M01 已完成 按用户最新训练范围结项
原14组算子与近百万参数 GNOT 已完成6000步。近百万 GNO 由用户在4852步终止，保留2000和4000步评估；WNO、GAOT均在2000步触发用户指定停止条件。未完成、已停止或不适用的评估栏统一以“-”占位，已取得的结果保留。完成表示本轮任务结项，不表示所有配置均训练到6000步或达到目标精度。
比较口径与不公平项
- 统一算子组与 TS3 MSE、FNO M07 使用同20个纯拉伸TRAIN案例、1,083,269个原TET10节点、50维输入、同normalized MSE、seed与学习率协议；每步累积20例，只在2000/4000/6000步评估。这里是单seed训练集拟合，不能作为泛化结论。
- 参数量不完全相等：原算子组从32,740到7,331,021；表中展示精确参数数及相对981,348参数TS3的倍数。新增四配置约98万至100万参数，仍未配平FLOPs、显存或训练耗时，不宣称等算力比较。
- MGN历史参考采用不同的物理相对平方训练损失，与本轮normalized MSE不同；早期56维输入、容量、密度/曲率监督及历史TS3/FNO实验在下方独立保留，不能与新50维协议合并当作单因素对照。
- 停止配置只参与其已实际完成的共同预算比较；不将4000步结果填入6000步，不将缺失值当零。MGN不补造未核对的四项局部指标。
新增近百万OFormer已完成：991,359参数（TS3的1.0102倍），同协议6000步，actualbest6000，活动用时91.3分钟。恰好6000步 U=1.175%、VM=6.880%；原1,363,588参数OFormer单独保留。宽度109、4层编码器和4层解码器，原forward不变；参数接近不代表算力匹配。补充实验六项曲线与完整预算结果 · CPU导出核对
参数量、实际预算与固定步数物理误差
数值为20例物理相对L2的算术平均；每格依次为 U / VM，越低越好。参数倍数仅供识别容量差异。 参数比≤1.05的配置统一放在上组，>1.05的放在下组，不适用或参数未确定的另列。点击表头2000/4000/6000步可切换预算并保留当前U/VM指标；点击对应列的U或VM可直接选择该步数与指标，再点同一标题切换升降序。本页所有表格均可点击标题排序。默认按6000步VM误差升序，同值按另一项误差排序；缺少所选步数结果的配置始终置于组末。MGN保留不同训练损失的参考标记。
当前排序：6000步 · VM误差升序（低→高）；各参数组分别排序，缺失结果始终放在组末。
| 配置 | 参数量 | 相对TS3参数 | 状态 | / | / | / |
|---|---|---|---|---|---|---|
| 参数比 ≤1.05× | ||||||
| MGN（历史参考） | 985,540 | 1.00× | 6000步；训练损失不同 | 2.531% / 9.234% | 2.276% / 7.418% | 2.084% / 6.652% |
| OFormer_1M | 991,359 | 1.01× | 6000步完成 | 1.624% / 7.783% | 1.383% / 7.264% | 1.175% / 6.880% |
| GNOT_1M | 984,276 | 1.00× | 6000步完成 | 2.562% / 10.074% | 2.480% / 8.585% | 1.958% / 7.605% |
| TS3 | 981,348 | 1.00× | 6000步完成 | 2.175% / 10.180% | 1.748% / 8.257% | 1.500% / 7.669% |
| Transolver | 985,156 | 1.00× | 6000步完成 | 2.253% / 10.113% | 1.896% / 8.505% | 1.585% / 7.706% |
| Transolver++ | 858,188 | 0.87× | 6000步完成 | 2.245% / 11.264% | 1.972% / 9.015% | 1.557% / 7.934% |
| FNO M07 | 981,310 | 1.00× | 6000步完成 | 3.160% / 13.621% | 2.897% / 12.980% | 2.582% / 12.226% |
| TFNO | 514,685 | 0.52× | 6000步完成 | 4.051% / 13.779% | 3.642% / 13.087% | 3.166% / 12.361% |
| GNO | 32,740 | 0.03× | 6000步完成 | 8.569% / 25.465% | 8.466% / 24.771% | 8.301% / 22.873% |
| DEEPONET | 419,332 | 0.43× | 6000步完成 | 7.743% / 26.728% | 6.597% / 25.907% | 5.682% / 22.897% |
| LSM | 937,661 | 0.96× | 6000步完成 | 26.344% / 36.027% | 29.396% / 40.942% | 29.586% / 45.814% |
| GNO_1M | 1,002,885 | 1.02× | 用户在4852步终止 | 3.372% / 14.467% | 3.082% / 13.641% | - |
| WNO_980K | 979,968 | 1.00× | 2000步条件停止 | 5.907% / 18.748% | - | - |
