# Toward accurate RUL and SoH estimation using reinforced graph-based physics-informed neural networks enhanced with dynamic weights

arXiv: https://arxiv.org/abs/2507.09766 · HTML: https://mlsanity.com/paper/2507.09766/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 55 references that are in the map.
- First posted on arXiv 13 Jul 2025.

## Builds on (most cited first, 7 of 7)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1801.06637/) (2018)
- [Temporal Attention Unit: Towards Efficient Spatiotemporal Predictive Learning](https://mlsanity.com/paper/2206.12126/) (2022)
- [EA-LSTM: Evolutionary Attention-based LSTM for Time Series Prediction](https://mlsanity.com/paper/1811.03760/) (2018)
- [A Survey on Graph Neural Networks for Remaining Useful Life Prediction: Methodologies, Evaluation and Future Trends](https://mlsanity.com/paper/2409.19629/) (2024)

## Abstract (arXiv)

Accurate estimation of Remaining Useful Life (RUL) and State of Health (SoH) is essential for reliable Prognostics and Health Management (PHM), supporting timely maintenance and dependable industrial operation. However, hybrid models that combine data-driven learning with physics-based regularization often rely on fixed loss weights and therefore lose accuracy when transferred across assets with different degradation behaviors. This study introduces Reinforced Graph-based Physics-informed Networks with Dynamic Weighting (RGPD), a unified framework for spatio-temporal degradation modeling and adaptive physics-guided regularization. Graph-based representation learning captures inter-sensor degradation structure, a Soft Actor-Critic (SAC) module refines latent features under noisy conditions, and a lightweight Q-learning policy adaptively balances monotonicity, smoothness, and latent-dynamics residual losses during training. The framework is evaluated on the C-MAPSS, PHM2012, and XJTU datasets, which represent engine, bearing, and battery degradation processes. Relative to the strongest compared baselines reported in the corresponding benchmark tables, RGPD improves average RMSE by up to 12 percent on PHM2012 and C-MAPSS, and reduces average MAPE by 20 percent on XJTU compared with the second-best reported model. Performance on these heterogeneous benchmarks further suggests the model's generalizability across degradation systems. The physics-informed component is implemented through degradation-consistent priors together with a Deep Hidden Physics Model-style residual, which improves physical plausibility without requiring a full first-principles model for each asset type.