# Probabilistic machine learning based predictive and interpretable digital twin for dynamical systems

arXiv: https://arxiv.org/abs/2212.09240 · HTML: https://mlsanity.com/paper/2212.09240/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 56 references that are in the map.
- First posted on arXiv 19 Dec 2022.

## Builds on (most cited first, 9 of 9)

- [An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications](https://mlsanity.com/paper/1908.10407/) (2019)
- [On spike-and-slab priors for Bayesian equation discovery of nonlinear dynamical systems via sparse linear regression](https://mlsanity.com/paper/2012.01937/) (2020)
- [The role of surrogate models in the development of digital twins of dynamic systems](https://mlsanity.com/paper/2001.09292/) (2020)
- [Stochastic projection based approach for gradient free physics informed learning](https://mlsanity.com/paper/2209.13724/) (2022)
- [Machine learning based digital twin for dynamical systems with multiple time-scales](https://mlsanity.com/paper/2005.05862/) (2020)
- [Physics-integrated hybrid framework for model form error identification in nonlinear dynamical systems](https://mlsanity.com/paper/2109.00538/) (2021)
- [Model-agnostic stochastic model predictive control](https://mlsanity.com/paper/2211.13012/) (2022)
- [Machine learning based digital twin for stochastic nonlinear multi-degree of freedom dynamical system](https://mlsanity.com/paper/2103.15636/) (2021)
- [A 5G Architecture for The Factory of the Future](https://mlsanity.com/paper/1809.09396/) (2018)

## Built on by (most cited first, 4 of 4)

- [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)
- [State-of-the-art review and synthesis: A requirement-based roadmap for standardized predictive maintenance automation using digital twin technologies](https://mlsanity.com/paper/2311.06993/) (2023)
- [A Bayesian framework for discovering interpretable Lagrangian of dynamical systems from data](https://mlsanity.com/paper/2310.06241/) (2023)

## Abstract (arXiv)

A framework for creating and updating digital twins for dynamical systems from a library of physics-based functions is proposed. The sparse Bayesian machine learning is used to update and derive an interpretable expression for the digital twin. Two approaches for updating the digital twin are proposed. The first approach makes use of both the input and output information from a dynamical system, whereas the second approach utilizes output-only observations to update the digital twin. Both methods use a library of candidate functions representing certain physics to infer new perturbation terms in the existing digital twin model. In both cases, the resulting expressions of updated digital twins are identical, and in addition, the epistemic uncertainties are quantified. In the first approach, the regression problem is derived from a state-space model, whereas in the latter case, the output-only information is treated as a stochastic process. The concepts of Ito calculus and Kramers-Moyal expansion are being utilized to derive the regression equation. The performance of the proposed approaches is demonstrated using highly nonlinear dynamical systems such as the crack-degradation problem. Numerical results demonstrated in this paper almost exactly identify the correct perturbation terms along with their associated parameters in the dynamical system. The probabilistic nature of the proposed approach also helps in quantifying the uncertainties associated with updated models. The proposed approaches provide an exact and explainable description of the perturbations in digital twin models, which can be directly used for better cyber-physical integration, long-term future predictions, degradation monitoring, and model-agnostic control.