case_id stringlengths 8 15 | split stringclasses 1
value | depth float64 0.02 0.03 | radius float64 0.01 0.02 | waist float64 0.04 0.38 | bow float64 0.01 0.03 | physical_load_N float64 1k 10k | mass_kg float64 1.07 1.53 | seat_deflection_mm_at_10kN float64 0.03 0.16 | training_prefix_index int64 0 127 | mesh_volume_relative_error float64 0 0.01 |
|---|---|---|---|---|---|---|---|---|---|---|
lhs64_38 | train | 0.021823 | 0.015871 | 0.260251 | 0.017256 | 1,000 | 1.211562 | 0.068577 | 0 | 0.003434 |
expand_09 | train | 0.015151 | 0.021777 | 0.095307 | 0.013791 | 10,000 | 1.281669 | 0.049736 | 1 | 0.007603 |
lhs64_27 | train | 0.023295 | 0.012201 | 0.104311 | 0.005224 | 1,000 | 1.21977 | 0.057513 | 2 | 0.008791 |
expand_06 | train | 0.031424 | 0.020319 | 0.254589 | 0.014571 | 10,000 | 1.477032 | 0.036328 | 3 | 0.008359 |
lhs64_10 | train | 0.024371 | 0.01932 | 0.081598 | 0.024122 | 1,000 | 1.416587 | 0.048658 | 4 | 0.008847 |
expand_11 | train | 0.028942 | 0.010141 | 0.269295 | 0.010903 | 10,000 | 1.163315 | 0.080939 | 5 | 0.004819 |
expand_14 | train | 0.016873 | 0.014169 | 0.374447 | 0.02833 | 10,000 | 1.085862 | 0.142929 | 6 | 0.011967 |
expand_15 | train | 0.030913 | 0.015167 | 0.204351 | 0.024441 | 10,000 | 1.338262 | 0.061929 | 7 | 0.006653 |
lhs64_17 | train | 0.022319 | 0.019452 | 0.182847 | 0.006141 | 1,000 | 1.340909 | 0.041687 | 8 | 0.004929 |
expand_01 | train | 0.016192 | 0.016194 | 0.23916 | 0.006908 | 10,000 | 1.16053 | 0.067362 | 9 | 0.008967 |
lhs64_09 | train | 0.018193 | 0.012092 | 0.161141 | 0.015771 | 1,000 | 1.133539 | 0.097611 | 10 | 0.01142 |
lhs64_34 | train | 0.025584 | 0.012446 | 0.117235 | 0.023167 | 1,000 | 1.23534 | 0.082061 | 11 | 0.007214 |
expand_08 | train | 0.029492 | 0.01258 | 0.359085 | 0.018713 | 10,000 | 1.193381 | 0.085677 | 12 | 0.008587 |
lhs64_15 | train | 0.025335 | 0.014944 | 0.315917 | 0.009603 | 1,000 | 1.225441 | 0.059146 | 13 | 0.007546 |
lhs64_22 | train | 0.019313 | 0.017327 | 0.093303 | 0.018821 | 1,000 | 1.27226 | 0.058767 | 14 | 0.006469 |
expand_10 | train | 0.018738 | 0.018502 | 0.314567 | 0.02906 | 10,000 | 1.187575 | 0.088523 | 15 | 0.008455 |
lhs64_21 | train | 0.02698 | 0.013056 | 0.185554 | 0.014497 | 1,000 | 1.256272 | 0.064522 | 16 | 0.011356 |
lhs64_40 | train | 0.020228 | 0.013541 | 0.224083 | 0.02465 | 1,000 | 1.155123 | 0.101568 | 17 | 0.007555 |
lhs64_39 | train | 0.025057 | 0.01832 | 0.133384 | 0.01291 | 1,000 | 1.388605 | 0.042083 | 18 | 0.008038 |
lhs64_37 | train | 0.02073 | 0.013356 | 0.217533 | 0.005421 | 1,000 | 1.173744 | 0.064483 | 19 | 0.007707 |
lhs64_13 | train | 0.027188 | 0.019792 | 0.240301 | 0.008652 | 1,000 | 1.407979 | 0.038146 | 20 | 0.010303 |
lhs64_11 | train | 0.018953 | 0.016649 | 0.353149 | 0.015537 | 1,000 | 1.160217 | 0.077499 | 21 | 0.007552 |
lhs64_32 | train | 0.026018 | 0.018015 | 0.303386 | 0.015983 | 1,000 | 1.306194 | 0.052453 | 22 | 0.010738 |
