STOCHOS DIM-GP: Benchmark Results Across Tabular Learning, Physics Simulation and Optimization

Overview

Engineering teams work with material measurements, design parameters, simulation fields and physical tests. Turning that information into a better design requires several connected steps: predict performance, understand which inputs matter, compare alternatives and choose the next simulation or experiment. The cost of each evaluation limits how many designs a team can explore.

STOCHOS brings probabilistic modeling, sensitivity analysis and Bayesian optimization into one engineering environment. Its DIM-GP model family covers tabular regression and classification, geometry-based field prediction and transient simulation. Predictions include uncertainty estimates that can inform both design assessment and the selection of the next evaluation.

Why we take a workstation-focused approach

STOCHOS supports foundation models and agentic AI workflows within a platform designed for affordable workstation hardware. STOCHOS Flow makes modeling and optimization accessible through visual workflows, connects to existing simulation tools and Python, and supports sharing trained models through prediction applications.

Our focus is the combination: a probabilistic modeling platform that can serve materials, simulation and design teams, incorporate their physical knowledge, and operate within their own computing environment.

Why these benchmarks matter

A benchmark gives competing methods a common problem, evaluation data and scoring rules. We evaluated DIM-GP across fourteen benchmark tasks and studies, covering tabular learning, fluid dynamics, structural mechanics and optimization. The series combines externally scored competitions with evaluations against published baselines and a virtual formulation study. We publish the results with named comparisons, evaluation conditions and computing requirements so customers can assess STOCHOS’s capabilities across a broad range of tasks.

Selected results

The strongest results span several application classes. In the PLAID snapshots of 4 September 2026 (7 September for 2D_profile), DIM-GP ranks first on four of the six boards examined when the standalone reconstructed-solver entry is excluded. This excludes the PhysicsX simulator on Tensile2d [44]. With all entries included, DIM-GP ranks first on three of six boards and second on Tensile2d. The comparison field includes NPco from NP Company and PXTransolver from PhysicsX.

On AhmedML and DrivAerML, DIM-GP has the lowest reported errors among the ten methods listed, including Emmi AI’s AB-UPT [40], across all five AhmedML channels and both DrivAerML surface channels.

On LagrangeBench, DIM-GP improves on the best of three published baselines in 19 of 21 dataset–metric comparisons. The baselines include Google DeepMind’s Graph Network-based Simulator (GNS) [34]. On DeformingPlate, DIM-GP achieves 57% lower RMSE than Google DeepMind’s MeshGraphNets [48] and ranks second among the three methods compared under the canonical protocol (§9).

In our reconstruction of the TabArena-Lite comparison, DIM-GP ranks third among 80 model entries, or sixth among 85 entries including AutoML systems, in an internal comparison using published results (§4). The field includes TabPFN-3 from Prior Labs, acquired by SAP in July 2026. On TALENT-300, it has the lowest average rank in each task type among the four models in our additional comparison. In a virtual concrete-formulation study based on public laboratory data, STOCHOS meets the modeled specification in 149 of 150 runs, compared with 137 for BoTorch’s qNEHVI.

The reported DIM-GP models train in less than one day on a local workstation, using at most one consumer GPU per run and a GPU-memory budget below 8 GB. CPU-only configurations are identified in the benchmark sections.

The scorecard

Bold type highlights DIM-GP results and selected summary findings. Error metrics are lower-is-better unless otherwise stated.

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The scorecard counts each tabular suite once, each PLAID board separately, and the other studies individually. Across its 12 ranked comparisons, DIM-GP outranks 203 competing benchmark entries. Each competing entry counts once per benchmark comparison.

Reference simulationDIM-GP prediction

PLAID positions use the archived 4 September 2026 snapshots, except for 2D_profile, which uses the 7 September snapshot. Automotive results are reported as of 7 September 2026.

Computational requirements

One DrivAerML reference simulation requires approximately 61,000 CPU core-hours according to the dataset’s reported setup (§11). Once reference data are available, a trained surrogate can evaluate additional geometries at substantially lower computational cost. Figure 2 reports the training resources for the automotive comparisons.

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Scope of the comparisons

The comparison includes named research methods and submissions from commercial vendors. On the five PLAID boards with entries from all three, DIM-GP has lower aggregate error than PXTransolver and NPco on VKI-LS59, Hyperelasticity and Tensile2d, and higher error on Rotor37 and 2D_profile. The separate PhysicsX simulator entry is reported in §15 [44].

