Latent attention on masked patches for flow reconstruction

Andrea N\'ovoa; Ben Eze; Luca Magri

arxiv: 2603.02028 · v2 · submitted 2026-03-02 · 💻 cs.LG

Latent attention on masked patches for flow reconstruction

Ben Eze , Luca Magri , Andrea N\'ovoa This is my paper

Pith reviewed 2026-05-15 17:29 UTC · model grok-4.3

classification 💻 cs.LG

keywords masked flow reconstructionvision transformerproper orthogonal decompositionsensor placementlaminar wakefluid dynamicsattention mechanismregression

0 comments

The pith

A single-layer attention model on POD-reduced patches reconstructs full flow fields from 90 percent masked noisy inputs.

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

The LAMP approach splits each flow snapshot into patches, compresses every patch with proper orthogonal decomposition, and trains a single-layer attention block by closed-form linear regression to fill in missing data. On laminar wakes the method recovers the complete velocity field even when 90 percent of the patches are masked and the signal carries 10 to 30 dB of noise. The learned attention weights directly supply multi-resolution maps that indicate where sensors should be placed to minimize reconstruction error. The same pipeline improves on gappy POD for chaotic wakes although absolute accuracy drops. The design is deliberately modular so that nonlinear patch compression or deeper attention layers can be swapped in later.

Core claim

LAMP accurately reconstructs the full flow field from a 90%-masked and noisy input on the laminar wake past a bluff body, across signal-to-noise ratios between 10 and 30 dB. The learned attention matrix yields interpretable multi-fidelity optimal sensor-placement maps. Performance is limited on the chaotic wake past two cylinders but still exceeds gappy POD. The modularity of the framework naturally accommodates nonlinear compression and deep attention blocks for future high-dimensional cases.

What carries the argument

Single-layer transformer attention trained via closed-form linear regression on patch-wise POD coefficients of masked flow snapshots.

If this is right

Full-field recovery remains possible when only 10 percent of the data is observed with added noise in laminar regimes.
Attention weights translate directly into multi-fidelity sensor placement maps without separate optimization.
The pipeline outperforms gappy POD on both laminar and chaotic wakes.
The modular structure supports replacement of linear POD with nonlinear autoencoders or deeper attention blocks.
The same patch-and-attend regression supplies an efficient baseline for nonlinear masked reconstruction tasks.

Where Pith is reading between the lines

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

The attention-derived placements could be compared against established sensor-selection algorithms to test whether they are truly optimal or merely competitive.
The patch-wise structure may extend to other sparse-data problems such as tomographic reconstruction or sparse sensor fusion in fluid experiments.
Introducing the suggested nonlinear compression could enable reconstruction in fully turbulent regimes where linear POD fails.
Varying patch size or number would expose accuracy-compute trade-offs not quantified in the current laminar and chaotic tests.

Load-bearing premise

Reducing each patch independently with POD and then applying linear attention is enough to recover the global flow field without deeper nonlinear layers.

What would settle it

Re-running the laminar-wake experiment at 90 percent masking and 20 dB SNR and obtaining average reconstruction errors substantially larger than those reported, or showing that attention-derived sensor locations produce higher error than classical greedy placement when tested in a separate validation loop.

Figures

Figures reproduced from arXiv: 2603.02028 by Andrea N\'ovoa, Ben Eze, Luca Magri.

**Figure 2.** Figure 2: Patch-wise POD reconstruction performance for varying patch size [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Figure 3: Reconstruction error L pred for varying noise levels, patch size P and latent dimension Ne, all with 10% patches unmasked. The input is noisy masked data with SNR = (a) ∞ (noise-free), (b) 30 dB, (c) 20 dB, (d) 10 dB. The loss is computed against the noise-free target Xtest and the model is trained on noise-free data. Horizontal dashed lines show the noise variance. L pred is calculated for 25 random patch… view at source ↗

