Update README.md

README.md

@@ -229,4 +229,612 @@ configs:
   data_files:
   - split: total
     path: snapshot/total-*
+license: other
+language:
+- en
+tags:
+- deal
+- neural_operators
+- graph-neural-networks
+pretty_name: Beam3D Elastic Dynamics Dataset
 ---
+
+
+
+# Beam3D Elastic Dynamics Dataset
+
+## Dataset Details
+
+### Dataset Description
+
+This dataset contains synthetic 3D beam simulations generated with a finite element solver based on `deal.II`.
+
+Each sample represents one dynamic simulation of a 3D elastic beam. The simulations include randomized geometry, material properties, damping parameters, and loading conditions.
+
+The dataset is intended for scientific machine learning tasks involving elastic dynamics, including surrogate modeling, graph neural networks, neural operators, reduced-order modeling, and spatio-temporal prediction.
+
+The dataset is organized into three Hugging Face configurations:
+
+| Configuration | Content |
+|---|---|
+| `geometry` | Mesh connectivity, graph connectivity, and static node-level information |
+| `snapshot` | Time-dependent physical fields stored component-wise |
+| `metadata` | Simulation-level scalar parameters |
+
+- **Curated by:** FAST Computing
+- **Shared by:** FAST Computing
+- **Language(s):** English
+- **License:** Other
+
+---
+
+## Uses
+
+### Direct Use
+
+This dataset can be used for:
+
+- training surrogate models for 3D elastic dynamics;
+- training graph neural networks on finite element meshes;
+- training neural operators or sequence models for displacement and velocity prediction;
+- learning the response of elastic beams under different loading conditions;
+- testing reduced-order modeling pipelines;
+- benchmarking scientific machine learning methods on structured simulation data.
+
+The dataset is especially suited for methods that use mesh information, graph connectivity, node-level physical quantities, and simulation metadata.
+
+### Out-of-Scope Use
+
+This dataset should not be used as a validated engineering benchmark for safety-critical structural design.
+
+The simulations are synthetic and depend on the numerical assumptions, mesh resolution, material model, and loading conditions used during generation. Any engineering use requires independent verification.
+
+---
+
+## Dataset Structure
+
+The dataset has three configurations:
+
+```python
+from datasets import load_dataset
+
+repo_id = "fastcomputing/first_beam3d_test_single_split"
+
+geometry = load_dataset(repo_id, name="geometry", split="total")
+snapshots = load_dataset(repo_id, name="snapshot", split="total")
+metadata = load_dataset(repo_id, name="metadata", split="total")
+```
+
+Each configuration contains one row per simulation sample.
+
+---
+
+## Configuration: `geometry`
+
+The `geometry` configuration stores mesh-related quantities and static node-level information.
+
+Each row corresponds to one simulation sample.
+
+| Field | Meaning | Expected shape | Type |
+|---|---|---:|---|
+| `sample_id` | Simulation identifier | scalar | `int32` |
+| `points_x` | Node coordinates in x direction | `(N, )` | `float32` |
+| `points_y` | Node coordinates in y direction | `(N, )` | `float32` |
+| `points_z` | Node coordinates in z direction | `(N, )` | `float32` |
+| `cells` | Hexahedral cell connectivity | `(C, 8)` | `int32` |
+| `edge_index` | Directed graph edges extracted from hexahedral cells | `(2, E)` | `int32` |
+| `constraint_mask_x` | Mask identifying constrained displacement components in x| `(N, )` | `int32` |
+| `constraint_mask_y` | Mask identifying constrained displacement components in y| `(N, )` | `int32` |
+| `constraint_mask_z` | Mask identifying constrained displacement components in z| `(N, )` | `int32` |
+| `constraint_value_x` | Prescribed displacement values for constrained components x| `(N, )` | `float32` |
+| `constraint_value_y` | Prescribed displacement values for constrained components y| `(N, )` | `float32` |
+| `constraint_value_z` | Prescribed displacement values for constrained components z| `(N, )` | `float32` |
+| `boundary_id` | Geometric boundary label associated with each node | `(N,)` | `int32` |
+| `node_type` | Semantic node classification | `(N,)` | `int32` |
+
+Where:
+
+```text
+N = number of mesh nodes
+C = number of hexahedral cells
+E = number of directed graph edges
+```
+
+### `points`
+
+`points` stores the node coordinates:
+
+```text
+points_x[i] = [x_i]
+points_y[i] = [y_i]
+points_z[i] = [z_i]
+```
+
+Shape:
+
+```text
+(N, )
+```
+
+### `cells`
+
+`cells` stores the hexahedral finite element connectivity.
