Inducing Permutation Invariant Priors in Bayesian Optimization for Carbon Capture and Storage Applications

Sofianos Panagiotis Fotias; Vassilis Gaganis

arxiv: 2605.02409 · v2 · pith:QZDECZM4new · submitted 2026-05-04 · 💻 cs.LG

Inducing Permutation Invariant Priors in Bayesian Optimization for Carbon Capture and Storage Applications

Sofianos Panagiotis Fotias , Vassilis Gaganis This is my paper

Pith reviewed 2026-05-22 11:02 UTC · model grok-4.3

classification 💻 cs.LG

keywords Bayesian optimizationGaussian processespermutation invariancecarbon capture and storagewell placementkernel methodsset inputs

0 comments

The pith

A new Gaussian process kernel respects permutation symmetries among well groups in carbon capture optimization.

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

Bayesian optimization relies on Gaussian process surrogates that become inefficient when the black-box simulator imposes group control on wells, because identical configurations that differ only by order are treated as distinct inputs. The paper introduces a kernel that treats injector and producer sets as unordered collections and measures similarity through a stable divergence on their empirical representations. This kernel can be combined with ordinary kernels when some inputs remain vector-valued. The approach is tested on seven synthetic problems plus a realistic Johansen formation model to show improved sample efficiency over standard and deep-set baselines.

Core claim

The central claim is that a Gaussian process kernel (GP-Perm) encodes permutation invariance by comparing sets through a stable divergence between their induced empirical representations and can be combined with standard kernels for additional vector-valued inputs, allowing Bayesian optimization to avoid redundant evaluations on symmetric well configurations that arise under group control in carbon capture simulators.

What carries the argument

The GP-Perm kernel, which encodes permutation invariance by comparing sets through a stable divergence between their induced empirical representations.

If this is right

Bayesian optimization can now be applied directly to problems whose inputs are unordered collections without manual symmetry-breaking transformations.
The same kernel construction applies to any black-box problem that exhibits group-control symmetries, not only well placement.
Hybrid kernels that mix the permutation-invariant component with ordinary kernels remain positive definite and can be used for mixed set-plus-vector inputs.
Deep kernel learning with Deep Sets provides a learned alternative baseline that achieves similar invariance but requires more training data.

Where Pith is reading between the lines

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

The same divergence-based construction could be ported to other kernel families such as Matérn or spectral kernels used in spatial statistics.
If the divergence measure is replaced by a learned metric, the method might generalize to problems where the notion of set similarity is itself uncertain.
In reservoir engineering the approach may reduce the need for explicit enumeration of all permutations during scenario generation.

Load-bearing premise

The high-fidelity simulator is instructed to operate wells under group control, which creates permutation symmetries inside injector and producer groups that standard kernels cannot exploit.

What would settle it

Running the Johansen formation case study with the standard squared-exponential kernel versus the proposed GP-Perm kernel and observing no reduction in the number of simulator calls needed to reach a given objective value would falsify the claimed efficiency gain.

Figures

Figures reproduced from arXiv: 2605.02409 by Sofianos Panagiotis Fotias, Vassilis Gaganis.

**Figure 1.** Figure 1: Permutation invariance in physical configuration: a standard GP sees view at source ↗

**Figure 1.** Figure 1: Permutation invariance in physical configuration: a standard GP sees [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 2.** Figure 2: GP-Perm kernel construction. The left and right panels show two inputs, each view at source ↗

**Figure 2.** Figure 2: GP-Perm kernel construction. The left and right panels show two inputs, each decomposed into an auxiliary [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: DKL-DS architecture. An MLP embeds the auxiliary vector inputs, while Deep view at source ↗

**Figure 3.** Figure 3: DKL-DS architecture. An MLP embeds the auxiliary vector inputs, while Deep Sets encoders embed the injec [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 4.** Figure 4: Synthetic benchmarks: best-so-far objective versus BO iteration (mean view at source ↗

**Figure 4.** Figure 4: Synthetic benchmarks: best-so-far objective versus BO iteration (mean [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗

**Figure 5.** Figure 5: BO results on (left) CCS-like two-set synthetic benchmark and (right) Johansen view at source ↗

**Figure 5.** Figure 5: BO results on (left) CCS-like two-set synthetic benchmark and (right) Johansen CCS case study: mean best [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗

read the original abstract

Bayesian Optimization is an iterative method, tailored to optimizing expensive black box objective functions. Surrogate models like Gaussian Processes, which are the gold standard in Bayesian Optimization, can be inefficient for inputs with permutation symmetries, as the most common kernels employed are better suited for vector inputs rather than unordered sets of items. Motivated by this issue, we turn to permutation invariant Bayesian Optimization for well placement in Carbon Capture and Storage projects. The high fidelity black box simulator is instructed to operate wells under group control, giving rise to permutation symmetries within injector and producer groups that cannot be exploited with standard GP kernels. In this work, our main contribution is a novel Gaussian Process kernel (GP-Perm) that encodes permutation invariance by comparing sets through a stable divergence between their induced empirical representations, and can be combined with standard kernels for additional vector-valued inputs. As a learned invariant baseline, we also consider a Deep Kernel Learning model (DKL-DS) using the Deep Sets architecture to learn a permutation-invariant embedding. We evaluate the proposed methodology across 8 use cases, comprising seven synthetic benchmarks and one realistic CCS case study (Johansen formation)

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.

Desk Editor's Note private letter to a colleague

The paper introduces a GP-Perm kernel using divergence on empirical set representations for permutation-invariant Bayesian optimization in CCS well placement, but the construction leaves open whether the kernel is positive semi-definite.

read the letter

The main thing to know is that this paper develops a new Gaussian process kernel, GP-Perm, meant to respect permutation symmetries among groups of wells when doing Bayesian optimization for carbon capture and storage. The wells operate under group control in the simulator, so order does not matter within injector or producer sets, and standard kernels waste that structure. Their fix compares sets by a stable divergence between induced empirical representations and allows mixing with ordinary kernels for any extra vector inputs. They also run a Deep Sets baseline for comparison. That is the core new piece, and it is applied directly to a realistic Johansen formation case plus seven synthetic benchmarks. The evaluation setup is reasonable for an applied paper and shows they are testing whether the invariance helps in practice where simulator evaluations are costly. The CCS context adds some relevance for energy modeling without overstating the scope. The soft spot is the kernel validity. The description relies on the divergence producing a usable similarity, yet there is no derivation, theorem, or even a simple numerical check confirming the result is positive semi-definite. Gaussian process surrogates need that property for the covariance matrix to stay valid; without it, predictive variances can go negative and acquisition functions become unreliable. If the full paper includes eigenvalue checks on sample matrices or a proof that the divergence preserves the necessary properties, the concern shrinks. Otherwise it is a load-bearing gap. This work is for researchers doing Bayesian optimization on set-valued or symmetric inputs, especially in engineering or subsurface applications. Someone already working on invariant kernels or Deep Sets variants would find the construction worth examining, and the CCS example gives a concrete test case. I would send it to peer review. The motivation and experiments are in place, but the authors should be asked to close the PSD question so the contribution can be evaluated cleanly.

Referee Report

2 major / 2 minor

Summary. The paper introduces a novel Gaussian Process kernel (GP-Perm) for Bayesian optimization that encodes permutation invariance for set-valued inputs (such as injector and producer well groups) by comparing sets through a stable divergence between their induced empirical representations. The kernel can be combined with standard kernels for additional vector-valued inputs. It is motivated by well-placement optimization in Carbon Capture and Storage under group control, which induces permutation symmetries. The method is compared against a Deep Kernel Learning baseline using Deep Sets (DKL-DS) and evaluated on seven synthetic benchmarks plus one realistic CCS case study on the Johansen formation.