**Figure 4.** Figure 4: Predictive-power maps for varying P and Ne. Patches with higher predictive power predict the rest of the patches with lower average loss. Despite the increased reconstruction loss compared to dataset 1, LAMP achieves a 26% lower reconstruction error L pred than gappy POD [5] on identical inputs (results not shown for brevity). Qualitatively, gappy POD tends to overestimate velocity fluctuations in region… view at source ↗

**Figure 5.** Figure 5: Masked reconstruction of the chaotic wake from 25% unmasked patches, [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

read the original abstract

Vision transformers have shown outstanding performance in image generation, yet their adoption in fluid dynamics remains limited. We introduce the Latent Attention on Masked Patches (LAMP) model, an interpretable regression-based modified vision transformer designed for masked flow reconstruction. LAMP follows a three-fold strategy: (i) partition of each flow snapshot into patches, (ii) patch-wise dimensionality reduction via proper orthogonal decomposition, and (iii) reconstruction of the full field from a masked input using a single-layer transformer trained via closed-form linear regression. We test the method on two canonical 2D unsteady wakes: a laminar wake past a bluff body, and a chaotic wake past two cylinders. On the laminar case, LAMP accurately reconstructs the full flow field from a 90%-masked and noisy input, across signal-to-noise ratios between 10 and 30dB. Further, the learned attention matrix yields interpretable multi-fidelity optimal sensor-placement maps. LAMP's performance on the chaotic wake is limited, but outperforms other regression methods such as gappy POD. The modularity of the framework, however, naturally accommodates nonlinear compression and deep attention blocks, thereby providing an efficient baseline for nonlinear, high-dimensional masked flow reconstruction.

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

LAMP gives a clean modular baseline for masked flow reconstruction via patch POD plus closed-form linear attention, but the accuracy and optimality claims rest on thin qualitative evidence.

read the letter

The paper's core contribution is a modular pipeline called LAMP that splits flow snapshots into patches, reduces each with proper orthogonal decomposition, and then reconstructs the full field from masked inputs using a single-layer transformer whose weights are fit by closed-form linear regression. On the laminar wake it handles 90 percent masking with added noise reasonably well, and the attention matrix produces sensor placement maps that look plausible at different fidelities. The chaotic case is harder and performance drops, but it still edges out gappy POD. What is actually new is this exact combination for flow reconstruction. Prior work has used POD and gappy POD, and vision transformers exist, but the patch-POD plus linear-regression attention setup is not standard. The paper does well by keeping everything linear and closed-form, which avoids black-box fitting and makes the attention weights directly interpretable as importance scores for patches. The modularity is a real strength: you can replace the POD step with nonlinear autoencoders later without changing the attention part. That gives a clean baseline for future nonlinear extensions. The soft spots are in the validation. The abstract claims accurate reconstruction but provides no error norms, no tables of RMSE across masking ratios or SNR levels, and no statistical comparisons beyond a qualitative statement. Without those, it's difficult to know how much better it is than existing methods in absolute terms. The claim that the attention matrix yields optimal sensor-placement maps also needs support; there is no benchmark against established algorithms like greedy combinatorial selection or convex relaxations on the same laminar wake data. The chaotic wake results are described only as limited, with no details on where the method breaks or how the error behaves. This work is aimed at researchers in data-driven fluid mechanics who need interpretable tools for reconstructing incomplete flow fields or designing sensor layouts. A reader who wants a reproducible starting point for masked data problems or ideas for combining linear compression with attention would get value from it. The setup is honest and the math is straightforward, so it deserves a serious referee even if the current evidence is thin on numbers. I would recommend sending it to peer review, with the expectation that the authors add quantitative error metrics and a sensor placement comparison section.

Referee Report

3 major / 2 minor

Summary. The manuscript introduces the Latent Attention on Masked Patches (LAMP) model, a regression-based modified vision transformer for masked flow reconstruction. It partitions snapshots into patches, performs patch-wise POD, and reconstructs the full field via single-layer attention trained with closed-form linear regression. Tests on laminar and chaotic 2D wakes claim accurate reconstruction from 90%-masked noisy inputs on the laminar case (SNR 10-30 dB) with interpretable optimal sensor maps from the attention matrix, plus outperformance of gappy POD on the chaotic case, while noting modularity for nonlinear extensions.

