Green Physics-Informed Machine Learning Models For Structural Health Monitoring

arXiv:2604.27638 · cs.LG · Submitted 2026-04-30 · Read on arXiv

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Introduction to the show: ident: AI Radio. Generated commentary on the latest Artificial Intelligence papers.

Tom: We're looking at the paper: "Green Physics-Informed Machine Learning Models For Structural Health Monitoring".

Jane: Here's the gist of the paper. Machine learning continues to emerge as an important tool to be utilised within structural engineering and structural health monitoring, due to its ability to accurately and quickly perform both regression and classification tasks These “grey-box” models take into account 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 compares black and grey-box models through a “green” lens, comparing them in terms of their environmental impact, and investigating how the high extrapolative performance of grey-box models can reduce their runtimes and therefore carbon emissions The authors aim to develop physics-informed models with reduced computational costs, while maintaining high performance, illustrated through a structural health monitoring case study The research addresses the gap in the literature by exploring the sustainability of ML models within an engineering (structural health monitoring (SHM)) context The authors explore the working hypothesis that reduced emissions are possible when the physical knowledge embedded in the model allows a reduction in training data without significantly increasing model complexity Research on the emissions produced by ML models has identified several contributing factors, such as the choice of hardware, the use and power usage effectiveness (PUE) of a data centre, the carbon intensity of the electricity generated to run the model/data centre, and the time taken for the model to run/train The authors use CodeCarbon

9: throughout this work to compare models using an estimation of their environmental footprints Model Comparison and Physics Integration The study compares black-box and grey-box models through the lens of environmental impact The authors develop three GP models with various “greyness”, where the embedded information/knowledge concerns the periodicity of the surface Black-1 is a commonly used black-box GP regression, while Grey-1 and Grey-2 use a periodic kernel to mimic scenarios of more or less information available on system parameters The comparison highlights that reduced emissions are possible when the physical knowledge embedded in the model allows a reduction in training data without significantly increasing model complexity Performance Trade-offs The amount of training data required to reach the threshold performance metric decreased as more physics knowledge was added into the models For the toy-box study, less coverage was required as more knowledge was embedded However, this did not consistently correspond to carbon savings due to additional hyperparameters in the physics-informed models The authors note that adding physics to a model can increase runtime when there is no training data reduction Scaling and Future Directions The results suggest that in Gaussian process regression, physics knowledge is more likely to reduce emissions when working with large amounts of training data Future work aims to quantify this trade-off and explore whether more complex GPs and other ML models observe a similar trend The authors note that runtime (and consequently carbon) savings would increase substantially with larger training data sizes, highlighting the potential benefits when scaling to industry-sized models

Paper summary: Tom: So, we’ve covered the high-level idea—that physics-informed ML can be greener—now let's go into what they actually claim. The paper "Green Physics-Informed Machine Learning Models For Structural Health Monitoring" is addressing the gap in literature about model sustainability in structural health monitoring, specifically looking at how adding physical knowledge affects emissions.

Jane: They start by pointing out that purely data-driven approaches can struggle when you don't have data for every possible operational condition, and that’s where these grey-box models come in by incorporating engineering intuition >

Lu: The paper compares a standard black-box model against two physics-informed machine learning or grey-box models to directly compare emissions with varying levels of embedded physics >

Meng: They set up these comparisons using three different GP models, Black-one Grey-one and Grey-two where the level of information you’re embedding is controlled by a periodic kernel > <ref:2604.27638#pg1>

Tom: The key claim they highlight in their test cases is that the grey-box model achieves much better performance with the same training data coverage when compared to the black-box model >

Jane: They show this with a specific comparison: Black-one has an NMSE of seventy-two point one, while Grey-two with only twenty percent training data coverage, achieves an NMSE of two point nine two > <ref:2604.27638#pg3>

Lu: That performance difference is huge for extrapolative scenarios; the black-box model cannot perform adequately outside its training set, but the grey-box one does >

Meng: But we have to remember that this performance gain comes with a trade-off in complexity; they note that model complexity often increases in return when you add more physics >

Tom: So, even though the training data requirement decreased when embedding physics, they also found that the amount of training data required to reach a certain threshold performance metric often decreased as more physics knowledge was added into the models >

Jane: That’s a very important distinction because it shows the relationship isn't linear; it’s not just more physics means less data needed, but there are other factors at play >

Conclusion: Tom: So, wrapping up this discussion on "Green Physics-Informed Machine Learning Models For Structural Health Monitoring," what does this all mean for structural engineers and the broader engineering field?

Jane: It suggests that using physics embedded models can be a way to make AI tools more sustainable by potentially reducing the data needed and lowering the computational costs associated with running those models >

Lu: The implication is that for applications like structural health monitoring, where you might not have massive datasets for every failure mode, incorporating physical knowledge offers a path toward lower energy consumption >

Meng: From a production standpoint, if we can train these models more efficiently because they use less data and run faster, it definitely makes deploying them at scale much more feasible economically >

Tom: So the authors are essentially showing that for structural health monitoring, physics-informed ML isn't just about better accuracy; it’s a tool to potentially reduce the environmental cost of using AI in this domain >

University of Sheffield

cs.LG

Submitted: 2026-04-30

Updated: 2026-10-29

Comments: 11 pages, 6 figures Presented at SC4RC 2026 and EURODYN2026 Updated version containes updated Figure 5

Project page: https://mlco2.github.io/codecarbon/methodology.html

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 79/100

The gist: Machine learning continues to emerge as an important tool to be utilised within structural engineering and structural health monitoring, due to its ability to accurately and quickly perform both

Key concepts

Black-box Model: These are machine learning models that take input data and produce an output without revealing how they reached that conclusion. They are often used in engineering but require large amounts of training data, which contributes to higher computational energy consumption.
Grey-box Model: These models incorporate some physical insights or knowledge about the structure being modeled. This embedded information allows the model to learn more efficiently, potentially requiring less data and leading to lower overall computational demands.
Physics-Informed Models: These are machine learning models that integrate known physical laws or constraints directly into their design. By doing so, they can achieve high performance with reduced training data requirements and potentially lower runtime, which directly translates to reduced environmental impact.
Extrapolative Performance: This refers to the model's ability to perform well on new, unseen data that is outside its original training set. Grey-box models are investigated because their high extrapolative performance, due to physical constraints, can be leveraged to reduce the necessary training effort.

