# Fusing Physics-based and Deep Learning Models for Prognostics

arXiv: https://arxiv.org/abs/2003.00732 · HTML: https://mlsanity.com/paper/2003.00732/

## Key facts

- Cited by 40 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Mar 2020.

## Built on by (most cited first, 30 of 40)

- [A Comprehensive Review of Digital Twin -- Part 1: Modeling and Twinning Enabling Technologies](https://mlsanity.com/paper/2208.14197/) (2022)
- [Uncertainty Quantification in Machine Learning for Engineering Design and Health Prognostics: A Tutorial](https://mlsanity.com/paper/2305.04933/) (2023)
- [Domain Adaptation via Alignment of Operation Profile for Remaining Useful Lifetime Prediction](https://mlsanity.com/paper/2302.01704/) (2023)
- [Residual-based Attention Physics-informed Neural Networks for Spatio-Temporal Ageing Assessment of Transformers Operated in Renewable Power Plants](https://mlsanity.com/paper/2405.06443/) (2024)
- [A Benchmark on Uncertainty Quantification for Deep Learning Prognostics](https://mlsanity.com/paper/2302.04730/) (2023)
- [A Framework for Interpretability in Machine Learning for Medical Imaging](https://mlsanity.com/paper/2310.01685/) (2023)
- [Graph Neural Networks for Virtual Sensing in Complex Systems: Addressing Heterogeneous Temporal Dynamics](https://mlsanity.com/paper/2407.18691/) (2024)
- [Combining physics-based and data-driven techniques for reliable hybrid analysis and modeling using the corrective source term approach](https://mlsanity.com/paper/2206.03451/) (2022)
- [Neurosymbolic AI and its Taxonomy: a survey](https://mlsanity.com/paper/2305.08876/) (2023)
- [Interpretable Prognostics with Concept Bottleneck Models](https://mlsanity.com/paper/2405.17575/) (2024)
- [Federated learning framework for collaborative remaining useful life prognostics: an aircraft engine case study](https://mlsanity.com/paper/2506.00499/) (2025)
- [A generic physics-informed neural network-based framework for reliability assessment of multi-state systems](https://mlsanity.com/paper/2112.00220/) (2021)
- [A Prescriptive Dirichlet Power Allocation Policy with Deep Reinforcement Learning](https://mlsanity.com/paper/2201.08445/) (2022)
- [A novel corrective-source term approach to modeling unknown physics in aluminum extraction process](https://mlsanity.com/paper/2209.10861/) (2022)
- [Controlled physics-informed data generation for deep learning-based remaining useful life prediction under unseen operation conditions](https://mlsanity.com/paper/2304.11702/) (2023)
- [Canonical Polyadic Decomposition and Deep Learning for Machine Fault Detection](https://mlsanity.com/paper/2107.09519/) (2021)
- [Fault Prognosis of Turbofan Engines: Eventual Failure Prediction and Remaining Useful Life Estimation](https://mlsanity.com/paper/2303.12982/) (2023)
- [Explainable Predictive Maintenance](https://mlsanity.com/paper/2306.05120/) (2023)
- [Intelligent Condition Monitoring of Industrial Plants: An Overview of Methodologies and Uncertainty Management Strategies](https://mlsanity.com/paper/2401.10266/) (2024)
- [Virtual Sensor for Real-Time Bearing Load Prediction Using Heterogeneous Temporal Graph Neural Networks](https://mlsanity.com/paper/2404.02304/) (2024)
- [Health Index Estimation Through Integration of General Knowledge with Unsupervised Learning](https://mlsanity.com/paper/2405.04990/) (2024)
- [Bayesian Physics Informed Neural Networks for Reliable Transformer Prognostics](https://mlsanity.com/paper/2509.15933/) (2025)
- [Hard-Constrained Neural Networks with Physics-Embedded Architecture for Residual Dynamics Learning and Invariant Enforcement in Cyber-Physical Systems](https://mlsanity.com/paper/2511.23307/) (2025)
- [Uncertainty-aware Remaining Useful Life predictor](https://mlsanity.com/paper/2104.03613/) (2021)
- [Physics-Informed Graph Learning](https://mlsanity.com/paper/2202.10679/) (2022)
- [Investigating Temporal Convolutional Neural Networks for Satellite Image Time Series Classification: A survey](https://mlsanity.com/paper/2204.08461/) (2022)
- [Physics-Infused Fuzzy Generative Adversarial Network for Robust Failure Prognosis](https://mlsanity.com/paper/2206.07762/) (2022)
- [A Hybrid Probabilistic Battery Health Management Approach for Robust Inspection Drone Operations](https://mlsanity.com/paper/2405.00055/) (2024)
- [Simulation and Prediction of Countercurrent Spontaneous Imbibition at Early and Late Times Using Physics-Informed Neural Networks](https://mlsanity.com/paper/2306.05554/) (2023)
- [Hybrid Adaptive Modeling in Process Monitoring: Leveraging Sequence Encoders and Physics-Informed Neural Networks](https://mlsanity.com/paper/2505.14252/) (2025)

## Abstract (arXiv)

Physics-based and data-driven models for remaining useful lifetime (RUL) prediction typically suffer from two major challenges that limit their applicability to complex real-world domains: (1) incompleteness of physics-based models and (2) limited representativeness of the training dataset for data-driven models. Combining the advantages of these two directions while overcoming some of their limitations, we propose a novel hybrid framework for fusing the information from physics-based performance models with deep learning algorithms for prognostics of complex safety-critical systems under real-world scenarios. In the proposed framework, we use physics-based performance models to infer unobservable model parameters related to a system's components health solving a calibration problem. These parameters are subsequently combined with sensor readings and used as input to a deep neural network to generate a data-driven prognostics model with physics-augmented features. The performance of the hybrid framework is evaluated on an extensive case study comprising run-to-failure degradation trajectories from a fleet of nine turbofan engines under real flight conditions. The experimental results show that the hybrid framework outperforms purely data-driven approaches by extending the prediction horizon by nearly 127%. Furthermore, it requires less training data and is less sensitive to the limited representativeness of the dataset compared to purely data-driven approaches.