Actuation manifold from snapshots data

OVERVIEW
This dataset accompanies the article titled "Actuation Manifold from Snapshots Data"
by Luigi Marra, Guy Y. Cornejo Maceda, Andrea Meilán-Vila, Vanesa Guerrero, Salma Rashwan, 
Bernd R. Noack, Stefano Discetti, and Andrea Ianiro.

The paper proposes a data-driven methodology to learn a low-dimensional actuation manifold 
of controlled flows. The methodology starts by resolving snapshot flow data for a representative 
ensemble of actuations. Key enablers for the actuation manifold are isometric mapping as an 
encoder and a combination of a neural network and 𝑘-nearest neighbour interpolation as a decoder. 
This methodology is tested for the fluidic pinball at Reynolds number Re = 30. 
The proposed methodology yields a five-dimensional manifold that describes a wide range 
of dynamics with a small representation error. The manifold is shown to be a key enabler for 
control-oriented flow estimation.

FILES
The database consists of 9 distinct files:
1) Grid.h5
2) TrainingDataset_1.h5
3) TrainingDataset_2.h5
4) TrainingDataset_3.h5
5) TestDataset.h5
6) IsomapResults.h5
7) IsomapVarke.h5
8) Reconstruction_KNN1.h5
9) Reconstruction_KNN.h5
10) Reconstruction_MLP1.h5
11) Reconstruction_MLP2.h5

DATA DESCRIPTION
1) "Grid.h5" contains:

- X_new:      x-component of each point in the fluidic pinball DNS mesh
- Y_new:      y-component of each point in the fluidic pinball DNS mesh
- dx:         x-dimension of the DNS grid step
- dy:         y-dimension of the DNS grid step
- dA:         DNS grid element area
- Mask:       Mask matrix of 0 and 1 to identify fluidic pinball cylinders

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2) "TrainingDataset_1.h5" contains:

- b:          Fluidic pinball actuation vector. b_1 (front), b_2 (top), b_3 (bottom). 
Matrix of the actuations explored in the training dataset.
- p:          Kiki parameters. p_1 (Boat-tailing/base-bleeding), p_2 (Magnus), p_3 (forward stagnation point). 
Matrix of the Kiki parameters explored in the training dataset.
- Cd:         Drag coefficient vector
- Cl:         Lift coefficient vector
- Cl_delayed: Vector of the time-delayed lift coefficient
- dCl_dt:     Vector of the time derivative of the lift coefficient
- u7_125:     Velocity measured at position (7,1.25), u-component
- v7_125:     Velocity measured at position (7,1.25), v-component
- u10_125:    Velocity measured at position (10,1.25), u-component
- v10_125:    Velocity measured at position (10,1.25), v-component

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3) "TrainingDataset_2.h5" contains:

- Snap_u:     Matrix with snapshots of u-component compiled column-wise

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4) "TrainingDataset_3.h5" contains:

- Snap_v:     Matrix with snapshots of v-component compiled column-wise

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5) "TestDataset.h5" contains:

The same variables as "TrainingDataset_1.h5", "TrainingDataset_2.h5", "TrainingDataset_3.h5" but for the test dataset.

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6) "IsomapResults.h5" contains:

- k_e:     Number of neighbours used to construct the KNN-graph
- D:       Matrix with Euclidean distances between snapshots
- Dg:      Matrix with Geodesic distances between snapshots
- Gamma:   Matrix with low-dimensional embedding 
- Rv:      Residual variance
- Phi_u:   Matrix with pseudomodes in column, u-component
- Phi_v:   Matrix with pseudomodes in column, v-component

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7) "IsomapVarke.h5" contains:

- Ke:           Vector of k_e instances analyzed in the encoding step
- FrobNormDg:   Frobenius norm of the geodesic distance matrix as k_e varies
- NpointsConn:  Number of points included in the KNN-graph as k_e varies

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8) "Reconstruction_KNN1.h5" contains:
Sensor information: lift coefficient and its one-quarter mean shedding period delay

- kd1:        Number of neighbours used in the first step of KNN snapshots reconstruction 
(Sensors+actuation->Manifold coordinates)
- kd2:        Number of neighbours used in the second step of KNN snapshots reconstruction 
(Manifold coordinates->Snapshot)
- Snap_u_hat: Matrix with reconstructed snapshots, u-component
- Snap_v_hat: Matrix with reconstructed snapshots, v-component

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9) "Reconstruction_KNN2.h5" contains:
Sensor information: v-component of the velocity at points (7,1.25) and (10,1.25)

Same variables as "Reconstruction_KNN1.h5" but for reconstruction done with sensor information 
the v-component of the velocity at points (7,1.25) and (10,1.25).

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10) "Reconstruction_MLP1.h5" contains:
Sensor information: lift coefficient and its one-quarter mean shedding period delay

- kd: Number of neighbours used in the second step of snapshots reconstruction. 
MLP (Sensors+actuation->Manifold coordinates) and KNN interpolation (Manifold coordinates->snapshots)
- Snap_u_hat: Matrix with reconstructed snapshots, u-component
- Snap_v_hat: Matrix with reconstructed snapshots, v-component

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11) "Reconstruction_MLP2.h5" contains:
Sensor information: v-component of the velocity at points (7,1.25) and (10,1.25)

Same variables as "Reconstruction_MLP1.h5" but for reconstruction done with sensor information 
the v-component of the velocity at points (7,1.25) and (10,1.25).

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CONTACT INFORMATION
For more information, please use the following email address: luigi.marra@uc3m.es

ADDITIONAL RESOURCES
Link to the code repository: https://github.com/Lmarra1/Actuation-manifold-from-snapshot-data.git

ISSUES AND FEEDBACK
If you encounter any issues or have feedback regarding this dataset, we encourage you to write to the authors. 
Your insights and suggestions are valuable, and we appreciate your contribution to improving the quality of this dataset.