Terminology

Hyperparameters — 12× in this paper · explained in 2 episodes
Gaussian Process — 6× in this paper
computational cost — 4× in this paper · explained in 2 episodes
Benchmark — 3× in this paper · explained in 2 episodes
Adam — 2× in this paper · explained in 3 episodes
Core — 2× in this paper · explained in 2 episodes
Accuracy — 1× in this paper · explained in 1 episode
Computational Biology — 1× in this paper · explained in 2 episodes
Gaussian Process (GP) — 1× in this paper · explained in 2 episodes
Hybrid Architecture — 1× in this paper · explained in 2 episodes
Hybrid Architectures — 1× in this paper · explained in 3 episodes
Interpretability — 1× in this paper · explained in 15 episodes
Language Models (LLMs) — 1× in this paper · explained in 2 episodes
Large Language Models (LLMs) — 1× in this paper · explained in 9 episodes
Machine Learning (ML) — 1× in this paper · explained in 2 episodes
Physics-Informed Neural Networks (PINNs) — 1× in this paper · explained in 8 episodes
Pruning — 1× in this paper · explained in 4 episodes
Scaling Law — 1× in this paper · explained in 2 episodes
Scaling Laws — 1× in this paper · explained in 5 episodes
Surrogate Model — 1× in this paper · explained in 3 episodes
Surrogate Models — 1× in this paper · explained in 3 episodes

Summary

Machine learning continues to emerge as an important tool to be utilised within structural engineering and structural health monitoring, due to its ability to accurately and quickly perform both regression and classification tasks These “grey-box” models take into account 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 compares black and grey-box models through a “green” lens, comparing them in terms of their environmental impact, and investigating how the high extrapolative performance of grey-box models can reduce their runtimes and therefore carbon emissions The authors aim to develop physics-informed models with reduced computational costs, while maintaining high performance, illustrated through a structural health monitoring case study

Motivation and Context

The research addresses the gap in the literature by exploring the sustainability of ML models within an engineering (structural health monitoring (SHM)) context The authors explore the working hypothesis that reduced emissions are possible when the physical knowledge embedded in the model allows a reduction in training data without significantly increasing model complexity Research on the emissions produced by ML models has identified several contributing factors, such as the choice of hardware, the use and power usage effectiveness (PUE) of a data centre, the carbon intensity of the electricity generated to run the model/data centre, and the time taken for the model to run/train The authors use CodeCarbon [9] throughout this work to compare models using an estimation of their environmental footprints

Model Comparison and Physics Integration

The study compares black-box and grey-box models through the lens of environmental impact The authors develop three GP models with various “greyness”, where the embedded information/knowledge concerns the periodicity of the surface Black-1 is a commonly used black-box GP regression, while Grey-1 and Grey-2 use a periodic kernel to mimic scenarios of more or less information available on system parameters The comparison highlights that reduced emissions are possible when the physical knowledge embedded in the model allows a reduction in training data without significantly increasing model complexity

Performance Trade-offs

The amount of training data required to reach the threshold performance metric decreased as more physics knowledge was added into the models For the toy-box study, less coverage was required as more knowledge was embedded However, this did not consistently correspond to carbon savings due to additional hyperparameters in the physics-informed models The authors note that adding physics to a model can increase runtime when there is no training data reduction

Scaling and Future Directions

The results suggest that in Gaussian process regression, physics knowledge is more likely to reduce emissions when working with large amounts of training data Future work aims to quantify this trade-off and explore whether more complex GPs and other ML models observe a similar trend The authors note that runtime (and consequently carbon) savings would increase substantially with larger training data sizes, highlighting the potential benefits when scaling to industry-sized models

Conclusion

Improvements for AI systems

Improved AI system can be developed to reduce model runtime and carbon emissions by using physics knowledge to reduce required training data. The paper shows that Fewer training data points were required to meet the performance threshold as physics input increased.
The improved system can perform structural health monitoring (SHM) predictions with better generalization outside of the training set, as grey-box models showed a far better performance with the same training data compared to black-box models in extrapolative scenarios.
The system can be purposefully designed for environmental sustainability by explicitly considering the trade-off between model error and computational burden, leveraging the understanding that We are able to say, perhaps more than in other disciplines, how good “good enough” actually is.

Abstract

Machine learning continues to emerge as an important tool to be utilised within structural engineering and structural health monitoring, due to its ability to accurately and quickly perform both regression and classification tasks. However, a purely data driven approach has its limitations, particularly where we lack data from relevant environmental and operational conditions, a situation that has led to the development of physics-informed machine learners for structural health monitoring. These "grey-box" models take into account 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 compares black and grey-box models through a "green" lens, comparing them in terms of their environmental impact, and investigating how the high extrapolative performance of grey-box models can reduce their runtimes and therefore carbon emissions. The authors aim to develop physics-informed models with reduced computational costs, while maintaining high performance, illustrated through a structural health monitoring case study.