Significance. If the quantitative claims are substantiated, the work supplies an efficient, modular baseline that combines linear POD compression with interpretable attention for masked reconstruction, offering a reproducible starting point for nonlinear high-dimensional flow problems and potential sensor-placement insights.

major comments (3)

[Abstract] Abstract and results on laminar wake: the claim of accurate reconstruction from 90%-masked noisy inputs supplies no quantitative error norms, RMSE values, cross-validation statistics, or direct numerical comparisons beyond a qualitative statement of outperformance versus gappy POD.
[Results (laminar case)] Results on attention matrix: labeling the learned attention matrix as yielding 'optimal' multi-fidelity sensor-placement maps lacks any benchmark against established algorithms (greedy combinatorial selection, E-optimal design, or convex relaxations) on the same laminar wake data.
[Results (chaotic case)] Chaotic wake experiments: performance is described as limited yet superior to gappy POD, but no specific error metrics, failure modes, or quantitative comparisons are provided to support the cross-method claim.

minor comments (2)

[Method] Clarify the exact definition of the single-layer attention matrix and its mapping to sensor locations with an explicit equation or pseudocode.
[Method] Specify the POD truncation rank per patch and its selection procedure, as this is listed among the free parameters.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments, which have helped us strengthen the quantitative aspects and clarify the claims in the manuscript. We have revised the abstract, results sections, and discussion to incorporate specific error metrics and adjusted terminology. Point-by-point responses follow.

read point-by-point responses

Referee: [Abstract] Abstract and results on laminar wake: the claim of accurate reconstruction from 90%-masked noisy inputs supplies no quantitative error norms, RMSE values, cross-validation statistics, or direct numerical comparisons beyond a qualitative statement of outperformance versus gappy POD.

Authors: We agree that quantitative support is essential. In the revised manuscript we have added explicit RMSE values (normalized by the flow-field standard deviation) and relative L2 error norms for the laminar wake across the 10–30 dB SNR range, together with direct numerical comparisons to gappy POD. Cross-validation statistics (5-fold) are now reported in the main text and supplementary material. revision: yes
Referee: [Results (laminar case)] Results on attention matrix: labeling the learned attention matrix as yielding 'optimal' multi-fidelity sensor-placement maps lacks any benchmark against established algorithms (greedy combinatorial selection, E-optimal design, or convex relaxations) on the same laminar wake data.

Authors: We accept that the unqualified term 'optimal' is misleading without comparative benchmarks. The revision replaces 'optimal' with 'attention-derived' throughout and adds an explicit statement that the maps reflect the learned attention weights rather than a claim of global optimality. A systematic comparison against greedy or E-optimal designs is outside the present scope; we have added a short paragraph noting this limitation and suggesting it as future work. revision: partial
Referee: [Results (chaotic case)] Chaotic wake experiments: performance is described as limited yet superior to gappy POD, but no specific error metrics, failure modes, or quantitative comparisons are provided to support the cross-method claim.

Authors: We have inserted quantitative metrics (mean RMSE and relative L2 errors) for the chaotic wake in the revised results section, along with a direct side-by-side table versus gappy POD. Failure modes are now discussed: the method captures the dominant coherent structures but shows elevated errors on the smaller-scale chaotic fluctuations, consistent with the linear POD compression step. These additions substantiate the comparative claim. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation; closed-form linear regression on POD coefficients yields independent reconstruction

full rationale

The paper's core procedure partitions snapshots into patches, applies patch-wise POD for dimensionality reduction, then reconstructs the full field via single-layer attention trained with closed-form linear regression on the resulting coefficients. This is a standard supervised regression setup with no self-referential equations, no fitted parameters renamed as predictions, and no load-bearing self-citations that reduce the central claim to its own inputs. The interpretation of the learned attention matrix as yielding 'optimal' sensor-placement maps is an empirical outcome of the regression rather than a definitional equivalence or ansatz smuggled via citation. The method remains self-contained against external benchmarks and does not invoke uniqueness theorems or prior author work to force its choices.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard optimality property of POD for linear dimensionality reduction and the assumption that linear attention on the reduced coefficients can recover the original field from masked inputs.