lhs64_20 | train | 0.025439 | 0.015239 | 0.166663 | 0.006408 | 1,000 | 1.297349 | 0.046984 | 23 | 0.00446 |
expand_00 | train | 0.02162 | 0.022624 | 0.112682 | 0.026169 | 10,000 | 1.413371 | 0.047818 | 24 | 0.004392 |
expand_07 | train | 0.026051 | 0.018752 | 0.181728 | 0.025062 | 10,000 | 1.366958 | 0.053802 | 25 | 0.002849 |
lhs64_44 | train | 0.022514 | 0.012665 | 0.316464 | 0.014998 | 1,000 | 1.148984 | 0.090443 | 26 | 0.012472 |
lhs64_16 | train | 0.018108 | 0.015938 | 0.322086 | 0.022787 | 1,000 | 1.143353 | 0.095066 | 27 | 0.0084 |
lhs64_14 | train | 0.020158 | 0.019234 | 0.251495 | 0.020734 | 1,000 | 1.259876 | 0.061563 | 28 | 0.009844 |
lhs64_24 | train | 0.027859 | 0.016524 | 0.210024 | 0.017566 | 1,000 | 1.337141 | 0.051493 | 29 | 0.005509 |
expand_05 | train | 0.022784 | 0.015675 | 0.141564 | 0.021389 | 10,000 | 1.270124 | 0.065168 | 30 | 0.007423 |
expand_04 | train | 0.027392 | 0.013178 | 0.231311 | 0.02748 | 10,000 | 1.228954 | 0.091092 | 31 | 0.011282 |
lhs64_19 | train | 0.023757 | 0.016068 | 0.234364 | 0.023119 | 1,000 | 1.251972 | 0.070225 | 32 | 0.008455 |
lhs64_43 | train | 0.022759 | 0.014689 | 0.213675 | 0.01094 | 1,000 | 1.228676 | 0.060708 | 33 | 0.008861 |
expand_12 | train | 0.025442 | 0.017574 | 0.102803 | 0.005904 | 10,000 | 1.396803 | 0.038684 | 34 | 0.008052 |
lhs64_06 | train | 0.023389 | 0.014233 | 0.092167 | 0.01033 | 1,000 | 1.275458 | 0.053979 | 35 | 0.008239 |
expand_03 | train | 0.02823 | 0.010754 | 0.286276 | 0.017029 | 10,000 | 1.164263 | 0.096521 | 36 | 0.006407 |
lhs64_04 | train | 0.022071 | 0.019877 | 0.111362 | 0.010229 | 1,000 | 1.388321 | 0.040232 | 37 | 0.0109 |
lhs64_08 | train | 0.021106 | 0.015084 | 0.350269 | 0.020144 | 1,000 | 1.163119 | 0.08878 | 38 | 0.012805 |
lhs64_47 | train | 0.018622 | 0.013416 | 0.141992 | 0.02043 | 1,000 | 1.163305 | 0.090951 | 39 | 0.008033 |
lhs64_36 | train | 0.024457 | 0.012974 | 0.20174 | 0.018337 | 1,000 | 1.203459 | 0.078541 | 40 | 0.003223 |
lhs64_02 | train | 0.019147 | 0.017537 | 0.157722 | 0.016776 | 1,000 | 1.255467 | 0.059513 | 41 | 0.011044 |
lhs64_42 | train | 0.026232 | 0.019528 | 0.126519 | 0.021296 | 1,000 | 1.436252 | 0.044332 | 42 | 0.00847 |
lhs64_33 | train | 0.025756 | 0.013911 | 0.192718 | 0.02475 | 1,000 | 1.245264 | 0.079276 | 43 | 0.009877 |
lhs64_28 | train | 0.021623 | 0.01557 | 0.356178 | 0.013904 | 1,000 | 1.175501 | 0.073687 | 44 | 0.008077 |
lhs64_41 | train | 0.023954 | 0.013172 | 0.176745 | 0.007541 | 1,000 | 1.221989 | 0.058479 | 45 | 0.006198 |
lhs64_29 | train | 0.022559 | 0.012835 | 0.299595 | 0.010754 | 1,000 | 1.155735 | 0.077235 | 46 | 0.008365 |
lhs64_31 | train | 0.021493 | 0.018587 | 0.204465 | 0.019247 | 1,000 | 1.291086 | 0.056207 | 47 | 0.008865 |
lhs64_35 | train | 0.02731 | 0.01231 | 0.295243 | 0.019745 | 1,000 | 1.185547 | 0.08931 | 48 | 0.0057 |
lhs64_26 | train | 0.019443 | 0.015398 | 0.287884 | 0.016533 | 1,000 | 1.162946 | 0.079171 | 49 | 0.004004 |
