# From Grey-Box to Green-Box: When can Physics-Informed Machine Learning Reduce Carbon Footprints in Structural Health Monitoring?

arXiv: https://arxiv.org/abs/2609.33387 · HTML: https://mlsanity.com/paper/2609.33387/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 52 references that are in the map.
- First posted on arXiv 27 Sep 2026.

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2401.06066/) (2024)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Quantifying the Carbon Emissions of Machine Learning](https://mlsanity.com/paper/1910.09700/) (2019)
- [Estimating the Carbon Footprint of BLOOM, a 176B Parameter Language Model](https://mlsanity.com/paper/2211.02001/) (2022)
- [Efficient Deep Learning: A Survey on Making Deep Learning Models Smaller, Faster, and Better](https://mlsanity.com/paper/2106.08962/) (2021)
- [Understanding and mitigating gradient pathologies in physics-informed neural networks](https://mlsanity.com/paper/2001.04536/) (2020)
- [Hilbert Space Methods for Reduced-Rank Gaussian Process Regression](https://mlsanity.com/paper/1401.5508/) (2014)
- [When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learning](https://mlsanity.com/paper/2203.16797/) (2022)
- [Eco2AI: carbon emissions tracking of machine learning models as the first step towards sustainable AI](https://mlsanity.com/paper/2208.00406/) (2022)
- [How to estimate carbon footprint when training deep learning models? A guide and review](https://mlsanity.com/paper/2306.08323/) (2023)
- [A spectrum of physics-informed Gaussian processes for regression in engineering](https://mlsanity.com/paper/2309.10656/) (2023)
- [Physics-Informed Neural Networks for Time-Domain Simulations: Accuracy, Computational Cost, and Flexibility](https://mlsanity.com/paper/2303.08994/) (2023)
- [Physics-Enhanced Machine Learning: a position paper for dynamical systems investigations](https://mlsanity.com/paper/2405.05987/) (2024)
- [Post Training Quantization of Large Language Models with Microscaling Formats](https://mlsanity.com/paper/2405.07135/) (2024)
- [Nonnegativity-Enforced Gaussian Process Regression](https://mlsanity.com/paper/2004.04632/) (2020)
- [Physics-informed machine learning for Structural Health Monitoring](https://mlsanity.com/paper/2206.15303/) (2022)
- [Ground-Truthing AI Energy Consumption: Validating CodeCarbon Against External Measurements](https://mlsanity.com/paper/2509.22092/) (2025)
- [Constraining Gaussian processes for physics-informed acoustic emission mapping](https://mlsanity.com/paper/2206.01495/) (2022)
- [Discussing the Spectrum of Physics-Enhanced Machine Learning; a Survey on Structural Mechanics Applications](https://mlsanity.com/paper/2310.20425/) (2023)

## Abstract (arXiv)

Machine learning plays an increasingly vital role in engineering, but the corresponding increase in compute time is not without environmental cost. Physics-informed machine learning or "grey-box" models have been developed to overcome some of the limitations of traditional black-box learners, utilising the physical insight that an engineer would have about the structure they are modelling and have shown promising results in the structural engineering field among many others. This work explores whether an additional advantage could be a reduced environmental impact, considering the relationship between training data quantity and training time, linking this duration to carbon emissions from computing. In a structural health monitoring context, four physics-informed machine learning approaches - spanning Gaussian processes and neural networks - are evaluated: residual modelling, input augmentation, hybrid modelling, and constrained learning. The emissions for training each of the models to reach a given error threshold is compared, and in most examples, shown to be lower for the physics-informed models (with input augmented models being an exception). This reduction in training emissions further compounds the environmental savings achieved by collecting and storing less data. Although promising results, we cannot expect a silver bullet and the case studies demonstrate that a trade-off is needed between the increased complexity that comes from introducing physics into a machine learner, against the gain from reduced training data requirements.