free parameters (1)

POD truncation rank per patch
Number of retained modes per patch controls information loss and is chosen without stated selection criterion or cross-validation.

axioms (1)

standard math Proper orthogonal decomposition yields an optimal linear basis for each patch
Invoked explicitly in step (ii) of the three-fold strategy.

pith-pipeline@v0.9.0 · 5512 in / 1278 out tokens · 64355 ms · 2026-05-15T17:29:11.442032+00:00 · methodology

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.

patch-wise dimensionality reduction via proper orthogonal decomposition... single-layer transformer trained via closed-form linear regression
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

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

learned attention matrix yields interpretable multi-fidelity optimal sensor-placement maps

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

19 extracted references · 19 canonical work pages

[1]

Journal of Fluid Mechanics 1024, A7 (2025)

Bekoglu, E., Bempedelis, N., Steiros, K.: Formation of turbulent secondary vortex street in absence of vortex shedding instability. Journal of Fluid Mechanics 1024, A7 (2025)

work page 2025
[2]

Annual Review of Fluid Mechanics 25, 539–575 (1993)

Berkooz, G., et al.: The proper orthogonal decomposition in the analysis of turbu- lent ﬂows. Annual Review of Fluid Mechanics 25, 539–575 (1993)

work page 1993
[3]

Journal of Computational Physics 496, 112581 (2024)

Cheng, S., Liu, C., Guo, Y., Arcucci, R.: Eﬃcient deep data assimilation with sparse observations and time-varying sensors. Journal of Computational Physics 496, 112581 (2024)

work page 2024
[4]

In: Proc

Dosovitskiy, A.: An image is worth 16 Œ 16 words: Transformers for image recog- nition at scale. In: Proc. of IEEE/CVF CVPR. pp. 45–67 (2021)

work page 2021
[5]

Journal of the Optical Society of America A 12(8), 1657–1664 (1995)

Everson, R., Sirovich, L.: Karhunen–loève procedure for gappy data. Journal of the Optical Society of America A 12(8), 1657–1664 (1995)

work page 1995
[6]

Journal of Fluid Mechanics 870, 106–120 (2019)

Fukami, K., Fukagata, K., Taira, K.: Super-resolution reconstruction of turbulent ﬂows with machine learning. Journal of Fluid Mechanics 870, 106–120 (2019)

work page 2019
[7]

In: Proc

He, K., Chen, X., Xie, S., Li, Y., Dollár, P., Girshick, R.: Masked autoencoders are scalable vision learners. In: Proc. of IEEE/CVF CVPR. pp. 16000–16009 (2022)

work page 2022
[8]

Science 382(6677), 1416–1421 (2023)

Lam, R., Sanchez-Gonzalez, A., Willson, M., Wirnsberger, P., Fortunato, M., Alet, F., Ravuri, S., Ewalds, T., Eaton-Rosen, Z., Hu, W., et al.: Learning skillful medium-range global weather forecasting. Science 382(6677), 1416–1421 (2023)

work page 2023
[9]

Experiments in Fluids 58(12), 171 (2017)

Lee, Y., Yang, H., Yin, Z.: Piv-dcnn: cascaded deep convolutional neural networks for particle image velocimetry. Experiments in Fluids 58(12), 171 (2017)

work page 2017
[10]

Data- Centric Engineering 7, e5 (2026)

Mo, Y., Magri, L.: Reconstruction of three-dimensional turbulent ﬂows from sparse and noisy planar measurements: a weight-sharing neural network approach. Data- Centric Engineering 7, e5 (2026)

work page 2026
[11]

Data- Centric Engineering 5, e38 (2024)

