# Robustness Verification of Deep Neural Networks using Star-Based Reachability Analysis with Variable-Length Time Series Input

arXiv: https://arxiv.org/abs/2307.13907 · HTML: https://mlsanity.com/paper/2307.13907/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 47 references that are in the map.
- First posted on arXiv 26 Jul 2023.

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

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [DeepFool: a simple and accurate method to fool deep neural networks](https://mlsanity.com/paper/1511.04599/) (2015)
- [NNV: The Neural Network Verification Tool for Deep Neural Networks and Learning-Enabled Cyber-Physical Systems](https://mlsanity.com/paper/2004.05519/) (2020)
- [Verification of Deep Convolutional Neural Networks Using ImageStars](https://mlsanity.com/paper/2004.05511/) (2020)
- [Optimization and Abstraction: A Synergistic Approach for Analyzing Neural Network Robustness](https://mlsanity.com/paper/1904.09959/) (2019)
- [The Third International Verification of Neural Networks Competition (VNN-COMP 2022): Summary and Results](https://mlsanity.com/paper/2212.10376/) (2022)
- [Counterexample-Guided Learning of Monotonic Neural Networks](https://mlsanity.com/paper/2006.08852/) (2020)
- [JuliaReach: a Toolbox for Set-Based Reachability](https://mlsanity.com/paper/1901.10736/) (2019)
- [A Tool for Neural Network Global Robustness Certification and Training](https://mlsanity.com/paper/2208.07289/) (2022)

## Built on by (most cited first, 2 of 2)

- [Formal Verification of Long Short-Term Memory based Audio Classifiers: A Star based Approach](https://mlsanity.com/paper/2311.12130/) (2023)
- [NNV3: Expanding Neural Network Verification to New Architectures and Domains](https://mlsanity.com/paper/2609.30050/) (2026)

## Abstract (arXiv)

Data-driven, neural network (NN) based anomaly detection and predictive maintenance are emerging research areas. NN-based analytics of time-series data offer valuable insights into past behaviors and estimates of critical parameters like remaining useful life (RUL) of equipment and state-of-charge (SOC) of batteries. However, input time series data can be exposed to intentional or unintentional noise when passing through sensors, necessitating robust validation and verification of these NNs. This paper presents a case study of the robustness verification approach for time series regression NNs (TSRegNN) using set-based formal methods. It focuses on utilizing variable-length input data to streamline input manipulation and enhance network architecture generalizability. The method is applied to two data sets in the Prognostics and Health Management (PHM) application areas: (1) SOC estimation of a Lithium-ion battery and (2) RUL estimation of a turbine engine. The NNs' robustness is checked using star-based reachability analysis, and several performance measures evaluate the effect of bounded perturbations in the input on network outputs, i.e., future outcomes. Overall, the paper offers a comprehensive case study for validating and verifying NN-based analytics of time-series data in real-world applications, emphasizing the importance of robustness testing for accurate and reliable predictions, especially considering the impact of noise on future outcomes.