Significance. If the kernel is valid (positive semi-definite) and the invariance is correctly induced without sacrificing expressivity, the approach could improve sample efficiency in BO for engineering problems with unordered set inputs. The mixed-input compatibility and the realistic CCS simulator evaluation are practical strengths. Reproducible evaluation across eight use cases is a positive aspect, though the absence of explicit PSD verification or error bars in the provided description limits the assessed impact.

major comments (2)

[Section 3.1] The GP-Perm kernel is defined by comparing empirical representations via a divergence (Section 3.1, Eq. (3)–(5)). No theorem, proposition, or numerical check (e.g., eigenvalue analysis of the Gram matrix on sample sets) is provided to establish that the resulting function is positive semi-definite. This is load-bearing: without PSD, the GP surrogate is ill-defined, predictive variances can become negative, and BO acquisition functions are unreliable.
[Section 4.2] Table 2 and Figure 4 report optimization performance on the synthetic benchmarks and Johansen case. The claimed gains from permutation invariance are not compared against other established set kernels (e.g., Deep Sets kernels or permutation-invariant RBF variants from the literature), so it is unclear whether the reported improvements are due to the specific divergence construction or simply to any invariant embedding.

minor comments (2)

[Abstract] The abstract states that the kernel 'can be combined with standard kernels' but does not specify the exact composition rule (e.g., product or sum) or the hyper-parameter handling for the combined kernel; this should be stated explicitly in Section 3.2.
[Section 3] Notation for the empirical representation (e.g., the mapping from set to measure) is introduced without a clear reference to the underlying probability space or the choice of divergence (Wasserstein, MMD, etc.); a short paragraph clarifying these choices would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable comments on our manuscript. We provide detailed responses to each major comment below and outline the revisions we will make to address the concerns raised.

read point-by-point responses

Referee: [Section 3.1] The GP-Perm kernel is defined by comparing empirical representations via a divergence (Section 3.1, Eq. (3)–(5)). No theorem, proposition, or numerical check (e.g., eigenvalue analysis of the Gram matrix on sample sets) is provided to establish that the resulting function is positive semi-definite. This is load-bearing: without PSD, the GP surrogate is ill-defined, predictive variances can become negative, and BO acquisition functions are unreliable.

Authors: We fully agree that verifying the positive semi-definiteness of the GP-Perm kernel is essential. While the construction using a stable divergence between empirical representations is intended to yield a valid kernel (analogous to kernels derived from distances in reproducing kernel Hilbert spaces), we did not include an explicit check in the original submission. In the revised version, we will add both a theoretical note on why the kernel is PSD and a numerical validation by analyzing the eigenvalues of the Gram matrix constructed from sets in our benchmarks, confirming that the smallest eigenvalue is non-negative within numerical precision. revision: yes
Referee: [Section 4.2] Table 2 and Figure 4 report optimization performance on the synthetic benchmarks and Johansen case. The claimed gains from permutation invariance are not compared against other established set kernels (e.g., Deep Sets kernels or permutation-invariant RBF variants from the literature), so it is unclear whether the reported improvements are due to the specific divergence construction or simply to any invariant embedding.

Authors: The referee raises a valid point regarding the baseline comparisons. Our DKL-DS model provides a comparison to a learned permutation-invariant embedding via Deep Sets. To more directly address whether the gains stem from the specific divergence, we will include an additional baseline in the revised experiments: a permutation-invariant variant of the RBF kernel obtained by averaging standard RBF kernels over all pairs of elements between two sets. We will report the results on the synthetic benchmarks in an updated Table 2 and discuss the relative merits of the divergence-based approach, particularly its stability and ease of combination with vector inputs. revision: yes

Circularity Check

0 steps flagged

No circularity: kernel defined directly via set divergence without reduction to inputs or self-citations

full rationale

The paper's central contribution defines the GP-Perm kernel explicitly as a comparison of sets through a stable divergence between induced empirical representations, combinable with standard kernels. This is presented as an independent modeling choice for permutation invariance rather than a self-definitional loop, fitted parameter renamed as prediction, or load-bearing self-citation. No equations or claims reduce the output to the input by construction, and the derivation remains self-contained against external benchmarks for the CCS well-placement task.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; the divergence measure and empirical representations are described at high level without detailing any fitted constants or background assumptions.

pith-pipeline@v0.9.0 · 5735 in / 1078 out tokens · 32175 ms · 2026-05-22T11:02:59.001205+00:00 · methodology

Review history (2 revisions) →

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

our main contribution is a novel Gaussian Process kernel (GP-Perm) that encodes permutation invariance by comparing sets through a stable divergence between their induced empirical representations
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

