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arxiv: 2507.21803 · v2 · submitted 2025-07-29 · 💻 cs.LG

Bayesian Neural Network Surrogates for Bayesian Optimization of Carbon Capture and Storage Operations

Sofianos Panagiotis Fotias , Vassilis Gaganis This is my paper

Pith reviewed 2026-05-19 02:39 UTC · model grok-4.3

classification 💻 cs.LG
keywords Bayesian optimizationBayesian neural networkscarbon capture and storagesurrogate modelingnet present valuereservoir optimizationderivative-free optimizationsustainable energy
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The pith

Bayesian neural network surrogates improve Bayesian optimization of carbon capture and storage operations over standard Gaussian process models in high-dimensional settings.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines Bayesian optimization for selecting injection parameters in carbon capture and storage projects to maximize net present value. It tests Bayesian neural networks and other non-Gaussian-process surrogates against the usual Gaussian process approach, specifically in regimes with many decision variables or inconsistently scaled objectives. A sympathetic reader would care because better surrogate models could produce higher-value operating plans while still meeting sustainability targets. The work presents this as the first such application inside reservoir engineering. If the performance gains hold, operators could reach better economic outcomes with the same simulation budget.

Core claim

The central claim is that replacing Gaussian processes with Bayesian neural networks inside a Bayesian optimization loop yields more effective search for decision variables in CCS reservoir models when the number of variables grows large or when objectives differ in scale, with net present value serving as the single scalar objective that balances revenue and emission reduction.

What carries the argument

Bayesian neural network surrogates inside the Bayesian optimization acquisition loop, used to model the black-box mapping from injection parameters to net present value.

If this is right

  • CCS project planners can optimize more decision variables without the surrogate becoming a bottleneck.
  • Single-objective net present value optimization can still produce plans that improve both economics and emission reduction.
  • The framework offers a derivative-free route to better operating policies for existing oil-field infrastructure repurposed for storage.
  • Similar surrogate swaps could be tested on other reservoir-management tasks that currently rely on Gaussian-process Bayesian optimization.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the same surrogate swap works for multi-objective formulations, operators could directly trade off net present value against long-term leakage risk without manual scaling.
  • The approach could extend to optimizing injection schedules across multiple wells or coupled surface-subsurface systems where dimensionality is even higher.
  • Validation against field data from actual CCS pilots would show whether the reported gains survive model mismatch and measurement noise.

Load-bearing premise

The observed advantages of Bayesian neural networks over Gaussian processes will transfer from the tested synthetic or simplified cases to full-scale, realistic CCS reservoir simulations.

What would settle it

Running the same Bayesian optimization budget on a detailed reservoir model and finding that the Gaussian-process version reaches equal or higher net present value than the Bayesian-neural-network version.

Figures

Figures reproduced from arXiv: 2507.21803 by Sofianos Panagiotis Fotias, Vassilis Gaganis.

Figure 1
Figure 1. Figure 1: Aquifer depth (z axis is scaled) [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Optimal well placements All injectors are placed at the bottom of the reservoir, at left side of [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Placement optimum configuration injection performance [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: reduced placement optimum Although it is not typical to budget the drilling of 6 wells for pressure maintenance as each one’s cost is in the range of tens of millions of dollars, it needs to be noted that most produc￾ers in the cluster could function as lateral extensions of a few multi-segment horizontal wells thereby reducing the costs. Regardless, by performing this aggregation, the total amount of CO2 … view at source ↗
Figure 5
Figure 5. Figure 5: Gas injection rate profile Similar to the previous case study, the group control policy of the three producers retained is removed. Their target rate as well as their allowable breakthrough rate is adjusted by the optimizer on a 90 days basis. Since the designed project duration is 40 years, the number of decision variables increased rapidly. Furthermore, a single decision variable is used for the target i… view at source ↗
Figure 6
Figure 6. Figure 6: Sequestration rate The results in [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Maximum objective function value vs iteration number [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Sequestration rate The placement optimum case is still the first one to have its sequestration rate drop off rapidly. All models besides Ensemble and Dropout converged to a solution that produced a similar se￾questration profile as variation one. Ensemble and Dropout however, explored more towards solutions of higher injection rate and while in both cases sequestration rate didn’t drop off until after 37 y… view at source ↗
Figure 9
Figure 9. Figure 9: Hypervolume vs iteration number [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Maximum objective function value vs iteration number [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Maximum objective function value vs iteration number [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Maximum objective function value vs iteration number [PITH_FULL_IMAGE:figures/full_fig_p020_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Maximum objective function value vs iteration number [PITH_FULL_IMAGE:figures/full_fig_p021_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Hypervolume vs iteration number [PITH_FULL_IMAGE:figures/full_fig_p022_14.png] view at source ↗
read the original abstract