lhs64_23 | train | 0.026695 | 0.017862 | 0.276013 | 0.012492 | 1,000 | 1.32448 | 0.047217 | 50 | 0.005917 |
expand_13 | train | 0.021245 | 0.014801 | 0.220232 | 0.021682 | 10,000 | 1.197909 | 0.080813 | 51 | 0.008124 |
lhs64_05 | train | 0.026863 | 0.014763 | 0.27159 | 0.00894 | 1,000 | 1.260871 | 0.053827 | 52 | 0.008797 |
lhs64_03 | train | 0.020814 | 0.013706 | 0.266449 | 0.00679 | 1,000 | 1.169584 | 0.067431 | 53 | 0.011115 |
lhs64_25 | train | 0.024222 | 0.016206 | 0.326397 | 0.011921 | 1,000 | 1.227626 | 0.059586 | 54 | 0.00393 |
lhs64_07 | train | 0.023893 | 0.014491 | 0.107814 | 0.006999 | 1,000 | 1.2846 | 0.049682 | 55 | 0.007687 |
lhs64_00 | train | 0.021132 | 0.016798 | 0.343951 | 0.017039 | 1,000 | 1.191589 | 0.071824 | 56 | 0.006768 |
lhs64_12 | train | 0.024574 | 0.017879 | 0.098461 | 0.015111 | 1,000 | 1.389739 | 0.044147 | 57 | 0.011839 |
lhs64_18 | train | 0.023477 | 0.013805 | 0.140664 | 0.009273 | 1,000 | 1.253266 | 0.056785 | 58 | 0.013023 |
lhs64_01 | train | 0.025903 | 0.018187 | 0.147538 | 0.023537 | 1,000 | 1.370999 | 0.052193 | 59 | 0.002576 |
expand_02 | train | 0.02444 | 0.017632 | 0.130737 | 0.007709 | 10,000 | 1.368991 | 0.041474 | 60 | 0.010777 |
lhs64_45 | train | 0.018829 | 0.017076 | 0.340108 | 0.021617 | 1,000 | 1.165611 | 0.084103 | 61 | 0.008171 |
lhs64_46 | train | 0.020515 | 0.015633 | 0.25844 | 0.019447 | 1,000 | 1.193019 | 0.076435 | 62 | 0.007562 |
lhs64_30 | train | 0.026441 | 0.017244 | 0.282732 | 0.013267 | 1,000 | 1.300933 | 0.050643 | 63 | 0.005341 |
fresh_train_000 | train | 0.022352 | 0.014192 | 0.272467 | 0.013266 | 10,000 | 1.193548 | 0.071687 | 64 | 0.012001 |
fresh_train_001 | train | 0.021278 | 0.013437 | 0.100865 | 0.013822 | 10,000 | 1.220007 | 0.067808 | 65 | 0.009122 |
fresh_train_002 | train | 0.026084 | 0.014477 | 0.31634 | 0.009524 | 10,000 | 1.22642 | 0.059669 | 66 | 0.00965 |
fresh_train_003 | train | 0.022919 | 0.021025 | 0.355539 | 0.028854 | 10,000 | 1.273149 | 0.068302 | 67 | 0.008321 |
fresh_train_004 | train | 0.027026 | 0.015999 | 0.123083 | 0.020173 | 10,000 | 1.355602 | 0.053238 | 68 | 0.008175 |
fresh_train_005 | train | 0.030622 | 0.010764 | 0.087771 | 0.022764 | 10,000 | 1.251334 | 0.084517 | 69 | 0.000969 |
fresh_train_006 | train | 0.024095 | 0.022182 | 0.230135 | 0.029704 | 10,000 | 1.391459 | 0.055019 | 70 | 0.01341 |
fresh_train_007 | train | 0.027967 | 0.013605 | 0.191406 | 0.022123 | 10,000 | 1.262247 | 0.071447 | 71 | 0.00319 |
fresh_train_008 | train | 0.018828 | 0.021223 | 0.185934 | 0.005087 | 10,000 | 1.316057 | 0.043411 | 72 | 0.008686 |
fresh_train_009 | train | 0.024408 | 0.013912 | 0.305186 | 0.019808 | 10,000 | 1.192395 | 0.083247 | 73 | 0.010852 |
fresh_train_010 | train | 0.015919 | 0.015093 | 0.331038 | 0.014483 | 10,000 | 1.104517 | 0.094683 | 74 | 0.004411 |
fresh_train_011 | train | 0.025869 | 0.010544 | 0.078516 | 0.023415 | 10,000 | 1.193808 | 0.100237 | 75 | 0.002379 |