| GAOT_980K | 980,590 | 1.00× | 2000步条件停止 | 4.865% / 21.216% | - | - |
| 参数比 >1.05× | ||||||
| GNOT | 3,877,268 | 3.95× | 6000步完成 | 1.830% / 7.789% | 1.572% / 7.245% | 1.330% / 6.766% |
| OFormer | 1,363,588 | 1.39× | 6000步完成 | 1.594% / 7.842% | 1.396% / 7.229% | 1.171% / 6.816% |
| GINOT | 2,862,917 | 2.92× | 6000步完成 | 5.647% / 9.360% | 3.991% / 8.449% | 3.238% / 7.911% |
| UNO | 7,331,021 | 7.47× | 6000步完成 | 3.298% / 10.365% | 2.962% / 9.880% | 2.588% / 9.407% |
| PCNO | 3,008,996 | 3.07× | 6000步完成 | 5.245% / 10.856% | 4.620% / 10.147% | 4.097% / 9.486% |
| FNOGNO | 1,619,588 | 1.65× | 6000步完成 | 10.370% / 20.546% | 10.071% / 19.504% | 9.466% / 18.481% |
| GINO | 1,616,150 | 1.65× | 6000步完成 | 10.513% / 20.750% | 10.063% / 19.995% | 9.384% / 19.144% |
| ONO | 1,608,452 | 1.64× | 6000步完成 | 107.885% / 84.947% | 105.759% / 87.424% | 106.000% / 83.020% |
| WNO 原配置 | 4,591,485 | 4.68× | 零步失败；以979,968参数配置重跑 | - | - | - |
| GAOT 原配置 | 1,587,806 | 1.62× | 零步失败；以980,590参数配置重跑 | - | - | - |
| 不适用或参数未确定 | ||||||
| GeoFNO | - | - | 原非均匀warp仅支持2D | - | - | - |
| RIGNO | - | - | 原三角形预处理不适用真四面体 | - | - | - |
| CNO | - | - | 原实现仅支持1D/2D | - | - | - |
0095典型算例 · 全部模型预测对比
点击上表模型名称可打开对应预测；也可在下方选择任意模型A/B，显示有限元真值、两组预测及两组绝对误差。25个有结果的模型配置、63个已保存预算快照均可切换；没有输出的配置说明原因。可选位移/VM、2000/4000/6000或最新保存、同步旋转与缩放、网格和原节点。
“最新保存”可能对应不同实际预算；MGN的6000预算导出为best5950，GNO最新4000、WNO/GAOT最新2000，界面均明确标注。只读取现有原节点预测，不新增NN/FE计算。
OFormer近百万补充实验曲线与0095精确6000步空间对照
仅实际2000/4000/6000评估点；原136万配置与近百万配置分开。下图为0095单例，不能替代20例平均，四场使用共同完整色标。
停止依据：WNO在2000步 U=5.907%、VM=18.748%；GAOT U=4.865%、VM=21.216%。两项均严格高于 TS3（2.175% / 10.180%）、GNOT近百万（2.562% / 10.074%）和 MGN（2.531% / 9.234%），因此停止。近百万GNO的4000步 U=3.082%、VM=13.641%，其后由用户明确终止。
全部配置在2000、4000、6000步的六项误差
top5%和top1%集合由真实VM定义；高曲率子集仅依赖几何。峰幅项为各例最大VM的绝对相对偏差均值。所有数值单位为%。
| 配置 | 参数量 | 步数 | U | VM | top5% VM | top1% VM | 高曲率 VM | 平均绝对峰幅偏差 |
|---|---|---|---|---|---|---|---|---|
| Transolver | 985,156 | 2000 | 2.253215 | 10.112773 | 12.688572 | 17.418675 | 10.983571 | 32.206721 |
| Transolver | 985,156 | 4000 | 1.895770 | 8.505164 | 10.945757 | 14.794338 | 9.167808 | 28.406998 |
| Transolver | 985,156 | 6000 | 1.584847 | 7.705983 | 9.927394 | 13.180286 | 8.284557 | 25.140534 |
| Transolver++ | 858,188 | 2000 | 2.245061 | 11.263933 | 13.698181 | 18.494733 | 12.382893 | 32.158480 |
| Transolver++ | 858,188 | 4000 | 1.972300 | 9.014869 | 11.224479 | 14.984764 | 9.733721 | 28.812278 |
