# A Probabilistic Graphical Model Foundation for Enabling Predictive Digital Twins at Scale

arXiv: https://arxiv.org/abs/2012.05841 · HTML: https://mlsanity.com/paper/2012.05841/

## Key facts

- Cited by 58 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Dec 2020.

## Built on by (most cited first, 30 of 58)

- [Machine Learning in Aerodynamic Shape Optimization](https://mlsanity.com/paper/2202.07141/) (2022)
- [Mind the Gap! A Study on the Transferability of Virtual vs Physical-world Testing of Autonomous Driving Systems](https://mlsanity.com/paper/2112.11255/) (2021)
- [A Comprehensive Review of Digital Twin -- Part 1: Modeling and Twinning Enabling Technologies](https://mlsanity.com/paper/2208.14197/) (2022)
- [The transformative potential of machine learning for experiments in fluid mechanics](https://mlsanity.com/paper/2303.15832/) (2023)
- [Physics-informed neural networks for solving forward and inverse problems in complex beam systems](https://mlsanity.com/paper/2303.01055/) (2023)
- [Deep Operator Network Approximation Rates for Lipschitz Operators](https://mlsanity.com/paper/2307.09835/) (2023)
- [A Comprehensive Review of Digital Twin -- Part 2: Roles of Uncertainty Quantification and Optimization, a Battery Digital Twin, and Perspectives](https://mlsanity.com/paper/2208.12904/) (2022)
- [Deep neural network enabled corrective source term approach to hybrid analysis and modeling](https://mlsanity.com/paper/2105.11521/) (2021)
- [Hybrid analysis and modeling, eclecticism, and multifidelity computing toward digital twin revolution](https://mlsanity.com/paper/2103.14629/) (2021)
- [Deep Neural Operator Enabled Digital Twin Modeling for Additive Manufacturing](https://mlsanity.com/paper/2405.09572/) (2024)
- [A digital twin framework for civil engineering structures](https://mlsanity.com/paper/2308.01445/) (2023)
- [Position: Foundation Models Need Digital Twin Representations](https://mlsanity.com/paper/2505.03798/) (2025)
- [Two is Better Than One: Digital Siblings to Improve Autonomous Driving Testing](https://mlsanity.com/paper/2305.08060/) (2023)
- [Towards Digital Twin Oriented Modelling of Complex Networked Systems and Their Dynamics: A Comprehensive Survey](https://mlsanity.com/paper/2202.09363/) (2022)
- [Neural Extended Kalman Filters for Learning and Predicting Dynamics of Structural Systems](https://mlsanity.com/paper/2210.04165/) (2022)
- [Structure-Preserving Digital Twins via Conditional Neural Whitney Forms](https://mlsanity.com/paper/2508.06981/) (2025)
- [Variational Inference with NoFAS: Normalizing Flow with Adaptive Surrogate for Computationally Expensive Models](https://mlsanity.com/paper/2108.12657/) (2021)
- [Digital Twins in Wind Energy: Emerging Technologies and Industry-Informed Future Directions](https://mlsanity.com/paper/2304.11405/) (2023)
- [Patient-specific, mechanistic models of tumor growth incorporating artificial intelligence and big data](https://mlsanity.com/paper/2308.14925/) (2023)
- [A Framework for Strategic Discovery of Credible Neural Network Surrogate Models under Uncertainty](https://mlsanity.com/paper/2403.08901/) (2024)
- [Targeted Digital Twin via Flow Map Learning and Its Application to Fluid Dynamics](https://mlsanity.com/paper/2510.07549/) (2025)
- [Physics Guided Machine Learning for Variational Multiscale Reduced Order Modeling](https://mlsanity.com/paper/2205.12419/) (2022)
- [Adaptive learning of effective dynamics: Adaptive real-time, online modeling for complex systems](https://mlsanity.com/paper/2304.01732/) (2023)
- [Optimal sequential decision making with probabilistic digital twins](https://mlsanity.com/paper/2103.07405/) (2021)
- [Knowledge Equivalence in Digital Twins of Intelligent Systems](https://mlsanity.com/paper/2204.07481/) (2022)
- [Decoding complexity: how machine learning is redefining scientific discovery](https://mlsanity.com/paper/2405.04161/) (2024)
- [The Deep Latent Space Particle Filter for Real-Time Data Assimilation with Uncertainty Quantification](https://mlsanity.com/paper/2406.02204/) (2024)
- [Model Uncertainty and Correctability for Directed Graphical Models](https://mlsanity.com/paper/2107.08179/) (2021)
- [Decentralized digital twins of complex dynamical systems](https://mlsanity.com/paper/2207.12245/) (2022)
- [Investigating Deep Learning Model Calibration for Classification Problems in Mechanics](https://mlsanity.com/paper/2212.00881/) (2022)

## Abstract (arXiv)

A unifying mathematical formulation is needed to move from one-off digital twins built through custom implementations to robust digital twin implementations at scale. This work proposes a probabilistic graphical model as a formal mathematical representation of a digital twin and its associated physical asset. We create an abstraction of the asset-twin system as a set of coupled dynamical systems, evolving over time through their respective state-spaces and interacting via observed data and control inputs. The formal definition of this coupled system as a probabilistic graphical model enables us to draw upon well-established theory and methods from Bayesian statistics, dynamical systems, and control theory. The declarative and general nature of the proposed digital twin model make it rigorous yet flexible, enabling its application at scale in a diverse range of application areas. We demonstrate how the model is instantiated to enable a structural digital twin of an unmanned aerial vehicle (UAV). The digital twin is calibrated using experimental data from a physical UAV asset. Its use in dynamic decision making is then illustrated in a synthetic example where the UAV undergoes an in-flight damage event and the digital twin is dynamically updated using sensor data. The graphical model foundation ensures that the digital twin calibration and updating process is principled, unified, and able to scale to an entire fleet of digital twins.