fresh_train_012 | train | 0.018542 | 0.021552 | 0.136244 | 0.02463 | 10,000 | 1.31964 | 0.055774 | 76 | 0.007928 |
fresh_train_013 | train | 0.024987 | 0.011608 | 0.07052 | 0.018275 | 10,000 | 1.224131 | 0.078797 | 77 | 0.004437 |
fresh_train_014 | train | 0.025247 | 0.010219 | 0.245242 | 0.018841 | 10,000 | 1.133264 | 0.114178 | 78 | 0.004391 |
fresh_train_015 | train | 0.031573 | 0.017271 | 0.259232 | 0.017747 | 10,000 | 1.381641 | 0.04676 | 79 | 0.004416 |
fresh_train_016 | train | 0.022442 | 0.014876 | 0.366138 | 0.016159 | 10,000 | 1.15758 | 0.080629 | 80 | 0.000275 |
fresh_train_017 | train | 0.031929 | 0.018752 | 0.143865 | 0.00855 | 10,000 | 1.529583 | 0.032337 | 81 | 0.011322 |
fresh_train_018 | train | 0.01745 | 0.016624 | 0.311657 | 0.012048 | 10,000 | 1.154446 | 0.073402 | 82 | 0.005129 |
fresh_train_019 | train | 0.017065 | 0.013829 | 0.050738 | 0.00623 | 10,000 | 1.185475 | 0.06291 | 83 | 0.007731 |
fresh_train_020 | train | 0.016542 | 0.019594 | 0.110813 | 0.012565 | 10,000 | 1.26421 | 0.052194 | 84 | 0.006328 |
fresh_train_021 | train | 0.02552 | 0.020037 | 0.378535 | 0.006615 | 10,000 | 1.305418 | 0.044866 | 85 | 0.007678 |
fresh_train_022 | train | 0.027668 | 0.014409 | 0.3358 | 0.024141 | 10,000 | 1.21731 | 0.082958 | 86 | 0.007642 |
fresh_train_023 | train | 0.020783 | 0.018032 | 0.043208 | 0.02599 | 10,000 | 1.328028 | 0.060017 | 87 | 0.006612 |
fresh_train_024 | train | 0.028647 | 0.020216 | 0.203209 | 0.022975 | 10,000 | 1.448281 | 0.04457 | 88 | 0.008462 |
fresh_train_025 | train | 0.019006 | 0.018704 | 0.323911 | 0.008378 | 10,000 | 1.205388 | 0.057798 | 89 | 0.003185 |
fresh_train_026 | train | 0.023343 | 0.013233 | 0.149763 | 0.014094 | 10,000 | 1.227075 | 0.067937 | 90 | 0.010727 |
fresh_train_027 | train | 0.031236 | 0.020676 | 0.225085 | 0.02867 | 10,000 | 1.47183 | 0.047823 | 91 | 0.002039 |
fresh_train_028 | train | 0.024809 | 0.015422 | 0.298982 | 0.012951 | 10,000 | 1.234607 | 0.061389 | 92 | 0.008573 |
fresh_train_029 | train | 0.023779 | 0.01929 | 0.076609 | 0.010513 | 10,000 | 1.423242 | 0.038126 | 93 | 0.007907 |
fresh_train_030 | train | 0.031125 | 0.021937 | 0.33951 | 0.029531 | 10,000 | 1.428925 | 0.051808 | 94 | 0.009811 |
fresh_train_031 | train | 0.015162 | 0.011294 | 0.231307 | 0.011792 | 10,000 | 1.072732 | 0.116634 | 95 | 0.013265 |
fresh_train_032 | train | 0.018305 | 0.018388 | 0.180724 | 0.025453 | 10,000 | 1.234359 | 0.072355 | 96 | 0.008089 |
fresh_train_033 | train | 0.017765 | 0.020953 | 0.178049 | 0.021567 | 10,000 | 1.273012 | 0.057703 | 97 | 0.003672 |
fresh_train_034 | train | 0.030358 | 0.021604 | 0.293921 | 0.015198 | 10,000 | 1.465597 | 0.036901 | 98 | 0.010071 |
fresh_train_035 | train | 0.026192 | 0.011792 | 0.090686 | 0.010187 | 10,000 | 1.251757 | 0.060311 | 99 | 0.010926 |
From finite elements to physical AI
176 three-dimensional FEM geometries. Real CAD, meshes and displacement fields. An open, reproducible starting point for geometry-conditioned physical learning.
