Source-linked AI summary
Sustainable Concrete via Bayesian Optimization
Sebastian Ament, Andrew Witte, Nishant Garg, Julius Kusuma
TL;DR
Cement production and concrete construction contribute substantially to CO2 emissions, while finding lower-carbon concrete is constrained by the time needed to measure 28-day strength. The paper combines a probabilistic strength model with multi-objective Bayesian optimization and real-world mixture testing; its proposed batches improve strength–GWP trade-offs over industry-inspired mixes.
Problem
Concrete contributes substantially to emissions, but finding lower-carbon mixtures requires balancing environmental impact with strength and measurements that include 28-day compressive strength.
Source: §1 · p. 1Method
Results
The experimentally proposed mixtures improve strength–GWP trade-offs over random initial and industry-practice-inspired mixtures, with greater GWP reductions requiring strength trade-offs.
Source: §5.2 · pp. 5–6Takeaways & Limitations
The authors conclude that their approach proposes real-world-testable mixtures and has potential to reduce the carbon footprint of data-center and broader construction.
Source: §6 · p. 6
Abstract
from arXiv · showhide
Eight percent of global carbon dioxide emissions can be attributed to the production of cement, the main component of concrete, which is also the dominant source of CO2 emissions in the construction of data centers. The discovery of lower-carbon concrete formulae is therefore of high significance for sustainability. However, experimenting with new concrete formulae is time consuming and labor intensive, as one usually has to wait to record the concrete's 28-day compressive strength, a quantity whose measurement can by its definition not be accelerated. This provides an opportunity for experimental design methodology like Bayesian Optimization (BO) to accelerate the search for strong and sustainable concrete formulae. Herein, we 1) propose modeling steps that make concrete strength amenable to be predicted accurately by a Gaussian process model with relatively few measurements, 2) formulate the search for sustainable concrete as a multi-objective optimization problem, and 3) leverage the proposed model to carry out multi-objective BO with real-world strength measurements of the algorithmically proposed mixes. Our experimental results show improved trade-offs between the mixtures' global warming potential (GWP) and their associated compressive strengths, compared to mixes based on current industry practices. Our methods are open-sourced at github.com/facebookresearch/SustainableConcrete.
1. Introduction
Cement production accounts for 8% of global CO2 emissions, and concrete is a leading source of emissions in data-center construction. This work targets concrete mixtures that balance sustainability with strength and curing speed.
1. Introduction
- Cement production contributes 8% of global CO2 emissions, while concrete accounts for 20–30% of emissions associated with data-center construction.Concrete is also described as the leading source of CO2 emissions in data-center construction.Source: §1 · p. 1
- The work targets trade-offs among concrete’s compressive strength, curing speed, and environmental impact, measured here by global warming potential (GWP).Conventional concrete is mainly optimized for cost, availability, and 28-day strength.Source: §1 · pp. 1–2
- The authors model strength curves probabilistically, formulate sustainable-concrete search as multi-objective optimization, and use Bayesian optimization with real-world strength measurements.The stated goal is to optimize strength–GWP trade-offs.Source: §1 · p. 2
2. Background
The background introduces Gaussian processes as probabilistic models and describes multi-objective Bayesian optimization as a search over competing objectives. Its acquisition function uses expected hypervolume improvement, and prior low-carbon concrete optimization is noted as using an evolutionary algorithm.
2.1 Gaussian Processes
- Gaussian processes define distributions over functions whose finite-dimensional marginals are multivariate Normal, enabling exact posterior inference and uncertainty quantification.The GP is commonly used in Bayesian optimization when objective evaluations are expensive.Source: §2.1 · p. 2
2.2 Multi-Objective Bayesian Optimization
- Multi-objective optimization seeks a Pareto frontier of trade-offs among competing objectives, subject to minimum acceptable values represented by a reference point.Hypervolume measures the quality of a discrete Pareto frontier relative to that reference point.Source: §2.2 · p. 2
- Expected hypervolume improvement is presented as a natural acquisition function; for one observation and independent GPs it has a closed form, while other cases require Monte Carlo approximations.The expected improvement is defined over obtaining a set of new observations.Source: §2.2 · p. 2
- DeRousseau et al. (2021) jointly optimized deterministic models of 28-day strength, cost, and embodied carbon using an evolutionary algorithm.The passage notes that evolutionary algorithms tend to be less sample efficient than Bayesian optimization for real-world experimentation.Source: §2.2 · p. 3
3. A Probabilistic Model of Compressive Strength
The proposed probabilistic model jointly predicts concrete compressive strength over time and composition, using data augmentation, a time transformation, and a customized kernel. On the UCI dataset, its predictions are reported as accurate and well calibrated, unlike a naïve GP application.
3. A Probabilistic Model of Compressive Strength
- The proposed probabilistic model predicts compressive strength as a function of composition and time, with accuracy in the low-data regime attributed to transformations, augmentations, and a customized kernel.Earlier cited approaches include temporal analytical forms, a non-temporal non-probabilistic kernel regressor, and discrete-time conditional variational autoencoders.Source: §3 · p. 3
- Artificial zero-strength observations at pouring time address generic models’ nonphysical predictions near time zero.The method adds a zero-time, zero-strength observation for every training mixture and additional such observations for a random subset of compositions.Source: §3 · p. 3
- Mapping time logarithmically accommodates strength’s rapid early increase and monotonic convergence toward terminal strength, while permitting stationary covariance kernels on log-time.Source: §3 · p. 3
- An additive composition-independent time component lets the kernel model the shared smooth shape of strength curves across compositions.The model combines an exponentiated quadratic time kernel with a Matérn-5/2 joint kernel; the authors say this yields physically sensible predictions at long horizons.Source: §3 · p. 3
- The proposed model’s strength-curve predictions are reported as accurate and well calibrated, while a naïve GP application is unsuccessful on the UCI concrete strength dataset.Figure 1 compares predictions for 100% cement and 20% fly-ash compositions.Source: Figure 1 · p. 4, §3 · p. 4
4. Sustainable Concrete as a Multi-Objective Optimization Problem
The search balances lower GWP with compressive strength at both short and long curing times, since low-carbon mixes must still meet application-specific strength needs. The paper formulates this as multi-objective optimization and uses Bayesian optimization to seek trade-offs.