| Transolver++ | 858,188 | 6000 | 1.556858 | 7.933768 | 9.925317 | 13.053070 | 8.535498 | 24.270680 |
| TFNO | 514,685 | 2000 | 4.051385 | 13.779340 | 16.773140 | 23.921706 | 15.540834 | 29.933619 |
| TFNO | 514,685 | 4000 | 3.642400 | 13.086687 | 15.934507 | 22.639207 | 14.766339 | 29.010222 |
| TFNO | 514,685 | 6000 | 3.166441 | 12.360863 | 15.134073 | 21.353480 | 13.962864 | 27.811881 |
| UNO | 7,331,021 | 2000 | 3.297897 | 10.364768 | 12.459911 | 17.642508 | 11.365275 | 25.840966 |
| UNO | 7,331,021 | 4000 | 2.961807 | 9.880414 | 12.035455 | 16.974289 | 10.813615 | 25.107120 |
| UNO | 7,331,021 | 6000 | 2.588298 | 9.407197 | 11.680267 | 16.414464 | 10.291711 | 24.218816 |
| DEEPONET | 419,332 | 2000 | 7.742522 | 26.727692 | 38.338828 | 51.051527 | 29.916035 | 52.671631 |
| DEEPONET | 419,332 | 4000 | 6.597211 | 25.907312 | 36.410196 | 48.909193 | 29.015161 | 52.584043 |
| DEEPONET | 419,332 | 6000 | 5.681766 | 22.896707 | 31.072368 | 43.328560 | 26.187498 | 51.652142 |
| GNOT | 3,877,268 | 2000 | 1.830094 | 7.789269 | 10.099407 | 13.746724 | 8.576921 | 25.955820 |
| GNOT | 3,877,268 | 4000 | 1.571676 | 7.245156 | 9.499250 | 12.839963 | 7.968232 | 24.044095 |
| GNOT | 3,877,268 | 6000 | 1.329970 | 6.766447 | 8.934931 | 11.926549 | 7.443516 | 21.522664 |
| ONO | 1,608,452 | 2000 | 107.885011 | 84.947464 | 68.148468 | 73.513189 | 70.135974 | 80.509175 |
| ONO | 1,608,452 | 4000 | 105.758895 | 87.423873 | 67.471675 | 72.613162 | 71.230226 | 80.523833 |
| ONO | 1,608,452 | 6000 | 106.000332 | 83.020009 | 75.330523 | 79.214748 | 74.339926 | 84.657015 |
| GNO | 32,740 | 2000 | 8.568709 | 25.465260 | 36.224314 | 48.842572 | 28.553123 | 52.585024 |
| GNO | 32,740 | 4000 | 8.465960 | 24.771477 | 34.935700 | 47.241846 | 27.659586 | 52.383122 |
| GNO | 32,740 | 6000 | 8.300587 | 22.873242 | 31.653528 | 43.451739 | 25.229379 | 50.119969 |
| GINO | 1,616,150 | 2000 | 10.513400 | 20.749506 | 26.189567 | 36.474527 | 22.650629 | 38.506206 |
| GINO | 1,616,150 | 4000 | 10.062943 | 19.994817 | 25.016727 | 35.009307 | 21.777044 | 36.838684 |
| GINO | 1,616,150 | 6000 | 9.383931 | 19.144157 | 23.654467 | 33.219957 | 20.829347 | 35.018360 |
| FNOGNO | 1,619,588 | 2000 | 10.370207 | 20.545646 | 26.072708 | 36.368133 | 22.482451 | 38.932671 |
| FNOGNO | 1,619,588 | 4000 | 10.070893 | 19.504202 | 24.655720 | 34.626626 | 21.298602 | 36.630601 |
