# Conformalized Prediction of Post-Fault Voltage Trajectories Using Pre-trained and Finetuned Attention-Driven Neural Operators

arXiv: https://arxiv.org/abs/2410.24162 · HTML: https://mlsanity.com/paper/2410.24162/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 68 references that are in the map.
- First posted on arXiv 31 Oct 2024.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [MIONet: Learning multiple-input operators via tensor product](https://mlsanity.com/paper/2202.06137/) (2022)
- [A physics-informed variational DeepONet for predicting the crack path in brittle materials](https://mlsanity.com/paper/2108.06905/) (2021)
- [PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs](https://mlsanity.com/paper/2306.08827/) (2023)
- [Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustness](https://mlsanity.com/paper/2305.17289/) (2023)
- [Multifidelity Deep Operator Networks For Data-Driven and Physics-Informed Problems](https://mlsanity.com/paper/2204.09157/) (2022)
- [Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loads](https://mlsanity.com/paper/2306.03645/) (2023)
- [DeepONet-Grid-UQ: A Trustworthy Deep Operator Framework for Predicting the Power Grid's Post-Fault Trajectories](https://mlsanity.com/paper/2202.07176/) (2022)
- [Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networks](https://mlsanity.com/paper/2402.15406/) (2024)
- [PPDONet: Deep Operator Networks for Fast Prediction of Steady-State Solutions in Disk-Planet Systems](https://mlsanity.com/paper/2305.11111/) (2023)
- [D2NO: Efficient Handling of Heterogeneous Input Function Spaces with Distributed Deep Neural Operators](https://mlsanity.com/paper/2310.18888/) (2023)
- [DeepGraphONet: A Deep Graph Operator Network to Learn and Zero-shot Transfer the Dynamic Response of Networked Systems](https://mlsanity.com/paper/2209.10622/) (2022)
- [On Approximating the Dynamic Response of Synchronous Generators via Operator Learning: A Step Towards Building Deep Operator-based Power Grid Simulators](https://mlsanity.com/paper/2301.12538/) (2023)
- [Physics-Informed Neural Networks for Time-Domain Simulations: Accuracy, Computational Cost, and Flexibility](https://mlsanity.com/paper/2303.08994/) (2023)
- [Deep Operator Learning-based Surrogate Models with Uncertainty Quantification for Optimizing Internal Cooling Channel Rib Profiles](https://mlsanity.com/paper/2306.00810/) (2023)
- [PINNSim: A Simulator for Power System Dynamics based on Physics-Informed Neural Networks](https://mlsanity.com/paper/2303.10256/) (2023)
- [A Frequency Domain Approach to Predict Power System Transients](https://mlsanity.com/paper/2111.01103/) (2021)
- [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)
- [A Review of Neural Network Based Machine Learning Approaches for Rotor Angle Stability Control](https://mlsanity.com/paper/1701.01214/) (2017)
- [Dynamic State Estimation for Power System Control and Protection](https://mlsanity.com/paper/2012.14927/) (2020)
- [Dynamic State Estimation of Nonlinear Differential Algebraic Equation Models of Power Networks](https://mlsanity.com/paper/2206.07623/) (2022)

## Built on by (most cited first, 5 of 5)

- [DeepONet as a Multi-Operator Extrapolation Model: Distributed Pretraining with Physics-Informed Fine-Tuning](https://mlsanity.com/paper/2411.07239/) (2024)
- [Conformalized-KANs: Uncertainty Quantification with Coverage Guarantees for Kolmogorov-Arnold Networks (KANs) in Scientific Machine Learning](https://mlsanity.com/paper/2504.15240/) (2025)
- [Locally Adaptive Conformal Inference for Operator Models](https://mlsanity.com/paper/2507.20975/) (2025)
- [Flow-Based Conformal Predictive Distributions](https://mlsanity.com/paper/2602.07633/) (2026)
- [Safety Screening for Voltage Control in Active Distribution Grids via Distributionally Robust Conformal Screening](https://mlsanity.com/paper/2608.30889/) (2026)

## Abstract (arXiv)

This paper proposes a new data-driven methodology for predicting intervals of post-fault voltage trajectories in power systems. We begin by introducing the Quantile Attention-Fourier Deep Operator Network (QAF-DeepONet), designed to capture the complex dynamics of voltage trajectories and reliably estimate quantiles of the target trajectory without any distributional assumptions. The proposed operator regression model maps the observed portion of the voltage trajectory to its unobserved post-fault trajectory. Our methodology employs a pre-training and fine-tuning process to address the challenge of limited data availability. To ensure data privacy in learning the pre-trained model, we use merging via federated learning with data from neighboring buses, enabling the model to learn the underlying voltage dynamics from such buses without directly sharing their data. After pre-training, we fine-tune the model with data from the target bus, allowing it to adapt to unique dynamics and operating conditions. Finally, we integrate conformal prediction into the fine-tuned model to ensure coverage guarantees for the predicted intervals. We evaluated the performance of the proposed methodology using the New England 39-bus test system considering detailed models of voltage and frequency controllers. Two metrics, Prediction Interval Coverage Probability (PICP) and Prediction Interval Normalized Average Width (PINAW), are used to numerically assess the model's performance in predicting intervals. The results show that the proposed approach offers practical and reliable uncertainty quantification in predicting the interval of post-fault voltage trajectories.