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1. STOCHOS in the engineering workflow

1.1 What DIM-GP is

DIM-GP stands for Deep Infinite Mixture of Gaussian Processes, the probabilistic model family within STOCHOS. It supports predictions from tables, particle states and unstructured meshes. An engineer can use these models to estimate a material property, predict an aerodynamic field or model a transient response, with uncertainty estimates accompanying the predictions.

The tabular evaluation uses a fixed configuration across the 51 TabArena and 300 TALENT datasets, including validation-based adaptation. Physics evaluations use task-appropriate configurations. The benchmark sections report the results of these configured workflows.

1.2 Incorporating physics into DIM-GP

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DIM-GP can incorporate inexpensive physical priors, post-training conditioning on known relationships, and geometric or physical features that help it learn from engineering data. STOCHOS calculates supported geometric features automatically during mesh processing; engineers can supply application-specific physical priors and constraints. Multi-fidelity modeling also allows lower-cost simulations and higher-fidelity simulations or measurements to contribute to the same modeling workflow.

1.3 From models to engineering decisions

STOCHOS Flow connects data import, model fitting, validation, sensitivity analysis and optimization in a visual workflow. Sensitivity analysis identifies influential inputs; Bayesian optimization uses predictions and uncertainty to propose the next design or experiment. Engineers can connect Ansys Workbench or Python solvers and export prediction applications for colleagues to use. Agentic AI assists with workflow creation and troubleshooting, with local model options available.

The benchmark series evaluates the prediction and optimization methods that support this workflow.

1.4 How the results are evaluated

PLAID provides externally scored evidence. Participants receive test inputs, such as geometries and operating conditions, and submit prediction files while the reference test outputs remain withheld. The platform scores the predictions and uses hidden test subsets to discourage overfitting (PLAID benchmark protocol, §4.3 and Appendix C). This allows STOCHOS to be evaluated without distributing its proprietary implementation.

The automotive and tabular sections compare our evaluations with published reference results; §4.2 explains the submission requirements behind the internal TabArena comparison. The formulation study uses a virtual test bench based on public laboratory data. Each section identifies its comparison field, metrics and evaluation conditions.

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2. Tabular benchmarks and evaluation protocol

Hardware. The experiments used an Intel Core i9-13900KS workstation (24 cores, 32 threads), 64 GB of DDR5-4200 memory and NVIDIA GeForce RTX 4090 graphics under Windows 11 Pro. The workstation contains two cards, used for separate experiments; each DIM-GP run uses at most one GPU, with GPU memory below 8 GB. Published baseline timings identify their own hardware.

Our TabArena comparison uses fold 0 under the official TabArena-Lite protocol and the corresponding published Lite results. TALENT uses its fixed splits.

2.0 Definitions

Let be the set of methods, the set of datasets, and the error of method on dataset under that dataset’s own metric — one minus ROC-AUC on the 30 binary sets, log-loss on the 8 multiclass sets, RMSE on the 13 regression sets. Lower is better throughout. Because these three quantities share no scale, no statistic below averages across datasets directly.

Elo. TabArena fits a Bradley–Terry model [29] to pairwise wins across datasets. The model assigns method a probability of beating method :

Reported Elo is the median over 200 task-level bootstrap rounds, with confidence bounds at the 2.5% and 97.5% quantiles. Elo reflects who wins; normalized error also reflects the size of error differences. Section 4.2 reports both, together with mean rank.

Normalized error. Per dataset, the error is rescaled against the best and the median method on that dataset, then clipped:

Here, denotes the best observed method and the median or a worse result. Clipping limits the influence of a single unusually large error on the aggregate.

Headroom (§2.1) measures how much a dataset separates methods at all, using the same two quantities as that denominator:

means the median error approaches the best observed error. Larger values indicate greater separation between the best and median.

Cost. Training and inference costs normalize the complete fit and prediction pass by the number of rows, then take the median across datasets:

These measures include fixed per-dataset overhead. Section 4.5 estimates fixed and per-row contributions with a robust Theil–Sen fit [30], .

2.1 What is in TabArena-51

TabArena contains 51 curated real-world datasets [1], checked for leakage, duplication and mislabelled task types. Each dataset has a fixed evaluation metric (Figure 4).

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The suite spans 748 to 150,000 rows and 4 to 1,776 features. Binary classification accounts for 30 of the 51 datasets and uses ROC-AUC, a measure of predicted ordering.

Where the data comes from, and how hard it is

TabArena covers commercial and scientific applications; business, marketing and finance account for nearly half the datasets. Figure 5 and the table below summarize their domains and the median-to-best error gaps defined in §2.0.