Mo, Y., Traverso, T., Magri, L.: Decoder decomposition for the analysis of the latent space of nonlinear autoencoders with wind-tunnel experimental data. Data- Centric Engineering 5, e38 (2024)

work page 2024
[12]

Physical Review Fluids 9(6), 064601 (2024)

Nista, L., Pitsch, H., Schumann, C.D., Bode, M., Grenga, T., MacArt, J.F., Attili, A.: Inﬂuence of adversarial training on super-resolution turbulence reconstruction. Physical Review Fluids 9(6), 064601 (2024)

work page 2024
[13]

Computer Methods in Applied Mechanics and En- gineering 450, 118600 (2026)

Özalp, E., Nóvoa, A., Magri, L.: Real-time forecasting of chaotic dynamics from sparse data and autoencoders. Computer Methods in Applied Mechanics and En- gineering 450, 118600 (2026)

work page 2026
[14]

In: Proc

Peebles, W., Xie, S.: Scalable diﬀusion models with transformers. In: Proc. of IEEE/CVF ICCV. pp. 4172–4182 (2023)

work page 2023
[15]

Data-Centric Engineering 6, e48 (2025)

Quattromini, M., Bucci, M.A., Cherubini, S., Semeraro, O.: Mean ﬂow data assim- ilation using physics-constrained graph neural networks. Data-Centric Engineering 6, e48 (2025)

work page 2025
[16]

Journal of Fluid Mechanics 975, A2 (2023)

Racca, A., Doan, N.A.K., Magri, L.: Predicting turbulent dynamics with the con- volutional autoencoder echo state network. Journal of Fluid Mechanics 975, A2 (2023)

work page 2023
[17]

Journal of Statistical Physics 65(3–4), 579–616 (1991)

Sauer, T., Yorke, J.A., Casdagli, M.: Embedology. Journal of Statistical Physics 65(3–4), 579–616 (1991)

work page 1991
[18]

Advances in neural information pro- cessing systems 30 (2017)

Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A.N., Kaiser, Ł., Polosukhin, I.: Attention is all you need. Advances in neural information pro- cessing systems 30 (2017)

work page 2017
[19]

Journal of Fluid Mechanics 981, A17 (2024)

Xia, C., Zhang, J., Kerrigan, E.C., Rigas, G.: Active ﬂow control for bluﬀ body drag reduction using reinforcement learning with partial measurements. Journal of Fluid Mechanics 981, A17 (2024)

work page 2024

[1] [1]

Journal of Fluid Mechanics 1024, A7 (2025)

Bekoglu, E., Bempedelis, N., Steiros, K.: Formation of turbulent secondary vortex street in absence of vortex shedding instability. Journal of Fluid Mechanics 1024, A7 (2025)

work page 2025

[2] [2]

Annual Review of Fluid Mechanics 25, 539–575 (1993)

Berkooz, G., et al.: The proper orthogonal decomposition in the analysis of turbu- lent ﬂows. Annual Review of Fluid Mechanics 25, 539–575 (1993)

work page 1993

[3] [3]

Journal of Computational Physics 496, 112581 (2024)

Cheng, S., Liu, C., Guo, Y., Arcucci, R.: Eﬃcient deep data assimilation with sparse observations and time-varying sensors. Journal of Computational Physics 496, 112581 (2024)

work page 2024

[4] [4]

In: Proc

Dosovitskiy, A.: An image is worth 16 Œ 16 words: Transformers for image recog- nition at scale. In: Proc. of IEEE/CVF CVPR. pp. 45–67 (2021)

work page 2021

[5] [5]

Journal of the Optical Society of America A 12(8), 1657–1664 (1995)

Everson, R., Sirovich, L.: Karhunen–loève procedure for gappy data. Journal of the Optical Society of America A 12(8), 1657–1664 (1995)

work page 1995

[6] [6]

Journal of Fluid Mechanics 870, 106–120 (2019)

