---
license: cc-by-4.0
language:
- en
- zh
task_categories:
- other
size_categories:
- 10K<n<100K
tags:
- agentfem
- soft-robotics
- programmable-matter
- structural-mechanics
- inverse-design
- scientific-machine-learning
pretty_name: AgentFEM Programmable Soft Rods
configs:
- config_name: multizone_v02
  data_files:
  - split: train
    path: multizone-v02/train.jsonl.gz
  - split: validation
    path: multizone-v02/validation.jsonl.gz
  - split: test
    path: multizone-v02/test.jsonl.gz
  - split: zone_ood
    path: multizone-v02/zone_ood.jsonl.gz
- config_name: equilibria
  data_files:
  - split: train
    path: states/train.jsonl.gz
  - split: validation
    path: states/validation.jsonl.gz
  - split: test
    path: states/test.jsonl.gz
  - split: parameter_ood
    path: states/parameter_ood.jsonl.gz
---

# AgentFEM · Programmable Soft Rods

**New: [multi-zone actuation supplement](multizone-v02/README.md)** — 4,080 additional states; 3/6/12 zones, with 8-zone holdout and mesh checks. The original 16,200-state collection remains available as `equilibria`.

**Learn shapes. Distinguish branches. Design actuation.**

![Three families of computed flexible-rod shapes](assets/overview.png)

**216 physical scenarios · 648 equilibrium sweeps · 16,200 states**

Planar flexible rods driven by end loads, three-zone intrinsic curvature, and
microscale forces. Each state contains its centerline, angle and strain fields,
control parameters, local stability, and solver evidence.

[Models & solver](https://huggingface.co/HaomingLuo/AgentFEM-Morph-Rod-Surrogates) ·
[AgentFEM](https://github.com/haoming-luo/agentfem) · [Mechanics & schema](SCHEMA.md)

## What can you study?

- Shape prediction under different actuation mechanisms.
- Multi-solution regression: identical loading can admit straight, up-bent and down-bent states.
- Bounded inverse design of endpoint positions or complete centerlines.
- Resolution sensitivity and local equilibrium stability.

This is the first data release of **AgentFEM Morph Lab**, a project on programmable
flexible structures. The JMPS microforce rod is one featured mechanism, alongside
conventional loading and distributed eigen-curvature actuation.

## Contents

| Collection | Included |
|---|---|
| End-force / end-moment rods | 72 scenarios, 5,400 equilibrium samples |
| Three-zone intrinsic-curvature rods | 72 scenarios, 5,400 equilibrium samples |
| Microforce rods | 72 scenarios, 5,400 samples across up/down/straight branches |
| Paired resolution checks | 216 pairs, 48 vs 96 angle elements |
| Native AgentFEM solids | 3 independent Figure 9 cases, actual downward solutions |
| Reproducibility | Source, tests, schema, numerical reports, hashes |

The 1D corpus is produced by the supplied NumPy/SciPy angle-FE solver. The three
2D checks use native AgentFEM/FEniCSx. Sample frames are not independent scenarios;
reversible sweeps can revisit the same shape.

## Load a sample

```python
from datasets import load_dataset
data = load_dataset("HaomingLuo/AgentFEM-Programmable-Soft-Rods", "equilibria")
sample = data["test"][0]
print(sample["controls"], sample["tip"], sample["stability"])
```

Without the datasets library:

```python
import gzip, json
from huggingface_hub import hf_hub_download
path = hf_hub_download("HaomingLuo/AgentFEM-Programmable-Soft-Rods",
                      "states/test.jsonl.gz", repo_type="dataset")
with gzip.open(path, "rt") as f:
    sample = json.loads(next(f))
```

## Validation

- Axial extension and constant-curvature analytic checks pass.
- Energy gradient and tangent verified by finite differences.
- First continuum bifurcation load: absolute discrepancy **1.09e-8** in dimensionless p.
- Figure 9 independent BVP vs 96-element rod: centerline RMSE below **5.87e-5 L**.
- All 216 resolution pairs: maximum centerline RMSE **1.72e-4 L**.
- Three 2D equivalent-solid vs paper-continuum errors: **0.758%, 0.176%, 0.394% of L**.
- PVD and XDMF both opened and warped in ParaView; all three fields share one geometry.

Full evidence: [validation](reports/validation.json), [generation](reports/generation.json),
[native FE metrics](native_fe/native_fe_metrics.csv), [ParaView checks](native_fe/paraview_checks.json).
These measurements apply to the stated checks, not an accuracy guarantee for arbitrary rods.

## Splits and baselines

126 training / 27 validation / 27 test / 36 stiffness-OOD scenes. All sweeps,
mirrored branches and mesh pairs of a scene stay in the same partition. The test
split was not used for fitting or checkpoint selection; there is no sealed test
or geometry-OOD benchmark in this release.

| Predictor | Supplied branch? | Test centerline RMSE / L |
|---|---:|---:|
| Ordinary MLP | No | 0.27097 |
| Branch-conditioned nearest neighbor | Yes | 0.13899 |
| Branch-conditioned MLP | Yes | 0.00661 |

The ordinary MLP receives ambiguous multi-solution inputs; this is an input
identifiability demonstration, not proof of a superior neural architecture.
The conditioned MLP's mean test endpoint error is **0.00784 L**. Stiffness-OOD
centerline RMSE is **0.00941 L**. See [all baseline results](reports/baselines.json).

## Physical scope

Dimensionless, conservative planar rods; fixed clamp; force control. Stability
labels come from the constrained discrete energy Hessian. Sweeps are quasi-static
equilibria, not physical-time trajectories. The supplied inverse examples use
bounded intrinsic curvature and numerical forward verification. They do not
establish general reachability, snap-through dynamics, contact or robot hardware control.

See [SCHEMA.md](SCHEMA.md) for equations, normalization, sampling, branch semantics,
and the difference between the paper's end force p and effective resultant p+2h.

## 中文

**可编程柔性杆：从形状预测到驱动设计。**

首批包含三类问题：端力／端矩驱动、三段本征曲率驱动，以及 JMPS 论文中的
微结构驱动。216 个独立场景、648 条平衡状态扫描、16,200 个采样状态；另有
216 组网格加密对照和 3 个 AgentFEM 二维实体核验算例。

数据可用于形状预测、多解回归和逆向设计。上下弯分支及同场景的不同路径不跨
训练／测试划分。三段本征曲率是一种理想化驱动模型；当前不含真实跳跃动力学、
接触或硬件实验。二维结果实际求解得到下弯形状，未在绘图时翻转。

下载 `native_fe/paraview/` 后打开 PVD，使用 `U` 做 Warp By Vector；XDMF 的
位移为 P1 插值副本，完整 Q2 系数另存于 `native_fe/scientific/`。

## Reproduce and cite

Version **0.1.0**, seed **20261014**. Install `requirements.txt`, then follow
[SCHEMA.md](SCHEMA.md#reproduction). Native FE additionally requires AgentFEM/FEniCSx.

Data and generated figures: **CC BY 4.0**. Code: **Apache-2.0**. The paper is cited,
not redistributed or relicensed.

Theory reference: Yang Ye, Andrea Piccolroaz, Davide Bigoni,
*Three Homogenization Models for a Nonlinear Heterogeneous Rod with Microscale Dead Loading*,
[DOI: 10.1016/j.jmps.2026.106870](https://doi.org/10.1016/j.jmps.2026.106870).

Please cite **Haoming Luo, AgentFEM Morph Lab: Programmable Soft Rods, v0.1.0 (2026)**,
the dataset URL and revision, and the theory reference when using the microforce cases.