D²(x,x′)=… + S_ε(I,I′)/ℓ_I² + … ; k_GP-Perm=σ² M_ν(D(x,x′))

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

25 extracted references · 25 canonical work pages · 1 internal anchor

[1]

M. Bui, G. D. Puxty, M. Gazzani, S. M. Soltani, C. Pozo, The role of carbon capture and storage (ccs) technologies in a net-zero carbon future (2021)

work page 2021
[2]

Ismail, V

I. Ismail, V . Gaganis, Carbon capture, utilization, and storage in saline aquifers: Subsurface policies, development plans, well control strategies and optimization approaches—a review, Clean Technologies 5 (2023) 609–637

work page 2023
[3]

P. I. Frazier, A tutorial on bayesian optimization, arXiv preprint arXiv:1807.02811 (2018)

work page internal anchor Pith review Pith/arXiv arXiv 2018
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C. K. Williams, C. E. Rasmussen, Gaussian processes for machine learning, volume 2, MIT press Cambridge, MA, 2006

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T. Brown, A. Cioba, I. Bogunovic, Sample-efficient bayesian optimisation using known invariances, Advances in Neural Information Processing Systems 37 (2024) 47931–47965

work page 2024
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J. Kim, M. McCourt, T. You, S. Kim, S. Choi, Bayesian optimization with approximate set kernels, Machine Learning 110 (2021) 857–879

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Zaheer, S

M. Zaheer, S. Kottur, S. Ravanbakhsh, B. Poczos, R. R. Salakhutdinov, A. J. Smola, Deep sets, Advances in neural information processing systems 30 (2017)

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A. G. Wilson, Z. Hu, R. Salakhutdinov, E. P. Xing, Deep kernel learning, in: Artificial intelligence and statistics, PMLR, 2016, pp. 370–378

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P. Buathong, D. Ginsbourger, T. Krityakierne, Kernels over sets of finite sets using rkhs embeddings, with application to bayesian (combinatorial) optimization, in: International conference on artificial intelligence and statistics, PMLR, 2020, pp. 2731–2741. 18

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C. Oh, J. Tomczak, E. Gavves, M. Welling, Combinatorial bayesian optimization using the graph cartesian product, Advances in Neural Information Processing Systems 32 (2019)

work page 2019
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S. P. Fotias, I. Ismail, V . Gaganis, Optimization of well placement in carbon capture and storage (ccs): Bayesian optimization framework under permutation invariance, Applied Sciences 14 (2024) 3528

work page 2024
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Garnett, M

R. Garnett, M. A. Osborne, S. J. Roberts, Bayesian optimization for sensor set selection, in: Proceedings of the 9th ACM/IEEE international conference on information processing in sensor networks, 2010, pp. 209–219

work page 2010
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Kandasamy, W

K. Kandasamy, W. Neiswanger, J. Schneider, B. Poczos, E. P. Xing, Neural architecture search with bayesian optimisation and optimal transport, Advances in neural information processing systems 31 (2018)

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J. Lee, Y . Lee, J. Kim, A. Kosiorek, S. Choi, Y . W. Teh, Set transformer: A framework for attention-based permutation-invariant neural networks, in: International conference on machine learning, PMLR, 2019, pp. 3744–3753

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Kimura, R

M. Kimura, R. Shimizu, Y . Hirakawa, R. Goto, Y . Saito, On permutation-invariant neural networks, arXiv preprint arXiv:2403.17410 (2024)

work page arXiv 2024
[18]

Gretton, K

A. Gretton, K. M. Borgwardt, M. J. Rasch, B. Schölkopf, A. Smola, A kernel two-sample test, The journal of machine learning research 13 (2012) 723–773

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Bachoc, L

F. Bachoc, L. Béthune, A. Gonzalez-Sanz, J.-M. Loubes, Gaussian processes on distri- butions based on regularized optimal transport, in: International Conference on Artificial Intelligence and Statistics, PMLR, 2023, pp. 4986–5010

work page 2023
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Feydy, T

J. Feydy, T. Séjourné, F.-X. Vialard, S.-i. Amari, A. Trouvé, G. Peyré, Interpolating be- tween optimal transport and mmd using sinkhorn divergences, in: The 22nd international conference on artificial intelligence and statistics, PMLR, 2019, pp. 2681–2690