4. Sustainable Concrete as a Multi-Objective Optimization Problem
- The objectives are to reduce global warming potential (GWP) while maintaining compressive strength at 1 and 28 days, since sustainability gains are not useful if mixes miss strength needs.GWP is the paper’s selected sustainability metric; the authors note that the broader methods can extend to complementary sustainability measures.Source: §4 · p. 4
- The model estimates strength at 1 and 28 days, while GWP is approximated as a deterministic linear function of mixture ingredients.The authors note that a more precise GWP estimate would also depend on location and transportation.Source: §4 · p. 4
- Figure 2 plots empirical Pareto frontiers for GWP against compressive strength at 1 day and 28 days; green circles mark Pareto-optimal measurements.Dark colors indicate human-generated mixes, while dark-orange-to-yellow colors indicate AI-proposed mixes.Source: Figure 2 · p. 5, §4 · p. 5
- Bayesian optimization uses qLogNEHVI to design batches of compositions for optimizing the Pareto frontier, with real-world strength experiments.The acquisition function is identified as the LogEI variant of qNEHVI.Source: §4 · p. 5
5. Experiments
The experiments combine standardized mortar-cube testing with Bayesian optimization and predicted frontiers conditioned on mixture constraints. AI-proposed batches extend measured strength–GWP trade-offs beyond human-generated sets, while stronger GWP reductions involve strength trade-offs.
5.1 Real-World Experimental Setup
- Mortar cubes were tested under ASTM C109 after curing at 22 °C, with three specimens prepared for each of 1-, 3-, 5-, and 28-day ages.Specimens were submerged in a lime-saturated water bath and tested at a constant loading rate of 400 lb/s.Source: §5.1 · p. 5
5.2 Empirical Optimization Results
- AI-proposed batches push the empirical Pareto frontier outward beyond random initial and industry-practice mixes; the highest-GWP Pareto mix dominates pure cement, while larger GWP cuts require strength trade-offs.The experiments compare compressive strength at 1 and 28 days against GWP.Source: §5.2 · pp. 5–6
5.3 Inferred Pareto Frontier
- Inferred frontiers can be conditioned on application-specific constraints to recommend compositions tailored to local ingredient availability.The paper names fly ash and slag as ingredients whose effective sourcing may be region-specific.Source: §5.3 · p. 6
- Predicted frontiers show that water-to-binder ratio affects strength, excluding fly ash has negligible effect on trade-offs through 28 days, and excluding slag has a significant negative effect.These are predictions that the authors say qualitatively match expert consensus; Figure 3 conditions the frontier on water-to-binder ratios and ingredient exclusions.Source: §5.3 · p. 6, Figure 3 · p. 6
6. Conclusion
The conclusion presents a probabilistic model of concrete strength over time and composition, then uses multi-objective optimization and Bayesian optimization to propose mixes for real-world testing. The methods are open-sourced, and the work may contribute to lowering construction’s carbon footprint.
6. Conclusion
- The paper introduces a probabilistic model for the temporal evolution of concrete compressive strength as a function of composition.It formalizes the search for strong, sustainable formulae as multi-objective optimization and uses Bayesian optimization to propose mixtures for real-world testing.Source: §6 · p. 6
- The authors open-source their methods and state that the work has potential to reduce the carbon footprint of data-center construction and the construction industry.The authors characterize the possible impact as global.Source: §6 · p. 6
Appendix A. Background
The background describes Gaussian processes as distributions over functions that support posterior inference, and notes that kernel choice shapes model behavior. Hyperparameters are optimized by marginal likelihood.
Appendix A. Background
- Given input-output pairs and a Gaussian likelihood, the GP posterior is itself a GP, defined by its posterior mean and kernel.The displayed posterior mean uses the prior mean and covariance together with observations and noise variance.Source: Appendix A · p. 9
- Without prior knowledge of target values, the kernel is the primary determinant of model behavior; marginal likelihood optimization tunes the model’s hyperparameters.Length-scales control how quickly the function is expected to vary across input dimensions.Source: Appendix A · p. 9
- A Gaussian process specifies distributions over functions through finite-dimensional multivariate Normal marginals; in the single-outcome setting, the function has a Normal distribution with mean and covariance.For sequential inputs, this reduces to a univariate Normal distribution with mean and variance.Source: Appendix A · p. 9
Appendix B. Probabilistic Compressive Strength Model
Cross-validation shows generally good predictive accuracy and well-calibrated uncertainties for day-1 strength predictions. The model’s predictive mean is already monotone in empirical observations, so explicit monotonicity constraints have not been added so far.
Appendix B. Probabilistic Compressive Strength Model
- Cross-validation shows generally good predictive accuracy and well-calibrated uncertainties across day-1 strength values in the dataset.The authors have not found the added complexity of explicit monotonicity constraints worth their potential performance increase so far.Source: Appendix B · pp. 9–10
- The model’s predictive mean is already monotone in empirical observations, supported by the log-time transform, additive time-dependent component, and varied training measurement times.Source: Appendix B · p. 10
- Adding a monotonicity constraint could increase practitioners’ trust and uptake of the model over the long term.Source: Appendix B · p. 10