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The suite includes imbalanced industrial and credit tasks, as well as categorical inputs. These characteristics make the stated metric and consistent preprocessing important to the comparison.

2.2 What is in TALENT-300

TALENT provides 300 datasets [2]: 119 regression, 101 binary and 80 multiclass, spanning 252 to 634,460 rows (median 3,389) and 3 to 970 features (median 16), across 15 application domains — finance and economics (53 datasets), healthcare (31), image and signal (28), industrial and sensors (27), biology and genomics (21), and others.

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TabArena emphasizes curated comparisons against an actively maintained field. TALENT extends the evaluation across more datasets and application domains.

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3. Tabular model families and competitive context

3.1 The three families in the field

The comparison includes three established families: gradient-boosted trees, neural networks trained per dataset and pretrained tabular models.

Gradient-boosted decision trees — LightGBM [18], CatBoost [19] and XGBoost [20] — are widely used tabular methods that fit per dataset and support CPU execution. The comparison includes both default and tuned configurations.

Neural networks for tabular data include RealMLP [21], TabM [22], ModernNCA [23] and xRFM [24]. RealMLP uses defaults developed across multiple datasets and is the highest-ranked non-pretrained entry in this comparison, at tenth place.

Tabular foundation models learn across tasks before adapting to a new dataset. The field includes TabPFN [5, 6] and its variants, TabICL [7], TabFM [3], EXAONE-Tabular [4], TabDPT [9], LimiX [8], Mitra [10] and other published models [11–17]. TabFM and EXAONE-Tabular lead the TabArena comparison presented here.

3.2 Parameter counts and interpretation

The released configurations illustrate the range of model sizes: TabFM [3] contains 1,639,444,298 parameters (1.64 billion) and EXAONE-Tabular [4] contains 20,807,434. Their TabArena-Lite Elo ratings in this comparison are 1793 and 1749, respectively.

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4. TabArena-51

DIM-GP ranks third among 80 model entries by Elo, mean rank and normalized error in our internal reconstruction of TabArena-Lite. Including AutoML systems places it sixth among 85 entries. The following sections describe the scoring check, comparison field and computational cost.

Hover for each entry's score and training time. The amber point is DIM-GP in the internal comparison of §4; hardware differences are discussed in §4.5.

4.1 Scoring validation

Our comparison was rebuilt from TabArena’s published per-method results and compared against the official splits_lite CSVs:

The selected reference ratings are reproduced within 4.9 Elo points. The official comparison data were obtained from the leaderboard Space’s published results.

4.2 Standing — internal

Comparison status. TabArena’s submission protocol requires executable training and evaluation code integrated into its benchmark. STOCHOS is licensed commercial software and was not provided through that integration route. Its results are therefore reported as an internal comparison with TabArena’s published results.

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Selected positions from the models field (AutoML systems excluded):

All entries are (default) configurations unless marked (t+e) = tuned + ensembled. Rows 1–7 are foundation models, 10 a neural network, 16 tree-based.

With systems included, DIM-GP is 6th of 85 at 1647, just above AutoGluon 1.5 extreme (1646) and TabPFN-3 (1639); AutoGluon 1.6 (1757/1831) and TabFM+ (1836) rank above.

Agreement across ranking measures

Mean rank averages each method’s position across datasets; normalized error also reflects the size of error differences (§2.0). Both give DIM-GP the same placement as Elo:

DIM-GP is third under all three measures, with the same ordering of the top nine entries. The margin to TabPFN-3 is small: approximately eight Elo points and normalized errors of 0.3902 versus 0.3909. The paired analysis below assesses the differences across datasets.

Split by task type, the picture matches §4.3:

Against TabPFN-3, DIM-GP has lower normalized error on classification (0.4234 versus 0.4334) and higher error on regression. TabArena contains 13 regression datasets; the complementary TALENT comparison covers 116 (§5.2).

Statistical comparisons

The paired analysis compares methods on the same 51 datasets using a Wilcoxon signed-rank test [31] on normalized-error differences and an exact sign test on wins and losses. Negative differences favour DIM-GP.

A Friedman test over thirteen leading methods rejects equal performance ( , ). The Nemenyi post-hoc comparison [32] uses a critical distance of 2.56 average-rank points at (Figure 9).

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Within this thirteen-method comparison, DIM-GP’s average rank is 5.16 and only TabFM is significantly ahead of DIM-GP under the Nemenyi analysis. RealMLP, TabDPT-Turbo, LimiX and both tuned tree ensembles are significantly behind. Neither paired test detects a significant difference between DIM-GP and TabPFN-3.

