# A Machine Learning Framework for Turbofan Health Estimation via Inverse Problem Formulation

arXiv: https://arxiv.org/abs/2604.08460 · HTML: https://mlsanity.com/paper/2604.08460/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 29 references that are in the map.
- First posted on arXiv 9 Apr 2026.

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

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [V-JEPA 2: Self-Supervised Video Models Enable Understanding, Prediction and Planning](https://mlsanity.com/paper/2506.09985/) (2025)
- [IntPhys 2: Benchmarking Intuitive Physics Understanding In Complex Synthetic Environments](https://mlsanity.com/paper/2506.09849/) (2025)
- [Soft Contrastive Learning for Time Series](https://mlsanity.com/paper/2312.16424/) (2023)
- [Joint Embedding vs Reconstruction: Provable Benefits of Latent Space Prediction for Self Supervised Learning](https://mlsanity.com/paper/2505.12477/) (2025)
- [Real-Time Model Calibration with Deep Reinforcement Learning](https://mlsanity.com/paper/2006.04001/) (2020)
- [I-GLIDE: Input Groups for Latent Health Indicators in Degradation Estimation](https://mlsanity.com/paper/2511.21208/) (2025)

## Built on by (most cited first, 1 of 1)

- [STEP: Learning STructured Embeddings for Progressive Time Series](https://mlsanity.com/paper/2605.31061/) (2026)

## Abstract (arXiv)

Estimating the health state of turbofan engines is a challenging ill-posed inverse problem, hindered by sparse sensing and complex nonlinear thermodynamics. Research in this area remains fragmented, with comparisons limited by the use of unrealistic datasets and insufficient exploration of the exploitation of temporal information. This work investigates how to recover component-level health indicators from operational sensor data under realistic degradation and maintenance patterns. To support this study, we introduce a new dataset that incorporates industry-oriented complexities such as maintenance events and usage changes. Using this dataset, we establish an initial benchmark that compares steady-state and nonstationary data-driven models, and Bayesian filters, classic families of methods used to solve this problem. In addition to this benchmark, we introduce self-supervised learning (SSL) approaches that learn latent representations without access to true health labels, a scenario reflective of real-world operational constraints. By comparing the downstream estimation performance of these unsupervised representations against the direct prediction baselines, we establish a practical lower bound on the difficulty of solving this inverse problem. Our results reveal that traditional filters remain strong baselines, while SSL methods reveal the intrinsic complexity of health estimation and highlight the need for more advanced and interpretable inference strategies. For reproducibility, both the generated dataset and the implementation used in this work are made accessible.