README.md

---
license: cc-by-4.0
task_categories:
- time-series-forecasting
- feature-extraction
- other
tags:
- finite-element-analysis
- structural-dynamics
- virtual-sensing
- reduced-order-modeling
- out-of-distribution
- agentfem
pretty_name: AgentFEM Structural Dynamics and Virtual Sensing
size_categories:
- n<1K
---

# AgentFEM Structural Dynamics and Virtual Sensing

T4 v1.1 contains **512 complete finite-element trajectories from 128 independent structural configurations**. Each configuration is a damped, aluminum-like plane-stress cantilever with varied geometry, stiffness, density, damping, and load amplitude. Four transient loads probe impulse response, sub-resonant vibration, near-resonant vibration, and swept-frequency response.

> **Version notice.** Release v1.1.0 supersedes v1.0.0. A publication-time model audit found that AgentFEM 0.3.7 reconstructed each component-wise displacement constraint on the parent vector space during implicit dynamics, doubling constrained scalar degrees of freedom at the clamp. All 512 trajectories were regenerated with component-preserving kinematic boundary conditions. The immutable v1.0.0 tag is retained for provenance and must not be used for model training or physical comparison.

The dataset connects two views of the same dynamics: five sparse displacement sensors sampled at every time step and displacement/velocity/acceleration fields saved throughout the structure. It supports virtual sensing, full-field reconstruction, reduced-order dynamics, system identification, neural operators, and tests of whether a learned model remains reliable under unseen excitation patterns or physical parameters.

![T4 v1.1 overview](preview.png)

## Choose your first task

- **Reconstruct a field:** use the five current sensor readings to estimate the current displacement field.
- **Predict a future:** use physical parameters and a load history to roll out the response without current-time measurements.

These are different information budgets. Keep their scores separate. The [released modal neural state-space model](https://huggingface.co/HaomingLuo/AgentFEM-T4-Modal-Neural-State-Space) provides a runnable baseline for the second task.

## Try a response comparison without the full download

Download [compare_excitations.py](compare_excitations.py), then run:

```bash
python -m pip install numpy matplotlib huggingface_hub
python compare_excitations.py
```

The script fetches only the small, revision-pinned v1.1 index, not the 1.12 GiB
field shards. It compares four load histories for configuration 119 and pairs
the two sinusoidal responses across the 16 test configurations. Select another
structure with `--configuration 0`; for offline use, pass `--index index.jsonl`.
The script is Apache-2.0 licensed and uses the existing CC BY 4.0 dataset.

![Peak response comparison for four excitation histories and paired test configurations](excitation-comparison.png)

For configuration 119, the published peak absolute tip displacements are
0.02318 mm (pulse), 0.04167 mm (sub-resonant sine), 0.20543 mm (near-resonant sine),
and 0.11396 mm (chirp). Each comparison holds the structure and traction-amplitude
parameter fixed, but changes the excitation history. These are peaks over the
0.5 s simulation window, **not steady-state frequency-response gains**, a
controlled damping study, or surrogate prediction scores. OOD means the frozen
excitation or parameter regime differs from the training set.

## What is independent

The reported sample count is the number of **complete trajectories**, not the number of time frames. The 128 physical configurations are sampled once, simulated under four excitations, and kept together when forming training, validation, and test sets. Thus fields from the same structure never cross an evaluation boundary.

## Physics and discretization

- linear isotropic elastodynamics under the plane-stress assumption;
- aluminum-like ranges: Young's modulus 60--80 GPa, density 2500--2900 kg/m³, Poisson ratio 0.33;
- length 0.80--1.20 m, height 0.035--0.065 m, target modal damping 0.5--3.0%, traction amplitude 0.5--5.0 kPa;
- 24 × 2 quadrilateral mesh with Q2 displacement interpolation;
- implicit Newmark integration, 0.5 s duration, 0.000125 s step;
- 4,001 sensor states and 201 full-field frames per trajectory;
- AgentFEM `0.3.7` at commit `882de08b9672ec96b6e7a6799bcce1155d8e01f0`, DOLFINx `0.11.0`.

These are bounded synthetic structures rather than measurements of a named commercial alloy or component. Every realized parameter, excitation, sensor coordinate, mesh, and solver setting is stored with the data.

## Leakage-safe evaluation protocol

| Cohort | Configurations | Trajectories | Purpose |
|---|---:|---:|---|
| Train | 96 | 384 | model fitting |
| Validation | 16 | 64 | model selection |
| Test ID | 8 | 32 | unseen in-range structures |
| Test excitation OOD | 4 | 16 | unseen frequency regimes |
| Test parameter OOD | 4 | 16 | physical parameters outside the training box |

The OOD cases are frozen before baseline fitting. `design.json` records the complete design and `index.csv` / `index.jsonl` provide trajectory-level metadata.

## Data layout

Eight HDF5 shards contain 16 configurations each. A trajectory group stores:

| Array | Shape | Meaning |
|---|---:|---|
| `time_s` | 4001 | sensor time grid |
| `force_scale` | 4001 | nondimensional excitation history |
| `sensor_displacement_m` | 4001 × 5 | vertical displacement at five beam stations |
| `fields/time_s` | 201 | full-field time grid |
| `fields/displacement_m` | 201 × 245 × 3 | nodal displacement |
| `fields/velocity_m_per_s` | 201 × 245 × 3 | nodal velocity |
| `fields/acceleration_m_per_s2` | 201 × 245 × 3 | nodal acceleration |

Each trajectory also includes strain and kinetic energy, external work, damping dissipation, and the discrete energy-balance residual. Four representative configurations are additionally supplied as native XDMF/HDF5 histories for ParaView.

## Verification

- all 128 configurations and 512 trajectories completed with finite arrays;
- maximum first-frequency error against the Euler--Bernoulli reference: `0.241%`;
- maximum modal/transient first-frequency difference: `0.313%`;
- maximum discrete energy-balance residual: `0.070%`;
- maximum five-sensor history change after halving the time step: `0.921%` across eight frozen configurations;
- all completeness, split, frequency, energy, and time-refinement gates passed.

The analytical frequency check is an independent low-order reference, not an assertion that beam theory reproduces every two-dimensional effect.

## Reproducible lower baselines

A compact PCA-16 plus ridge package is fitted only on the 96 training configurations. PCA retains `100.000%` of training displacement-field energy. On the full frozen test set:

- sparse sensors → current full field: relative L2 `0.672%`, RMSE `0.0010 mm`;
- autonomous second-order latent rollout: relative L2 `107.827%`, RMSE `0.1620 mm`.

| Test subset | Sensor-to-field relative L2 | Latent rollout relative L2 |
|---|---:|---:|
| ID | 0.354% | 105.460% |
| Excitation OOD | 0.786% | 130.245% |
| Parameter OOD | 0.810% | 108.492% |

The baselines define transparent lower bars; they are not presented as state-of-the-art architectures.

## Minimal loading

```python
from load_t4_structural_dynamics_v1 import trajectory_ids, load_trajectory

ids = trajectory_ids('.')
sample = load_trajectory(ids[0], '.', include_fields=True)
print(sample['record'])
print(sample['arrays']['sensor_displacement_m'].shape)
print(sample['arrays']['displacement_m'].shape)
```

## Scope

T4 v1.1 isolates linear, small-deformation structural dynamics. It does not include plasticity, contact, joints, geometric nonlinearity, damage, sensor noise, or experimental uncertainty. Those effects should be added as separately versioned challenges so that the source of each difficulty remains measurable.

Data are CC BY 4.0. Code in `code/` is Apache-2.0 licensed. The eight formal shards occupy `1.12 GiB`.