# Residual-based Attention Physics-informed Neural Networks for Spatio-Temporal Ageing Assessment of Transformers Operated in Renewable Power Plants

arXiv: https://arxiv.org/abs/2405.06443 · HTML: https://mlsanity.com/paper/2405.06443/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 47 references that are in the map.
- First posted on arXiv 10 May 2024.

## Builds on (most cited first, 16 of 16)

- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism](https://mlsanity.com/paper/2009.04544/) (2020)
- [Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons](https://mlsanity.com/paper/2201.07766/) (2022)
- [Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems](https://mlsanity.com/paper/1809.08327/) (2018)
- [Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systems](https://mlsanity.com/paper/2104.13386/) (2021)
- [Tackling the Curse of Dimensionality with Physics-Informed Neural Networks](https://mlsanity.com/paper/2307.12306/) (2023)
- [Residual-based attention in physics-informed neural networks](https://mlsanity.com/paper/2307.00379/) (2023)
- [Potential, Challenges and Future Directions for Deep Learning in Prognostics and Health Management Applications](https://mlsanity.com/paper/2005.02144/) (2020)
- [Fusing Physics-based and Deep Learning Models for Prognostics](https://mlsanity.com/paper/2003.00732/) (2020)
- [Delta-PINNs: physics-informed neural networks on complex geometries](https://mlsanity.com/paper/2209.03984/) (2022)
- [Physics-informed neural networks for solving forward and inverse problems in complex beam systems](https://mlsanity.com/paper/2303.01055/) (2023)
- [Physics-aware Reduced-order Modeling of Transonic Flow via β-Variational Autoencoder](https://mlsanity.com/paper/2205.00608/) (2022)
- [Learning Unknown Physics of non-Newtonian Fluids](https://mlsanity.com/paper/2009.01658/) (2020)
- [Learning in PINNs: Phase transition, diffusion equilibrium, and generalization](https://mlsanity.com/paper/2403.18494/) (2024)
- [Transfer learning for improved generalizability in causal physics-informed neural networks for beam simulations](https://mlsanity.com/paper/2311.00578/) (2023)
- [Gradient-Enhanced Physics-Informed Neural Networks for Power Systems Operational Support](https://mlsanity.com/paper/2206.10579/) (2022)

## Built on by (most cited first, 11 of 11)

- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [A Variational Framework for Residual-Based Adaptivity in Neural PDE Solvers and Operator Learning](https://mlsanity.com/paper/2509.14198/) (2025)
- [Bayesian Physics Informed Neural Networks for Reliable Transformer Prognostics](https://mlsanity.com/paper/2509.15933/) (2025)
- [MILP initialization for solving parabolic PDEs with PINNs](https://mlsanity.com/paper/2501.16153/) (2025)
- [Optimal Sensor Placement in Power Transformers Using Physics-Informed Neural Networks](https://mlsanity.com/paper/2502.00552/) (2025)
- [Physics-Informed Machine Learning for Transformer Condition Monitoring -- Part II: Physics-Informed Neural Networks and Uncertainty Quantification](https://mlsanity.com/paper/2512.22189/) (2025)
- [Disentangling Aleatoric and Epistemic Uncertainty in Physics-Informed Neural Networks. Application to Insulation Material Degradation Prognostics](https://mlsanity.com/paper/2601.03673/) (2026)
- [UniPINN: A Unified PINN Framework for Multi-task Learning of Diverse Navier-Stokes Equations](https://mlsanity.com/paper/2603.10466/) (2026)
- [Residual Attention Physics-Informed Neural Networks for Robust Multiphysics Simulation of Steady-State Electrothermal Energy Systems](https://mlsanity.com/paper/2603.23578/) (2026)
- [Learning the Stellar Structure Equations via Self-supervised Physics-Informed Neural Networks](https://mlsanity.com/paper/2604.06255/) (2026)
- [Physics-Informed Machine Learning in Prognostics and Health Management: A Systematic Literature Review](https://mlsanity.com/paper/2608.10047/) (2026)

## Abstract (arXiv)

Transformers are crucial for reliable and efficient power system operations, particularly in supporting the integration of renewable energy. Effective monitoring of transformer health is critical to maintain grid stability and performance. Thermal insulation ageing is a key transformer failure mode, which is generally tracked by monitoring the hotspot temperature (HST). However, HST measurement is complex, costly, and often estimated from indirect measurements. Existing HST models focus on space-agnostic thermal models, providing worst-case HST estimates. This article introduces a spatio-temporal model for transformer winding temperature and ageing estimation, which leverages physics-based partial differential equations (PDEs) with data-driven Neural Networks (NN) in a Physics Informed Neural Networks (PINNs) configuration to improve prediction accuracy and acquire spatio-temporal resolution. The computational accuracy of the PINN model is improved through the implementation of the Residual-Based Attention (PINN-RBA) scheme that accelerates the PINN model convergence. The PINN-RBA model is benchmarked against self-adaptive attention schemes and classical vanilla PINN configurations. For the first time, PINN based oil temperature predictions are used to estimate spatio-temporal transformer winding temperature values, validated through PDE numerical solution and fiber optic sensor measurements. Furthermore, the spatio-temporal transformer ageing model is inferred, which supports transformer health management decision-making. Results are validated with a distribution transformer operating on a floating photovoltaic power plant.