# MAntRA: A framework for model agnostic reliability analysis

arXiv: https://arxiv.org/abs/2212.06303 · HTML: https://mlsanity.com/paper/2212.06303/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 86 references that are in the map.
- First posted on arXiv 13 Dec 2022.

## Builds on (most cited first, 4 of 4)

- [Sparse identification of nonlinear dynamics for model predictive control in the low-data limit](https://mlsanity.com/paper/1711.05501/) (2017)
- [Sparse learning of stochastic dynamic equations](https://mlsanity.com/paper/1712.02432/) (2017)
- [On spike-and-slab priors for Bayesian equation discovery of nonlinear dynamical systems via sparse linear regression](https://mlsanity.com/paper/2012.01937/) (2020)
- [Model-agnostic stochastic model predictive control](https://mlsanity.com/paper/2211.13012/) (2022)

## Built on by (most cited first, 5 of 5)

- [A Bayesian Framework for learning governing Partial Differential Equation from Data](https://mlsanity.com/paper/2306.04894/) (2023)
- [Discovering stochastic partial differential equations from limited data using variational Bayes inference](https://mlsanity.com/paper/2306.15873/) (2023)
- [A Bayesian framework for discovering interpretable Lagrangian of dynamical systems from data](https://mlsanity.com/paper/2310.06241/) (2023)
- [Discovering governing equation in structural dynamics from acceleration-only measurements](https://mlsanity.com/paper/2407.13704/) (2024)
- [Harnessing physics-informed operators for high-dimensional reliability analysis problems](https://mlsanity.com/paper/2409.04708/) (2024)

## Abstract (arXiv)

We propose a novel model agnostic data-driven reliability analysis framework for time-dependent reliability analysis. The proposed approach -- referred to as MAntRA -- combines interpretable machine learning, Bayesian statistics, and identifying stochastic dynamic equation to evaluate reliability of stochastically-excited dynamical systems for which the governing physics is textitapriori unknown. A two-stage approach is adopted: in the first stage, an efficient variational Bayesian equation discovery algorithm is developed to determine the governing physics of an underlying stochastic differential equation (SDE) from measured output data. The developed algorithm is efficient and accounts for epistemic uncertainty due to limited and noisy data, and aleatoric uncertainty because of environmental effect and external excitation. In the second stage, the discovered SDE is solved using a stochastic integration scheme and the probability failure is computed. The efficacy of the proposed approach is illustrated on three numerical examples. The results obtained indicate the possible application of the proposed approach for reliability analysis of in-situ and heritage structures from on-site measurements.