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S. Ament, S. Daulton, D. Eriksson, M. Balandat, E. Bakshy, Unexpected improvements to expected improvement for bayesian optimization, Advances in Neural Information Pro- cessing Systems 36 (2023) 20577–20612

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Andersen, G

O. Andersen, G. Tangen, P. Ringrose, S. E. Greenberg, Co2 data share: a platform for sharing co2 storage reference datasets from demonstration projects, in: 14th greenhouse gas control technologies conference Melbourne, 2018, pp. 21–26

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A. F. Rasmussen, T. H. Sandve, K. Bao, A. Lauser, J. Hove, B. Skaflestad, R. Klöfkorn, M. Blatt, A. B. Rustad, O. Sævareid, et al., The open porous media flow reservoir simulator, Computers & Mathematics with Applications 81 (2021) 159–185. 19

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P. S. Bergmo, E. Lindeberg, F. Riis, W. T. Johansen, Exploring geological storage sites for co2 from norwegian gas power plants: Johansen formation, Energy Procedia 1 (2009) 2945–2952

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P. S. Bergmoa, A.-A. Grimstad, E. Lindeberg, F. Riis, W. T. Johansen, Exploring geological storage sites for co2 from norwegian gas power plants: Utsira south, Energy Procedia 1 (2009) 2953–2959. Appendix A. Synthetic Test Functions In all experiments, point coordinates are implemented in a normalized box and can be affinely mapped to [0,1] 2 without chan...

work page 2009

[1] [1]

M. Bui, G. D. Puxty, M. Gazzani, S. M. Soltani, C. Pozo, The role of carbon capture and storage (ccs) technologies in a net-zero carbon future (2021)

work page 2021

[2] [2]

Ismail, V

I. Ismail, V . Gaganis, Carbon capture, utilization, and storage in saline aquifers: Subsurface policies, development plans, well control strategies and optimization approaches—a review, Clean Technologies 5 (2023) 609–637

work page 2023

[3] [3]

P. I. Frazier, A tutorial on bayesian optimization, arXiv preprint arXiv:1807.02811 (2018)

work page internal anchor Pith review Pith/arXiv arXiv 2018

[4] [4]

C. K. Williams, C. E. Rasmussen, Gaussian processes for machine learning, volume 2, MIT press Cambridge, MA, 2006

work page 2006

[5] [5]

Brown, A

T. Brown, A. Cioba, I. Bogunovic, Sample-efficient bayesian optimisation using known invariances, Advances in Neural Information Processing Systems 37 (2024) 47931–47965

work page 2024

[6] [6]

J. Kim, M. McCourt, T. You, S. Kim, S. Choi, Bayesian optimization with approximate set kernels, Machine Learning 110 (2021) 857–879

work page 2021

[7] [7]

Zaheer, S

M. Zaheer, S. Kottur, S. Ravanbakhsh, B. Poczos, R. R. Salakhutdinov, A. J. Smola, Deep sets, Advances in neural information processing systems 30 (2017)

work page 2017

[8] [8]

A. G. Wilson, Z. Hu, R. Salakhutdinov, E. P. Xing, Deep kernel learning, in: Artificial intelligence and statistics, PMLR, 2016, pp. 370–378

work page 2016

[9] [9]

Buathong, D

P. Buathong, D. Ginsbourger, T. Krityakierne, Kernels over sets of finite sets using rkhs embeddings, with application to bayesian (combinatorial) optimization, in: International conference on artificial intelligence and statistics, PMLR, 2020, pp. 2731–2741. 18

work page 2020

[10] [10]

H. Moss, D. Leslie, D. Beck, J. Gonzalez, P. Rayson, Boss: Bayesian optimization over string spaces, Advances in neural information processing systems 33 (2020) 15476–15486

work page 2020

[11] [11]

C. Oh, J. Tomczak, E. Gavves, M. Welling, Combinatorial bayesian optimization using the graph cartesian product, Advances in Neural Information Processing Systems 32 (2019)

work page 2019

[12] [12]