| FNOGNO | 1,619,588 | 6000 | 9.466497 | 18.480548 | 23.139076 | 32.619003 | 20.199805 | 34.223727 |
| GINOT | 2,862,917 | 2000 | 5.647089 | 9.359718 | 10.481947 | 14.003126 | 9.857666 | 19.460540 |
| GINOT | 2,862,917 | 4000 | 3.991072 | 8.449016 | 9.537988 | 12.609242 | 8.846612 | 18.105461 |
| GINOT | 2,862,917 | 6000 | 3.237501 | 7.911358 | 8.898056 | 11.631118 | 8.246836 | 17.193858 |
| PCNO | 3,008,996 | 2000 | 5.244635 | 10.856000 | 13.991442 | 20.302887 | 12.213884 | 32.188283 |
| PCNO | 3,008,996 | 4000 | 4.620453 | 10.147458 | 13.098271 | 18.982704 | 11.372661 | 31.461664 |
| PCNO | 3,008,996 | 6000 | 4.096963 | 9.486052 | 12.211576 | 17.600037 | 10.552432 | 30.107131 |
| LSM | 937,661 | 2000 | 26.343830 | 36.027039 | 35.433234 | 37.925945 | 36.177914 | 24.011988 |
| LSM | 937,661 | 4000 | 29.395598 | 40.941987 | 39.928585 | 41.348090 | 40.811911 | 21.173491 |
| LSM | 937,661 | 6000 | 29.585943 | 45.813670 | 42.234920 | 41.904823 | 44.957636 | 22.731831 |
| OFormer | 1,363,588 | 2000 | 1.594423 | 7.842270 | 9.993770 | 13.222770 | 8.463612 | 22.330079 |
| OFormer | 1,363,588 | 4000 | 1.395789 | 7.228725 | 9.365296 | 12.359392 | 7.836404 | 19.814785 |
| OFormer | 1,363,588 | 6000 | 1.171340 | 6.815726 | 8.931498 | 11.820078 | 7.417905 | 18.434776 |
| TS3 | 981,348 | 2000 | 2.175231 | 10.179617 | 12.373644 | 16.661297 | 11.053000 | 30.810303 |
| TS3 | 981,348 | 4000 | 1.748425 | 8.257339 | 10.338207 | 13.849406 | 8.879978 | 26.721121 |
| TS3 | 981,348 | 6000 | 1.500378 | 7.668623 | 10.022538 | 13.432556 | 8.246307 | 24.474378 |
| FNO M07 | 981,310 | 2000 | 3.160341 | 13.620959 | 16.902367 | 24.445624 | 15.577443 | 30.969424 |
| FNO M07 | 981,310 | 4000 | 2.897250 | 12.979784 | 16.134706 | 23.302489 | 14.852547 | 30.426579 |
| FNO M07 | 981,310 | 6000 | 2.582199 | 12.225843 | 15.200638 | 21.905276 | 13.949414 | 29.833282 |
| GNO_1M | 1,002,885 | 2000 | 3.372378 | 14.467032 | 17.524063 | 25.442580 | 15.843365 | 36.417215 |
| GNO_1M | 1,002,885 | 4000 | 3.081610 | 13.641110 | 16.426381 | 23.861031 | 14.976415 | 35.251745 |
| GNO_1M | 1,002,885 | 6000 | - | - | - | - | - | - |
| GNOT_1M | 984,276 | 2000 | 2.561658 | 10.074070 | 12.107335 | 16.300677 | 11.058107 | 28.740417 |
| GNOT_1M | 984,276 | 4000 | 2.480281 | 8.585128 | 10.710495 | 14.337965 | 9.325466 | 26.497408 |
