# Assessment of DeepONet for reliability analysis of stochastic nonlinear dynamical systems

arXiv: https://arxiv.org/abs/2201.13145 · HTML: https://mlsanity.com/paper/2201.13145/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 46 references that are in the map.
- First posted on arXiv 31 Jan 2022.

## Builds on (most cited first, 5 of 5)

- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Zero-Shot Learning -- A Comprehensive Evaluation of the Good, the Bad and the Ugly](https://mlsanity.com/paper/1707.00600/) (2017)
- [Transfer learning based multi-fidelity physics informed deep neural network](https://mlsanity.com/paper/2005.10614/) (2020)
- [A Gaussian process latent force model for joint input-state estimation in linear structural systems](https://mlsanity.com/paper/1904.00093/) (2019)
- [Structured Bayesian Gaussian process latent variable model: applications to data-driven dimensionality reduction and high-dimensional inversion](https://mlsanity.com/paper/1807.04302/) (2018)

## Built on by (most cited first, 11 of 11)

- [Wavelet neural operator: a neural operator for parametric partial differential equations](https://mlsanity.com/paper/2205.02191/) (2022)
- [Improved generalization with deep neural operators for engineering systems: Path towards digital twin](https://mlsanity.com/paper/2301.06701/) (2023)
- [Variational Bayes Deep Operator Network: A data-driven Bayesian solver for parametric differential equations](https://mlsanity.com/paper/2206.05655/) (2022)
- [Koopman operator for time-dependent reliability analysis](https://mlsanity.com/paper/2203.02658/) (2022)
- [Generative adversarial wavelet neural operator: Application to fault detection and isolation of multivariate time series data](https://mlsanity.com/paper/2401.04004/) (2024)
- [Spatio-spectral graph neural operator for solving computational mechanics problems on irregular domain and unstructured grid](https://mlsanity.com/paper/2409.00604/) (2024)
- [Deep Physics Corrector: A physics enhanced deep learning architecture for solving stochastic differential equations](https://mlsanity.com/paper/2209.09750/) (2022)
- [Emulating the dynamics of complex systems using autoregressive models on manifolds (mNARX)](https://mlsanity.com/paper/2306.16335/) (2023)
- [mNARX+: A surrogate model for complex dynamical systems using manifold-NARX and automatic feature selection](https://mlsanity.com/paper/2507.13301/) (2025)
- [Surrogate modeling for uncertainty quantification in nonlinear dynamics](https://mlsanity.com/paper/2507.12358/) (2025)
- [Solving Coupled Differential Equation Groups Using PINO-CDE](https://mlsanity.com/paper/2210.00222/) (2022)

## Abstract (arXiv)

Time dependent reliability analysis and uncertainty quantification of structural system subjected to stochastic forcing function is a challenging endeavour as it necessitates considerable computational time. We investigate the efficacy of recently proposed DeepONet in solving time dependent reliability analysis and uncertainty quantification of systems subjected to stochastic loading. Unlike conventional machine learning and deep learning algorithms, DeepONet learns is a operator network and learns a function to function mapping and hence, is ideally suited to propagate the uncertainty from the stochastic forcing function to the output responses. We use DeepONet to build a surrogate model for the dynamical system under consideration. Multiple case studies, involving both toy and benchmark problems, have been conducted to examine the efficacy of DeepONet in time dependent reliability analysis and uncertainty quantification of linear and nonlinear dynamical systems. Results obtained indicate that the DeepONet architecture is accurate as well as efficient. Moreover, DeepONet posses zero shot learning capabilities and hence, a trained model easily generalizes to unseen and new environment with no further training.