+
+Each row contains the 8 node indices of one hexahedral cell:
+
+```text
+cells[c] = [n0, n1, n2, n3, n4, n5, n6, n7]
+```
+
+Shape:
+
+```text
+(C, 8)
+```
+
+This is not the raw VTK flat cell array.  
+
+### `edge_index`
+
+`edge_index` stores graph connectivity derived from the hexahedral cells.
+
+For each hexahedral cell, the 12 standard hexahedron edges are extracted. Both directions are stored for each edge, so the graph is directed:
+
+```text
+edge_index[:, e] = [source_node, target_node]
+```
+
+Shape:
+
+```text
+(2, E)
+```
+
+The local hexahedral edges used to build the graph are:
+
+```text
+(0, 1), (1, 2), (2, 3), (3, 0),
+(4, 5), (5, 6), (6, 7), (7, 4),
+(0, 4), (1, 5), (2, 6), (3, 7)
+```
+
+For each edge `(i, j)`, both `(i, j)` and `(j, i)` are added. Duplicate edges are removed.
+
+### `constraint_mask`
+
+`constraint_mask_x` identifies which displacement components in x are constrained.
+
+Shape:
+
+```text
+(N, )
+```
+
+Examples:
+
+```text
+[1] -> fixed in x node
+[0] -> free node
+```
+
+### `constraint_value`
+
+`constraint_value_x` stores the prescribed displacement in x value for constrained components.
+
+Shape:
+
+```text
+(N, )
+```
+
+For a homogeneous fixed boundary condition:
+
+```text
+constraint_value_x[i] = [0]
+```
+
+The `constraint_mask` tells whether a component is constrained.  
+The `constraint_value` tells the imposed value.
+
+### `boundary_id`
+
+`boundary_id` identifies the geometric boundary region associated with each node.
+
+Shape:
+
+```text
+(N,)
+```
+
+It answers:
+
+```text
+Which mesh boundary does this node belong to?
+```
+
+Example:
+
+```text
+boundary_id = 1 -> left beam end
+boundary_id = 2 -> right beam end
+boundary_id = 3 -> loaded surface
+```
+
+The exact meaning depends on the mesh labeling used during data generation.
+
+### `node_type`
+
+`node_type` gives the semantic role of the node in the simulation.
+
+Shape:
+
+```text
+(N,)
+```
+
+Current convention:
+
+```text
+0 = internal node
+1 = Dirichlet boundary node
+2 = Neumann boundary node
+3 = boundary node without explicitly assigned boundary condition
+```
+
+In short:
+
+```text
+boundary_id tells where the node is.
+node_type tells what role the node has.
+```
+
+---
+
+## Configuration: `snapshot`
+
+The `snapshot` configuration stores time-dependent fields.
+
+Each row corresponds to one simulation sample and contains the full temporal evolution of the saved physical quantities.
+
+The dynamic vector fields are stored component-wise. Acceleration is not stored in the current Hugging Face dataset.