Interactive lab · Trained model · AgentFEM · AgentFEM-Learning
What is inside
A symmetric double-arm support bracket under a uniform downward top-seat load, with fixed foot undersides. Four parameters vary the arm half-width, half-thickness, waist and bow. Material: linear isotropic elasticity, E = 70 GPa, nu = 0.33, density = 2700 kg/m³. Height: 189 mm.
128 training / 16 validation / 32 fresh test geometries. Nested training prefixes: 32, 64, 128. The first 64 training cases reuse the existing campaign; 64 new training cases, 4 new validation cases and 32 fresh test cases were computed for this release.
| Files | Contents |
|---|---|
train.csv, validation.csv, test.csv |
Parameters, loads, mass, top-seat displacement, nested prefix order |
fields-*.zip |
fem/<id>/fields.npz and summary.json |
geometry-*.zip |
Optional STEP solids and Gmsh tetrahedral meshes |
protocol.json |
Frozen split, sampling seeds, bounds and training settings |
reproduce.zip |
Geometry generation, AgentFEM campaign, training and evaluation code |
evaluation.json, learning_curve.csv |
Per-case errors and all three training seeds |
fields.npz: points (N,3) in metres; displacement (N,3) in metres; stress (N,) sampled von Mises stress in Pa; triangles (F,3) surface connectivity indexing points.
Raw fields retain their physical load, either 1000 or 10000 N, recorded in each summary.json.
Multiply displacement/stress by target_load_N / physical_load_N for this linear-elastic problem.
Learning uses a 1000 N reference; the gallery and CSV deflection use 10000 N. Load scaling is not a new independent geometry sample.
Start with NumPy
from huggingface_hub import hf_hub_download
import io, zipfile, numpy as np
archive = hf_hub_download("HaomingLuo/AgentFEM-Bracket-Elasticity", "fields-test-00.zip", repo_type="dataset")
with zipfile.ZipFile(archive) as z:
sample = next(n for n in z.namelist() if n.endswith("fields.npz"))
d = np.load(io.BytesIO(z.read(sample)), allow_pickle=False)
points, displacement = d["points"], d["displacement"]
Learning curves
| Training geometries | GINO field error | GINO + correction | Coordinate MLP |
|---|---|---|---|
| 32 | 30.74% | 7.99% | 6.44% |
| 64 | 30.05% | 5.49% | 4.05% |
| 128 | 24.86% | 3.27% | 2.85% |
Values are mean test surface-node displacement relative L2, averaged over three training seeds. The same 32 fresh test geometries are used in every row; checkpoints are selected on validation only. Full per-case, scalar-deflection and baseline results are included. Whiskers show seed range, not confidence bounds. The inherited 64-case pool mixes inner-domain and wider-domain samples; this is a practical nested expansion, not an iid scaling-law experiment.
Reproduce or extend
Extract reproduce.zip, then extract the field archives into bracket_lab/study_128/.
Install a FEniCSx environment (tested: DOLFINx 0.11.0, Gmsh 4.15.2, Python 3.11),
AgentFEM and AgentFEM-Learning; tested source revisions are listed in environment.json.
Run run_study.py prepare, run_study.py gino, run_study.py correction, then evaluate_study.py.
Missing FEM fields are regenerated from the protocol; existing fields are reused. The example inference in the model repository does not require FEniCSx.
Numerical scope
AgentFEM solves 3D quadratic displacement elements; exported displacement is sampled at linear mesh nodes. Reported learning metrics use all surface nodes, not a volume/energy norm. Top-seat deflection is a nodal mean. Every case is checked for finite fields, fixed-face zero displacement, parameter/load consistency and disconnected IDs. The nominal mesh size is 9 mm; this V1 is not a mesh-converged industrial qualification dataset. Sharp junction stress values are provided as raw FEM outputs, not validated strength labels. No bolt contact, plasticity, fracture or experimental measurements are represented.
Attribution
Data and geometry: CC BY 4.0, Haoming Luo (2026). Code: Apache-2.0. Please cite this repository, its exact revision, AgentFEM, and the relevant model method. GINO: Li et al., NeurIPS 2023. This release is a computational benchmark, not a claim of a new GINO architecture.
- Downloads last month
- 176