| GNOT_1M | 984,276 | 6000 | 1.957628 | 7.605477 | 9.841209 | 13.202650 | 8.288318 | 23.831808 |
| WNO_980K | 979,968 | 2000 | 5.907486 | 18.748457 | 24.333096 | 34.898733 | 20.610675 | 37.873663 |
| WNO_980K | 979,968 | 4000 | - | - | - | - | - | - |
| WNO_980K | 979,968 | 6000 | - | - | - | - | - | - |
| GAOT_980K | 980,590 | 2000 | 4.864684 | 21.215522 | 27.956615 | 38.884724 | 23.192787 | 38.108641 |
| GAOT_980K | 980,590 | 4000 | - | - | - | - | - | - |
| GAOT_980K | 980,590 | 6000 | - | - | - | - | - | - |
| OFormer_1M | 991,359 | 2000 | 1.623887 | 7.783354 | 9.934194 | 13.027330 | 8.372222 | 23.295291 |
| OFormer_1M | 991,359 | 4000 | 1.383056 | 7.263629 | 9.383577 | 12.276092 | 7.840163 | 20.586328 |
| OFormer_1M | 991,359 | 6000 | 1.174806 | 6.879593 | 9.062961 | 11.974707 | 7.448397 | 19.030848 |
实际保存步数、actualbest与活动时间
actualbest仅在已完成组的三次规定评估中选择；停止组不补造6000预算best。活动分钟包含训练、评估、保存及其它开销，恢复、排队与墙钟不等同；并行组活动时间有重叠，不能视为独占GPU吞吐。
| 配置 | 保存步数 | actualbest步数 | 活动分钟 | 训练分钟 | 评估分钟 | 保存分钟 |
|---|---|---|---|---|---|---|
| Transolver | 6000 | 6000 | 211.81 | 198.33 | 0.04 | 0.38 |
| Transolver++ | 6000 | 6000 | 263.81 | 246.52 | 0.03 | 0.41 |
| TFNO | 6000 | 6000 | 45.48 | 41.38 | 0.02 | 0.30 |
| UNO | 6000 | 6000 | 130.90 | 118.75 | 0.03 | 2.18 |
| DEEPONET | 6000 | 6000 | 86.87 | 78.69 | 0.02 | 0.19 |
| GNOT | 6000 | 6000 | 403.04 | 367.44 | 0.07 | 1.24 |
| ONO | 6000 | 6000 | 358.36 | 327.67 | 0.08 | 0.47 |
| GNO | 6000 | 6000 | 111.29 | 101.26 | 0.03 | 0.08 |
| GINO | 6000 | 6000 | 105.26 | 95.43 | 0.05 | 0.44 |
| FNOGNO | 6000 | 6000 | 93.65 | 86.37 | 0.03 | 0.49 |
| GINOT | 6000 | 6000 | 134.38 | 125.58 | 0.04 | 0.73 |
| PCNO | 6000 | 6000 | 95.84 | 90.19 | 0.03 | 0.58 |
| LSM | 6000 | 2000 | 77.83 | 72.69 | 0.04 | 0.30 |
| OFormer | 6000 | 6000 | 92.77 | 85.57 | 0.02 | 0.36 |
| TS3 | 6000 | 6000 | 152.25 | - | - | - |
| FNO M07 | 6000 | 6000 | 26.76 | - | - | - |
| GNO_1M | 4852 | - | - | 894.88 | 0.06 | 0.18 |
| GNOT_1M | 6000 | 6000 | 423.82 | 389.95 | 0.08 | 0.88 |
| WNO_980K | 2000 | - | 32.12 | 30.55 | 0.01 | 0.10 |
| GAOT_980K | 2000 | - | 66.28 | 62.95 | 0.01 | 0.21 |
| OFormer_1M | 6000 | 6000 | 91.32 | 83.31 | 0.04 | 0.30 |
原14组完整曲线与GNOT的0095空间对照
0095仅为单例，不能替代20例平均；图为GNOT近百万恰好6000步，全原外表面节点、四场共同完整物理色标，不以actualbest替换。
完整指标与参数 JSON · 固定预算六项误差 CSV · 独立结果页
原零步故障与不适用实现保留原因；没有以2D投影或其他网络替代。原V100全量训练与暂停FP64不计作已完成计算，后续预算记“-”，按本次用户结项指示不作为M01继续进行的前置条件。旧实验数据与离线PDF保留原时间范围。