+
+| Field | Meaning | Expected shape | Type |
+|---|---|---:|---|
+| `sample_id` | Simulation identifier | scalar | `int32` |
+| `time` | Saved output times | `(T,)` | `float32` |
+| `displacement_x` | x-component of nodal displacement | `(T, N)` | `float32` |
+| `displacement_y` | y-component of nodal displacement | `(T, N)` | `float32` |
+| `displacement_z` | z-component of nodal displacement | `(T, N)` | `float32` |
+| `velocity_x` | x-component of nodal velocity | `(T, N)` | `float32` |
+| `velocity_y` | y-component of nodal velocity | `(T, N)` | `float32` |
+| `velocity_z` | z-component of nodal velocity | `(T, N)` | `float32` |
+| `body_force_x` | x-component of nodal body force | `(T, N)` | `float32` |
+| `body_force_y` | y-component of nodal body force | `(T, N)` | `float32` |
+| `body_force_z` | z-component of nodal body force | `(T, N)` | `float32` |
+| `traction_x` | x-component of nodal surface traction | `(T, N)` | `float32` |
+| `traction_y` | y-component of nodal surface traction | `(T, N)` | `float32` |
+| `traction_z` | z-component of nodal surface traction | `(T, N)` | `float32` |
+
+Where:
+
+```text
+T = number of saved output times
+N = number of mesh nodes
+```
+
+Examples:
+
+```text
+displacement_x[k][i] = x-displacement of node i at time step k
+displacement_y[k][i] = y-displacement of node i at time step k
+velocity_y[k][i]     = y-velocity of node i at time step k
+traction_y[k][i]     = y-component of the surface traction at node i and time step k
+```
+
+To reconstruct a full vector field:
+
+```python
+import numpy as np
+
+u = np.stack(
+    [
+        dyn["displacement_x"],
+        dyn["displacement_y"],
+        dyn["displacement_z"],
+    ],
+    axis=-1,
+)
+
+print(u.shape)
+# (T, N, 3)
+```
+
+The same convention can be used for velocity, body force, and traction.
+
+---
+
+## Configuration: `metadata`
+
+The `metadata` configuration stores scalar simulation parameters and bookkeeping information.
+
+Each row corresponds to one simulation sample.
+
+### Execution and file information
+
+| Field | Meaning |
+|---|---|
+| `sample_id` | Simulation identifier |
+| `valid` | Whether the simulation sample is valid |
+| `sample_name` | Sample folder name |
+| `sample_dir` | Sample directory |
+| `geo_path` | Path to the `.geo` geometry file |
+| `mesh_path` | Path to the mesh file |
+| `result_dir` | Directory containing solver outputs |
+| `mpi_np` | Number of MPI processes used |
+| `solver_executable` | Solver executable path or name |
+| `gmsh_executable` | Gmsh executable path or name |
+| `solution_file_type` | Type of solution file used, for example `.pvtu` |
+| `n_solution_files` | Number of solution files found |
+| `first_solution_file` | First solution file |
+| `last_solution_file` | Last solution file |
+
+### Material parameters
+
+| Field | Meaning |
+|---|---|
+| `E` | Young's modulus |
+| `nu` | Poisson's ratio |
+| `lambda` | First Lamé parameter |
+| `mu` | Second Lamé parameter |
+| `rho` | Density |
+| `c_damp` | Damping coefficient |
+
+### Loading parameters
+
+| Field | Meaning |
+|---|---|
+| `F0` | Nominal force amplitude |
+| `traction_type` | Type of applied surface traction |
+| `spatial_profile` | Spatial profile of the applied traction |
+| `traction_amplitude_y_nominal_uniform` | Nominal uniform traction amplitude in the y direction |
+| `frequency_hz` | Loading frequency, if applicable |
+| `phase` | Loading phase, if applicable |
+| `load_start_time` | Start time of the applied load |
+| `load_end_time` | End time of the applied load |
+| `load_center_x` | Load center coordinate in x |
+| `load_center_y` | Load center coordinate in y |
+| `load_center_z` | Load center coordinate in z |
+| `load_sigma_x` | Load width in x for Gaussian profiles |
+| `load_sigma_y` | Load width in y for Gaussian profiles |
+| `load_sigma_z` | Load width in z for Gaussian profiles |
+| `load_center_x_rel` | Relative load center coordinate in x |
+| `load_center_z_rel` | Relative load center coordinate in z |
+| `load_sigma_x_rel` | Relative Gaussian width in x |
+| `load_sigma_z_rel` | Relative Gaussian width in z |
+| `moving_direction` | Direction of motion for moving loads |
+| `load_velocity` | Physical velocity of the moving load |
+| `load_velocity_rel` | Relative velocity of the moving load |
+| `impact_time` | Central time of the impact or pulse load |
+| `impact_duration` | Duration of the impact or pulse load |
+
+Some parameters may be unused depending on the selected `traction_type`. They are still stored to keep a fixed schema across all samples.
