi-Operator Learning: Architectures and Approximation Theory](https://mlsanity.com/paper/2510.25379/) (2025)
- [Conformalized Prediction of Post-Fault Voltage Trajectories Using Pre-trained and Finetuned Attention-Driven Neural Operators](https://mlsanity.com/paper/2410.24162/) (2024)
- [A Physics-Guided Bi-Fidelity Fourier-Featured Operator Learning Framework for Predicting Time Evolution of Drag and Lift Coefficients](https://mlsanity.com/paper/2311.03639/) (2023)
- [Generalization Bounds and Statistical Guarantees for Multi-Task and Multiple Operator Learning with MNO Networks](https://mlsanity.com/paper/2604.01961/) (2026)
- [B-LSTM-MIONet: Bayesian LSTM-based Neural Operators for Learning the Response of Complex Dynamical Systems to Length-Variant Multiple Input Functions](https://mlsanity.com/paper/2311.16519/) (2023)
- [A Unified Approach for Learning the Dynamics of Power System Generators and Inverter-based Resources](https://mlsanity.com/paper/2409.14454/) (2024)
- [Physics-Informed Learning of Proprietary Inverter Models for Grid Dynamic Studies](https://mlsanity.com/paper/2507.15259/) (2025)
- [Neural Controlled Differential Equations for EMT-Level Surrogate Modeling of Grid-Forming Inverters](https://mlsanity.com/paper/2607.16258/) (2026)

## 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.