# Machine learning based digital twin for dynamical systems with multiple time-scales

arXiv: https://arxiv.org/abs/2005.05862 · HTML: https://mlsanity.com/paper/2005.05862/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in MoE theory and gating functions, one of 12 directions in Mixture-of-experts.
- First posted on arXiv 12 May 2020.

## Placed in

- Mixture-of-experts / [MoE theory and gating functions](https://mlsanity.com/moe/moe-theory-and-gating-functions/)

## Built on by (most cited first, 9 of 9)

- [A Comprehensive Review of Digital Twin -- Part 1: Modeling and Twinning Enabling Technologies](https://mlsanity.com/paper/2208.14197/) (2022)
- [Hybrid analysis and modeling, eclecticism, and multifidelity computing toward digital twin revolution](https://mlsanity.com/paper/2103.14629/) (2021)
- [Machine learning based digital twin for stochastic nonlinear multi-degree of freedom dynamical system](https://mlsanity.com/paper/2103.15636/) (2021)
- [Probabilistic machine learning based predictive and interpretable digital twin for dynamical systems](https://mlsanity.com/paper/2212.09240/) (2022)
- [Digital Twin in Industries: A Comprehensive Survey](https://mlsanity.com/paper/2412.00209/) (2024)
- [Decentralized digital twins of complex dynamical systems](https://mlsanity.com/paper/2207.12245/) (2022)
- [Enhanced multi-fidelity modelling for digital twin and uncertainty quantification](https://mlsanity.com/paper/2306.14430/) (2023)
- [Through-life Monitoring of Resource-constrained Systems and Fleets](https://mlsanity.com/paper/2301.01017/) (2023)
- [Point Cloud Data Simulation and Modelling with Aize Workspace](https://mlsanity.com/paper/2301.07947/) (2023)

## Abstract (arXiv)

Digital twin technology has a huge potential for widespread applications in different industrial sectors such as infrastructure, aerospace, and automotive. However, practical adoptions of this technology have been slower, mainly due to a lack of application-specific details. Here we focus on a digital twin framework for linear single-degree-of-freedom structural dynamic systems evolving in two different operational time scales in addition to its intrinsic dynamic time-scale. Our approach strategically separates into two components -- (a) a physics-based nominal model for data processing and response predictions, and (b) a data-driven machine learning model for the time-evolution of the system parameters. The physics-based nominal model is system-specific and selected based on the problem under consideration. On the other hand, the data-driven machine learning model is generic. For tracking the multi-scale evolution of the system parameters, we propose to exploit a mixture of experts as the data-driven model. Within the mixture of experts model, Gaussian Process (GP) is used as the expert model. The primary idea is to let each expert track the evolution of the system parameters at a single time-scale. For learning the hyperparameters of the `mixture of experts using GP', an efficient framework the exploits expectation-maximization and sequential Monte Carlo sampler is used. Performance of the digital twin is illustrated on a multi-timescale dynamical system with stiffness and/or mass variations. The digital twin is found to be robust and yields reasonably accurate results. One exciting feature of the proposed digital twin is its capability to provide reasonable predictions at future time-steps. Aspects related to the data quality and data quantity are also investigated.