+
+### Geometry and mesh parameters
+
+| Field | Meaning |
+|---|---|
+| `L` | Beam length |
+| `H` | Beam height |
+| `B` | Beam width |
+| `A` | Cross-sectional area |
+| `I` | Second moment of area |
+| `nx` | Nominal number of mesh divisions in x |
+| `ny` | Nominal number of mesh divisions in y |
+| `nz` | Nominal number of mesh divisions in z |
+| `lc` | Nominal mesh size |
+
+### Boundary, time, and storage information
+
+| Field | Meaning |
+|---|---|
+| `dirichlet_boundary_ids` | Boundary IDs with Dirichlet conditions |
+| `neumann_boundary_ids` | Boundary IDs with Neumann conditions |
+| `dt` | Time step size |
+| `t_end` | Final simulation time |
+| `output_dt` | Output time interval |
+| `n_nodes` | Number of nodes read from the output mesh |
+| `n_cells` | Number of cells read from the output mesh |
+| `n_edges` | Number of directed graph edges |
+| `n_saved_times` | Number of saved output times |
+| `snapshot_storage_format` | Storage format used for snapshot fields |
+
+---
+
+## Dataset Creation
+
+### Curation Rationale
+
+The dataset was created to provide simulation data for machine learning models that learn the dynamic response of 3D elastic structures.
+
+The goal is to expose models to different combinations of geometry, material properties, damping, and loading conditions, while keeping a consistent data structure across samples.
+
+### Source Data
+
+The data are fully synthetic. They are generated by numerical finite element simulations of 3D elastic beams.
+
+#### Data Collection and Processing
+
+For each simulation:
+
+1. A set of input parameters is sampled.
+2. A 3D beam mesh is generated or loaded.
+3. The linear elastodynamic problem is solved with `deal.II`.
+4. The mesh and physical fields are exported to `.pvtu` or `.vtu` files.
+5. The exported simulation data are converted into Hugging Face datasets.
+
+The governing equation is the linear elastodynamic equation:
+
+```text
+  c * du/dt - div(sigma(u)) = f
+```
+
+where:
+
+| Symbol | Meaning |
+|---|---|
+| `u(x,t)` | Displacement field |
+| `du/dt` | Velocity field |
+| `rho` | Material density |
+| `c` | Damping coefficient |
+| `f(x,t)` | Body force |
+| `sigma(u)` | Linear elastic stress tensor |
+
+The material is linear, isotropic, and elastic.
+
+The stress tensor is:
+
+```text
+sigma(u) = lambda * tr(epsilon(u)) * I + 2 * mu * epsilon(u)
+```
+
+with:
+
+```text
+epsilon(u) = 0.5 * (grad(u) + grad(u)^T)
+```
+
+The Lamé parameters `lambda` and `mu` are computed from Young's modulus `E` and Poisson's ratio `nu`.
+
+Continuous parameters are sampled using Latin Hypercube Sampling in a normalized space `[0, 1]^d`. Each sampled value is then mapped to its physical range using either a uniform or log-uniform transformation.
+
+#### Who are the source data producers?
+
+The source data are produced automatically by the simulation pipeline. No human-generated text, personal data, or user-generated content is included.
