# GDFlow: Anomaly Detection with NCDE-based Normalizing Flow for Advanced Driver Assistance System

arXiv: https://arxiv.org/abs/2409.05346 · HTML: https://mlsanity.com/paper/2409.05346/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 42 references that are in the map.
- First posted on arXiv 9 Sep 2024.

## Builds on (most cited first, 21 of 21)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding](https://mlsanity.com/paper/1802.04431/) (2018)
- [Anomaly Transformer: Time Series Anomaly Detection with Association Discrepancy](https://mlsanity.com/paper/2110.02642/) (2021)
- [How to train your neural ODE: the world of Jacobian and kinetic regularization](https://mlsanity.com/paper/2002.02798/) (2020)
- [Unsupervised Anomaly Detection via Variational Auto-Encoder for Seasonal KPIs in Web Applications](https://mlsanity.com/paper/1802.03903/) (2018)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [Graph Neural Controlled Differential Equations for Traffic Forecasting](https://mlsanity.com/paper/2112.03558/) (2021)
- [Toward Supervised Anomaly Detection](https://mlsanity.com/paper/1401.6424/) (2014)
- [Graph-Augmented Normalizing Flows for Anomaly Detection of Multiple Time Series](https://mlsanity.com/paper/2202.07857/) (2022)
- [Attentive Neural Controlled Differential Equations for Time-series Classification and Forecasting](https://mlsanity.com/paper/2109.01876/) (2021)
- [EXIT: Extrapolation and Interpolation-based Neural Controlled Differential Equations for Time-series Classification and Forecasting](https://mlsanity.com/paper/2204.08771/) (2022)
- [Detecting Multivariate Time Series Anomalies with Zero Known Label](https://mlsanity.com/paper/2208.02108/) (2022)
- [Multivariate Quantile Function Forecaster](https://mlsanity.com/paper/2202.11316/) (2022)
- [Clustering and Unsupervised Anomaly Detection with L2 Normalized Deep Auto-Encoder Representations](https://mlsanity.com/paper/1802.00187/) (2018)
- [Real-World Anomaly Detection by using Digital Twin Systems and Weakly-Supervised Learning](https://mlsanity.com/paper/2011.06296/) (2020)
- [When Model Meets New Normals: Test-time Adaptation for Unsupervised Time-series Anomaly Detection](https://mlsanity.com/paper/2312.11976/) (2023)
- [Ergo, SMIRK is Safe: A Safety Case for a Machine Learning Component in a Pedestrian Automatic Emergency Brake System](https://mlsanity.com/paper/2204.07874/) (2022)
- [Precursor-of-Anomaly Detection for Irregular Time Series](https://mlsanity.com/paper/2306.15489/) (2023)
- [Quantile-based Maximum Likelihood Training for Outlier Detection](https://mlsanity.com/paper/2310.06085/) (2023)

## Built on by (most cited first, 3 of 3)

- [A Survey on Foundation-Model-Based Industrial Defect Detection](https://mlsanity.com/paper/2502.19106/) (2025)
- [Faithful Embeddings of Irregular and Asynchronous Data for Online Log-NCDEs](https://mlsanity.com/paper/2605.30213/) (2026)
- [Advances in Neural Controlled Differential Equations](https://mlsanity.com/paper/2607.05280/) (2026)

## Abstract (arXiv)

For electric vehicles, the Adaptive Cruise Control (ACC) in Advanced Driver Assistance Systems (ADAS) is designed to assist braking based on driving conditions, road inclines, predefined deceleration strengths, and user braking patterns. However, the driving data collected during the development of ADAS are generally limited and lack diversity. This deficiency leads to late or aggressive braking for different users. Crucially, it is necessary to effectively identify anomalies, such as unexpected or inconsistent braking patterns in ADAS, especially given the challenge of working with unlabelled, limited, and noisy datasets from real-world electric vehicles. In order to tackle the aforementioned challenges in ADAS, we propose Graph Neural Controlled Differential Equation Normalizing Flow (GDFlow), a model that leverages Normalizing Flow (NF) with Neural Controlled Differential Equations (NCDE) to learn the distribution of normal driving patterns continuously. Compared to the traditional clustering or anomaly detection algorithms, our approach effectively captures the spatio-temporal information from different sensor data and more accurately models continuous changes in driving patterns. Additionally, we introduce a quantile-based maximum likelihood objective to improve the likelihood estimate of the normal data near the boundary of the distribution, enhancing the model's ability to distinguish between normal and anomalous patterns. We validate GDFlow using real-world electric vehicle driving data that we collected from Hyundai IONIQ5 and GV80EV, achieving state-of-the-art performance compared to six baselines across four dataset configurations of different vehicle types and drivers. Furthermore, our model outperforms the latest anomaly detection methods across four time series benchmark datasets. Our approach demonstrates superior efficiency in inference time compared to existing methods.