# Neural Predictive Monitoring under Partial Observability

arXiv: https://arxiv.org/abs/2108.07134 · HTML: https://mlsanity.com/paper/2108.07134/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 35 references that are in the map.
- First posted on arXiv 16 Aug 2021.

## Builds on (most cited first, 10 of 10)

- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Verisig: verifying safety properties of hybrid systems with neural network controllers](https://mlsanity.com/paper/1811.01828/) (2018)
- [Equilibrated adaptive learning rates for non-convex optimization](https://mlsanity.com/paper/1502.04390/) (2015)
- [Neural Simplex Architecture](https://mlsanity.com/paper/1908.00528/) (2019)
- [JuliaReach: a Toolbox for Set-Based Reachability](https://mlsanity.com/paper/1901.10736/) (2019)
- [Smoothed Model Checking for Uncertain Continuous Time Markov Chains](https://mlsanity.com/paper/1402.1450/) (2014)
- [Neural State Classification for Hybrid Systems](https://mlsanity.com/paper/1807.09901/) (2018)
- [A Distributed Simplex Architecture for Multi-Agent Systems](https://mlsanity.com/paper/2012.10153/) (2020)
- [Runtime Monitoring for Markov Decision Processes](https://mlsanity.com/paper/2105.12322/) (2021)

## Built on by (most cited first, 7 of 7)

- [Safe Perception-Based Control under Stochastic Sensor Uncertainty using Conformal Prediction](https://mlsanity.com/paper/2304.00194/) (2023)
- [Conformal Quantitative Predictive Monitoring of STL Requirements for Stochastic Processes](https://mlsanity.com/paper/2211.02375/) (2022)
- [Distributionally Robust Statistical Verification with Imprecise Neural Networks](https://mlsanity.com/paper/2308.14815/) (2023)
- [Conformal Off-Policy Prediction for Multi-Agent Systems](https://mlsanity.com/paper/2403.16871/) (2024)
- [Learning-Based Approaches to Predictive Monitoring with Conformal Statistical Guarantees](https://mlsanity.com/paper/2312.01959/) (2023)
- [Conformal Predictive Monitoring for Multi-Modal Scenarios](https://mlsanity.com/paper/2509.01338/) (2025)
- [Vision-Based Runtime Monitoring under Varying Specifications using Semantic Latent Representations](https://mlsanity.com/paper/2605.13923/) (2026)

## Abstract (arXiv)

We consider the problem of predictive monitoring (PM), i.e., predicting at runtime future violations of a system from the current state. We work under the most realistic settings where only partial and noisy observations of the state are available at runtime. Such settings directly affect the accuracy and reliability of the reachability predictions, jeopardizing the safety of the system. In this work, we present a learning-based method for PM that produces accurate and reliable reachability predictions despite partial observability (PO). We build on Neural Predictive Monitoring (NPM), a PM method that uses deep neural networks for approximating hybrid systems reachability, and extend it to the PO case. We propose and compare two solutions, an end-to-end approach, which directly operates on the rough observations, and a two-step approach, which introduces an intermediate state estimation step. Both solutions rely on conformal prediction to provide 1) probabilistic guarantees in the form of prediction regions and 2) sound estimates of predictive uncertainty. We use the latter to identify unreliable (and likely erroneous) predictions and to retrain and improve the monitors on these uncertain inputs (i.e., active learning). Our method results in highly accurate reachability predictions and error detection, as well as tight prediction regions with guaranteed coverage.