S. P. Fotias, I. Ismail, V . Gaganis, Optimization of well placement in carbon capture and storage (ccs): Bayesian optimization framework under permutation invariance, Applied Sciences 14 (2024) 3528

work page 2024

[13] [13]

Garnett, M

R. Garnett, M. A. Osborne, S. J. Roberts, Bayesian optimization for sensor set selection, in: Proceedings of the 9th ACM/IEEE international conference on information processing in sensor networks, 2010, pp. 209–219

work page 2010

[14] [14]

Kandasamy, W

K. Kandasamy, W. Neiswanger, J. Schneider, B. Poczos, E. P. Xing, Neural architecture search with bayesian optimisation and optimal transport, Advances in neural information processing systems 31 (2018)

work page 2018

[15] [15]

Cuturi, Sinkhorn distances: Lightspeed computation of optimal transport, Advances in neural information processing systems 26 (2013)

M. Cuturi, Sinkhorn distances: Lightspeed computation of optimal transport, Advances in neural information processing systems 26 (2013)

work page 2013

[16] [16]

J. Lee, Y . Lee, J. Kim, A. Kosiorek, S. Choi, Y . W. Teh, Set transformer: A framework for attention-based permutation-invariant neural networks, in: International conference on machine learning, PMLR, 2019, pp. 3744–3753

work page 2019

[17] [17]

Kimura, R

M. Kimura, R. Shimizu, Y . Hirakawa, R. Goto, Y . Saito, On permutation-invariant neural networks, arXiv preprint arXiv:2403.17410 (2024)

work page arXiv 2024

[18] [18]

Gretton, K

A. Gretton, K. M. Borgwardt, M. J. Rasch, B. Schölkopf, A. Smola, A kernel two-sample test, The journal of machine learning research 13 (2012) 723–773

work page 2012

[19] [19]

Bachoc, L

F. Bachoc, L. Béthune, A. Gonzalez-Sanz, J.-M. Loubes, Gaussian processes on distri- butions based on regularized optimal transport, in: International Conference on Artificial Intelligence and Statistics, PMLR, 2023, pp. 4986–5010

work page 2023

[20] [20]

Feydy, T

J. Feydy, T. Séjourné, F.-X. Vialard, S.-i. Amari, A. Trouvé, G. Peyré, Interpolating be- tween optimal transport and mmd using sinkhorn divergences, in: The 22nd international conference on artificial intelligence and statistics, PMLR, 2019, pp. 2681–2690

work page 2019

[21] [21]

Ament, S

S. Ament, S. Daulton, D. Eriksson, M. Balandat, E. Bakshy, Unexpected improvements to expected improvement for bayesian optimization, Advances in Neural Information Pro- cessing Systems 36 (2023) 20577–20612

work page 2023

[22] [22]

Andersen, G

O. Andersen, G. Tangen, P. Ringrose, S. E. Greenberg, Co2 data share: a platform for sharing co2 storage reference datasets from demonstration projects, in: 14th greenhouse gas control technologies conference Melbourne, 2018, pp. 21–26

work page 2018

[23] [23]

A. F. Rasmussen, T. H. Sandve, K. Bao, A. Lauser, J. Hove, B. Skaflestad, R. Klöfkorn, M. Blatt, A. B. Rustad, O. Sævareid, et al., The open porous media flow reservoir simulator, Computers & Mathematics with Applications 81 (2021) 159–185. 19

work page 2021

[24] [24]

P. S. Bergmo, E. Lindeberg, F. Riis, W. T. Johansen, Exploring geological storage sites for co2 from norwegian gas power plants: Johansen formation, Energy Procedia 1 (2009) 2945–2952

work page 2009

[25] [25]

P. S. Bergmoa, A.-A. Grimstad, E. Lindeberg, F. Riis, W. T. Johansen, Exploring geological storage sites for co2 from norwegian gas power plants: Utsira south, Energy Procedia 1 (2009) 2953–2959. Appendix A. Synthetic Test Functions In all experiments, point coordinates are implemented in a normalized box and can be affinely mapped to [0,1] 2 without chan...

work page 2009