+
+---
+
+## Personal and Sensitive Information
+
+This dataset does not contain personal, sensitive, or private information.
+
+All samples are generated synthetically from numerical simulations.
+
+---
+
+## Bias, Risks, and Limitations
+
+The dataset is limited by the numerical model and simulation setup used to generate it.
+
+Main limitations include:
+
+- the material model is linear elastic and isotropic;
+- the results depend on the mesh resolution;
+- the loading profiles are limited to the implemented traction models;
+- the data are synthetic and may not represent experimental noise or real structural uncertainty;
+- the dataset should not be treated as a certified engineering benchmark;
+- acceleration may be computed by the solver but is not stored in the current Hugging Face dataset.
+
+### Recommendations
+
+Users should verify the assumptions of the dataset before using it for engineering or scientific conclusions.
+
+For machine learning research, users should consider:
+
+- checking the distribution of geometry, material, and loading parameters;
+- normalizing physical quantities before training;
+- validating models on held-out simulations;
+- avoiding extrapolation far outside the sampled parameter ranges;
+- verifying mesh consistency when using graph-based models.
+
+---
+
+## Loading Profiles
+
+Possible values of `traction_type` include:
+
+| `traction_type` | Meaning |
+|---|---|
+| `uniform` | Uniform surface traction |
+| `gaussian_step` | Spatial Gaussian load active over a time window |
+| `gaussian_harmonic` | Spatial Gaussian load with harmonic time dependence |
+| `gaussian_pulse` | Spatial Gaussian load with pulse-like time dependence |
+| `moving_gaussian` | Gaussian load moving along a prescribed direction |
+
+Possible values of `spatial_profile` include:
+
+| `spatial_profile` | Meaning |
+|---|---|
+| `uniform` | No spatial localization |
+| `x` | Gaussian localization along x only |
+| `xz` | Gaussian localization along x and z |
+
+A negative sigma value may be used to disable localization in one direction. For example:
+
+```text
+load_sigma_z < 0
+```
+
+means that the load is uniform along the z direction.
+
+---
+
+## Minimal Usage Example
+
+```python
+from datasets import load_dataset
+import numpy as np
+
+repo_id = "fastcomputing/first_beam3d_test_single_split"
+
+geometry = load_dataset(repo_id, name="geometry", split="total")
+snapshot = load_dataset(repo_id, name="snapshot", split="total")
+metadata = load_dataset(repo_id, name="metadata", split="total")
+
+sample_idx = 0
+
+geom = geometry[sample_idx]
+dyn = snapshot[sample_idx]
+meta = metadata[sample_idx]
+
+points_x = np.asarray(geom["points_x"], dtype=np.float32)
+points_y = np.asarray(geom["points_y"], dtype=np.float32)
+points_z = np.asarray(geom["points_z"], dtype=np.float32)
+cells = np.asarray(geom["cells"], dtype=np.int64)
+edge_index = np.asarray(geom["edge_index"], dtype=np.int64)
+
+u = np.stack(
+    [
+        np.asarray(dyn["displacement_x"], dtype=np.float32),
+        np.asarray(dyn["displacement_y"], dtype=np.float32),
+        np.asarray(dyn["displacement_z"], dtype=np.float32),
+    ],
+    axis=-1,
+)
+
+x = np.stack(
+    [
+        np.asarray(dyn["points_x"], dtype=np.float32),
+        np.asarray(dyn["points_y"], dtype=np.float32),
+        np.asarray(dyn["points_z"], dtype=np.float32),
+    ],
+    axis=-1,
+)
+
+print("points:", points.shape)        # (N, 3)
+print("cells:", cells.shape)          # (C, 8)
+print("edge_index:", edge_index.shape) # (2, E)
+print("u:", u.shape)                  # (T, N, 3)
+print("metadata keys:", meta.keys())
+```
+
+---
+
+## Dataset Card Authors
+
+FAST Computing
+System theme
+TOS
+Privacy
+About
+Careers
+Models