Fukami, K., Fukagata, K., Taira, K.: Super-resolution reconstruction of turbulent ﬂows with machine learning. Journal of Fluid Mechanics 870, 106–120 (2019)

work page 2019

[7] [7]

In: Proc

He, K., Chen, X., Xie, S., Li, Y., Dollár, P., Girshick, R.: Masked autoencoders are scalable vision learners. In: Proc. of IEEE/CVF CVPR. pp. 16000–16009 (2022)

work page 2022

[8] [8]

Science 382(6677), 1416–1421 (2023)

Lam, R., Sanchez-Gonzalez, A., Willson, M., Wirnsberger, P., Fortunato, M., Alet, F., Ravuri, S., Ewalds, T., Eaton-Rosen, Z., Hu, W., et al.: Learning skillful medium-range global weather forecasting. Science 382(6677), 1416–1421 (2023)

work page 2023

[9] [9]

Experiments in Fluids 58(12), 171 (2017)

Lee, Y., Yang, H., Yin, Z.: Piv-dcnn: cascaded deep convolutional neural networks for particle image velocimetry. Experiments in Fluids 58(12), 171 (2017)

work page 2017

[10] [10]

Data- Centric Engineering 7, e5 (2026)

Mo, Y., Magri, L.: Reconstruction of three-dimensional turbulent ﬂows from sparse and noisy planar measurements: a weight-sharing neural network approach. Data- Centric Engineering 7, e5 (2026)

work page 2026

[11] [11]

Data- Centric Engineering 5, e38 (2024)

Mo, Y., Traverso, T., Magri, L.: Decoder decomposition for the analysis of the latent space of nonlinear autoencoders with wind-tunnel experimental data. Data- Centric Engineering 5, e38 (2024)

work page 2024

[12] [12]

Physical Review Fluids 9(6), 064601 (2024)

Nista, L., Pitsch, H., Schumann, C.D., Bode, M., Grenga, T., MacArt, J.F., Attili, A.: Inﬂuence of adversarial training on super-resolution turbulence reconstruction. Physical Review Fluids 9(6), 064601 (2024)

work page 2024

[13] [13]

Computer Methods in Applied Mechanics and En- gineering 450, 118600 (2026)

Özalp, E., Nóvoa, A., Magri, L.: Real-time forecasting of chaotic dynamics from sparse data and autoencoders. Computer Methods in Applied Mechanics and En- gineering 450, 118600 (2026)

work page 2026

[14] [14]

In: Proc

Peebles, W., Xie, S.: Scalable diﬀusion models with transformers. In: Proc. of IEEE/CVF ICCV. pp. 4172–4182 (2023)

work page 2023

[15] [15]

Data-Centric Engineering 6, e48 (2025)

Quattromini, M., Bucci, M.A., Cherubini, S., Semeraro, O.: Mean ﬂow data assim- ilation using physics-constrained graph neural networks. Data-Centric Engineering 6, e48 (2025)

work page 2025

[16] [16]

Journal of Fluid Mechanics 975, A2 (2023)

Racca, A., Doan, N.A.K., Magri, L.: Predicting turbulent dynamics with the con- volutional autoencoder echo state network. Journal of Fluid Mechanics 975, A2 (2023)

work page 2023

[17] [17]

Journal of Statistical Physics 65(3–4), 579–616 (1991)

Sauer, T., Yorke, J.A., Casdagli, M.: Embedology. Journal of Statistical Physics 65(3–4), 579–616 (1991)

work page 1991

[18] [18]

Advances in neural information pro- cessing systems 30 (2017)

Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A.N., Kaiser, Ł., Polosukhin, I.: Attention is all you need. Advances in neural information pro- cessing systems 30 (2017)

work page 2017

[19] [19]

Journal of Fluid Mechanics 981, A17 (2024)

Xia, C., Zhang, J., Kerrigan, E.C., Rigas, G.: Active ﬂow control for bluﬀ body drag reduction using reinforcement learning with partial measurements. Journal of Fluid Mechanics 981, A17 (2024)

work page 2024