# Variational Digital Twins

arXiv: https://arxiv.org/abs/2507.01047 · HTML: https://mlsanity.com/paper/2507.01047/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 65 references that are in the map.
- First posted on arXiv 25 Jun 2025.

## Builds on (most cited first, 13 of 13)

- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [A Survey of Deep Active Learning](https://mlsanity.com/paper/2009.00236/) (2020)
- [Advances in Variational Inference](https://mlsanity.com/paper/1711.05597/) (2017)
- [DiffusionPDE: Generative PDE-Solving Under Partial Observation](https://mlsanity.com/paper/2406.17763/) (2024)
- [Variational Bayesian Last Layers](https://mlsanity.com/paper/2404.11599/) (2024)
- [Digital Twins: State of the Art Theory and Practice, Challenges, and Open Research Questions](https://mlsanity.com/paper/2011.02833/) (2020)
- [A Multi-scale Time-series Dataset with Benchmark for Machine Learning in Decarbonized Energy Grids](https://mlsanity.com/paper/2110.06324/) (2021)
- [Real-Time Decision-Making for Digital Twin in Additive Manufacturing with Model Predictive Control using Time-Series Deep Neural Networks](https://mlsanity.com/paper/2501.07601/) (2025)
- [Reinforcement Twinning: from digital twins to model-based reinforcement learning](https://mlsanity.com/paper/2311.03628/) (2023)
- [Model Calibration of the Liquid Mercury Spallation Target using Evolutionary Neural Networks and Sparse Polynomial Expansions](https://mlsanity.com/paper/2202.09353/) (2022)
- [Multi-module based CVAE to predict HVCM faults in the SNS accelerator](https://mlsanity.com/paper/2304.10639/) (2023)

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

- [Physics-based Digital Twins for Integrated Thermal Energy Systems Using Active Learning](https://mlsanity.com/paper/2605.06756/) (2026)
- [High-fidelity Modeling of Full-scale Pressurized Water Reactor Flow Fields for Machine Learning Applications](https://mlsanity.com/paper/2605.24763/) (2026)
- [Learning to Resolve Neutron Resonances with Fully Convolutional Neural Networks](https://mlsanity.com/paper/2608.04027/) (2026)
- [NuclearDiffusion: Text-to-Image Foundation Models for Learning Nuclear Energy Concepts](https://mlsanity.com/paper/2608.04030/) (2026)

## Abstract (arXiv)

While digital twins (DT) hold promise for providing real-time insights into complex energy assets, much of the current literature either does not offer a clear framework for information exchange between the model and the asset, lacks key features needed for real-time implementation, or gives limited attention to model uncertainty. Here, we aim to solve these gaps by proposing a variational digital twin (VDT) framework that augments standard neural architectures with a single Bayesian output layer. This lightweight addition, along with a novel VDT updating algorithm, lets a twin update in seconds on commodity GPUs while producing calibrated uncertainty bounds that can inform experiment design, control algorithms, and model reliability. The VDT is evaluated on four energy-sector problems. For critical-heat-flux prediction, uncertainty-driven active learning reaches R2 = 0.98 using 47 % fewer experiments and one-third the training time of random sampling. A three-year renewable-generation twin maintains R2 > 0.95 for solar output and curbs error growth for volatile wind forecasts via monthly updates that process only one month of data at a time. A nuclear reactor transient cooldown twin reconstructs thermocouple signals with R2 > 0.99 and preserves accuracy after 50 % sensor loss, demonstrating robustness to degraded instrumentation. Finally, a physics-informed Li-ion battery twin, retrained after every ten discharges, lowers voltage mean-squared error by an order of magnitude relative to the best static model while adapting its credible intervals as the cell approaches end-of-life. These results demonstrate that combining modest Bayesian augmentation with efficient update schemes turns conventional surrogates into uncertainty-aware, data-efficient, and computationally tractable DTs, paving the way for dependable models across industrial and scientific energy systems.