# Generative adversarial wavelet neural operator: Application to fault detection and isolation of multivariate time series data

arXiv: https://arxiv.org/abs/2401.04004 · HTML: https://mlsanity.com/paper/2401.04004/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 55 references that are in the map.
- First posted on arXiv 8 Jan 2024.

## Builds on (most cited first, 12 of 12)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [Real-valued (Medical) Time Series Generation with Recurrent Conditional GANs](https://mlsanity.com/paper/1706.02633/) (2017)
- [A Multimodal Anomaly Detector for Robot-Assisted Feeding Using an LSTM-based Variational Autoencoder](https://mlsanity.com/paper/1711.00614/) (2017)
- [MAD-GAN: Multivariate Anomaly Detection for Time Series Data with Generative Adversarial Networks](https://mlsanity.com/paper/1901.04997/) (2019)
- [TadGAN: Time Series Anomaly Detection Using Generative Adversarial Networks](https://mlsanity.com/paper/2009.07769/) (2020)
- [TAnoGAN: Time Series Anomaly Detection with Generative Adversarial Networks](https://mlsanity.com/paper/2008.09567/) (2020)
- [Assessment of DeepONet for reliability analysis of stochastic nonlinear dynamical systems](https://mlsanity.com/paper/2201.13145/) (2022)
- [A foundational neural operator that continuously learns without forgetting](https://mlsanity.com/paper/2310.18885/) (2023)
- [Randomized prior wavelet neural operator for uncertainty quantification](https://mlsanity.com/paper/2302.01051/) (2023)

## Built on by (most cited first, 6 of 6)

- [Spatio-spectral graph neural operator for solving computational mechanics problems on irregular domain and unstructured grid](https://mlsanity.com/paper/2409.00604/) (2024)
- [Neural Operator induced Gaussian Process framework for probabilistic solution of parametric partial differential equations](https://mlsanity.com/paper/2404.15618/) (2024)
- [Towards Gaussian Process for operator learning: an uncertainty aware resolution independent operator learning algorithm for computational mechanics](https://mlsanity.com/paper/2409.10972/) (2024)
- [Generative flow induced neural architecture search: Towards discovering optimal architecture in wavelet neural operator](https://mlsanity.com/paper/2405.06910/) (2024)
- [Harnessing physics-informed operators for high-dimensional reliability analysis problems](https://mlsanity.com/paper/2409.04708/) (2024)
- [Event-driven physics-informed operator learning for reliability analysis](https://mlsanity.com/paper/2511.06083/) (2025)

## Abstract (arXiv)

Fault detection and isolation in complex systems are critical to ensure reliable and efficient operation. However, traditional fault detection methods often struggle with issues such as nonlinearity and multivariate characteristics of the time series variables. This article proposes a generative adversarial wavelet neural operator (GAWNO) as a novel unsupervised deep learning approach for fault detection and isolation of multivariate time series processes.The GAWNO combines the strengths of wavelet neural operators and generative adversarial networks (GANs) to effectively capture both the temporal distributions and the spatial dependencies among different variables of an underlying system. The approach of fault detection and isolation using GAWNO consists of two main stages. In the first stage, the GAWNO is trained on a dataset of normal operating conditions to learn the underlying data distribution. In the second stage, a reconstruction error-based threshold approach using the trained GAWNO is employed to detect and isolate faults based on the discrepancy values. We validate the proposed approach using the Tennessee Eastman Process (TEP) dataset and Avedore wastewater treatment plant (WWTP) and N2O emissions named as WWTPN2O datasets. Overall, we showcase that the idea of harnessing the power of wavelet analysis, neural operators, and generative models in a single framework to detect and isolate faults has shown promising results compared to various well-established baselines in the literature.