Carbon Capture and Storage (CCS) stands as a pivotal technology for fostering a sustainable future. The process, which involves injecting supercritical CO$_2$ into underground formations, a method already widely used for Enhanced Oil Recovery, serves a dual purpose: it not only curbs CO$_2$ emissions and addresses climate change but also extends the operational lifespan and sustainability of oil fields and platforms, easing the shift toward greener practices. This paper delivers a thorough comparative evaluation of strategies for optimizing decision variables in CCS project development, employing a derivative-free technique known as Bayesian Optimization. In addition to Gaussian Processes, which usually serve as the gold standard in BO, various novel stochastic models were examined and compared within a BO framework. This research investigates the effectiveness of utilizing more exotic stochastic models than GPs for BO in environments where GPs have been shown to underperform, such as in cases with a large number of decision variables or multiple objective functions that are not similarly scaled. By incorporating Net Present Value (NPV) as a key objective function, the proposed framework demonstrates its potential to improve economic viability while ensuring the sustainable deployment of CCS technologies. Ultimately, this study represents the first application in the reservoir engineering industry of the growing body of BO research, specifically in the search for more appropriate stochastic models, highlighting its potential as a preferred method for enhancing sustainability in the energy sector.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript presents a comparative evaluation of Bayesian Optimization (BO) frameworks for optimizing decision variables in Carbon Capture and Storage (CCS) operations. It replaces the standard Gaussian Process (GP) surrogate with alternatives including Bayesian Neural Networks (BNNs) and other stochastic models, using Net Present Value (NPV) as the objective. The work is framed as the first application of such non-GP BO research in reservoir engineering, targeting scenarios with high-dimensional inputs or unequally scaled multi-objective functions.

Significance. If the reported advantages of BNN surrogates hold under the tested conditions, the paper supplies an early industry-oriented demonstration that could encourage adoption of more flexible surrogates in energy-sector optimization. It directly addresses known GP limitations in certain regimes and links the optimization to both economic and sustainability metrics via NPV.

major comments (2)
  1. [§5] §5, Experimental Results: the performance tables compare BNN and GP surrogates on NPV but report only point estimates without error bars, number of independent runs, or statistical tests; this weakens the claim that BNNs are demonstrably superior in the CCS setting.
  2. [§4.1] §4.1, Reservoir Model Description: the number and scaling of decision variables (e.g., injection rates, well locations) are not quantified, so it is impossible to verify that the test case actually falls into the regime where GPs are known to underperform.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'various novel stochastic models' is used without listing them; the introduction or methods section should enumerate the exact set of surrogates examined.
  2. [Figure 3] Figure 3: axis labels and legend entries are too small for readability; increase font size or split into multiple panels.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which highlight important aspects for strengthening the presentation of our results and the description of the experimental setup. We address each major comment below.

read point-by-point responses

  1. Referee: §5, Experimental Results: the performance tables compare BNN and GP surrogates on NPV but report only point estimates without error bars, number of independent runs, or statistical tests; this weakens the claim that BNNs are demonstrably superior in the CCS setting.

    Authors: We agree that reporting only point estimates limits the robustness of the comparison. In the revised manuscript we will rerun the experiments with a sufficient number of independent random seeds, report mean NPV values together with error bars (standard deviation), explicitly state the number of runs, and include statistical significance tests (e.g., Wilcoxon rank-sum test with p-values) between the BNN and GP variants. These additions will be placed in the updated Section 5 and its associated tables. revision: yes

  2. Referee: §4.1, Reservoir Model Description: the number and scaling of decision variables (e.g., injection rates, well locations) are not quantified, so it is impossible to verify that the test case actually falls into the regime where GPs are known to underperform.

    Authors: We acknowledge that the current text does not provide explicit counts or ranges for the decision variables. Section 4.1 will be expanded to state the total dimensionality of the input space, the number of injection-rate and well-location variables, and the numerical bounds and scaling applied to each. This information will allow readers to confirm that the test case lies in the high-dimensional or unequally scaled regime where the advantages of BNN surrogates are expected. revision: yes

Circularity Check

0 steps flagged

No significant circularity: empirical comparison only

full rationale

The manuscript is framed as an empirical study comparing Bayesian Optimization performance with Gaussian Process versus Bayesian Neural Network and other non-GP surrogates on a CCS reservoir optimization task using NPV as objective. No derivation chain, first-principles equations, or predictive claims that reduce to fitted parameters or self-referential definitions appear. The central result is a set of experimental metrics on synthetic and reservoir models; these are not forced by construction from any internal fit or self-citation. Self-citations, if present, are incidental and not load-bearing for the reported comparisons. The work is self-contained against external benchmarks and does not invoke uniqueness theorems or ansatzes that collapse to prior author work.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no specific free parameters, axioms, or invented entities are described in the provided text.

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