Pairwise p-values are unadjusted across the eight comparisons; the Nemenyi procedure controls its thirteen-method comparison. EXAONE-Tabular differs under the unadjusted Wilcoxon test but falls within the Nemenyi critical distance. The paired table and model-only aggregate table use different normalization pools, so their mean-error differences are computed separately.

4.3 Per-axis reading

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Selected task-wise comparisons against TabPFN-3:

DIM-GP has higher Elo on four of the six reported axes and lower Elo on regression and medium-sized datasets in these descriptive subgroup comparisons.

4.4 Which field DIM-GP is compared in

TabArena distinguishes individual models from AutoML systems that manage model selection and training budgets. The evaluated DIM-GP configuration is fixed across datasets. Section 4.2 reports its placement in both comparison fields.

4.5 Computational cost and hardware

Using TabArena’s cost definition (§2.0), DIM-GP records median times of 30.26 seconds per 1,000 training rows and 2.509 seconds per 1,000 prediction rows on the RTX 4090 (51 datasets, fold 0), placing 32nd of 80 by reported fit cost. The robust timing fit separates fixed per-dataset and per-row contributions:

These fits describe complete training or conditioning procedures. Baseline timings come from the published leaderboard; DIM-GP timings are measured on our RTX 4090.

Hardware sensitivity. The official benchmark records H200 timings for TabPFN-3, TabICLv2, TabPFN-2.6 and LimiX; RTX PRO 6000 timings for TabFM and TabDPT-Turbo; and A100 timings for TabPFN-Wide. To examine the effect of hardware, we ran TabICLv2 through the official harness on our RTX 4090, using the same data splits, preprocessing and eight-fold bagging configuration:

The RTX 4090-to-H200 fit-time ratio ranges from 0.99 to 2.78 across these datasets, showing that hardware effects depend on the workload.

Applying the fitted size-dependent factor to DIM-GP gives an illustrative H200-equivalent estimate of 21.02 s/1K, versus 30.26 s/1K measured on our RTX 4090. This is not a measured DIM-GP H200 run; transferring a calibration from another model adds uncertainty.

The official entries use eight-fold bagging, while DIM-GP uses a single fit. The cost comparison reports these configurations on the shared tasks and split.

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Full TabArena-51 board, 80 entries (click to expand; every column sorts; ¹ DIM-GP times are our own measurement on an RTX 4090, section 4.5)

#	model	Type	Elo	fit s/1k	infer s/1k	Class.	Regr.	Binary	Multi.	Small	Medium
1	TabFM (default)	Foundation Model	1793.0	40.79	6.991	1752.0	2168.0	1780.0	1699.0	1785.0	1911.0
2	EXAONE-Tabular (default)	Foundation Model	1749.0	6.17	0.623	1747.0	1919.0	1756.0	1752.0	1698.0	2021.0
3	DIM-GP	Foundation Model	1651.5	30.26¹	2.509¹	1635.4	1860.9	1654.0	1606.1	1649.0	1751.0
4	TabPFN-3 (default)	Foundation Model	1644.0	3.59	0.395	1617.0	1897.0	1634.0	1594.0	1624.0	1789.0
5	TabPFN-2.6 (default)	Foundation Model	1613.0	5.75	0.6	1590.0	1847.0	1585.0	1645.0	1596.0	1747.0
6	RealTabPFN-2.5 (tuned + ensembled)	Foundation Model	1600.0	2059.94	9.785	1573.0	1849.0	1547.0	1745.0	1595.0	1700.0
7	TabICLv2 (default)	Foundation Model	1555.0	1.96	0.146	1554.0	1696.0	1573.0	1520.0	1536.0	1691.0
8	RealTabPFN-2.5 (tuned)	Foundation Model	1547.0	2059.94	1.03	1535.0	1727.0	1516.0	1661.0	1538.0	1654.0
9	RealTabPFN-2.5 (default)	Foundation Model	1523.0	5.72	0.611	1531.0	1626.0	1536.0	1542.0	1562.0	1513.0
10	RealMLP (tuned + ensembled)	Neural Network	1490.0	2791.97	13.886	1475.0	1666.0	1489.0	1451.0	1476.0	1608.0
11	TabDPT (tuned + ensembled)	Foundation Model	1423.0	6155.04	386.158	1367.0	1786.0	1369.0	1388.0	1433.0	1459.0
12	RealMLP (tuned)	Neural Network	1416.0	2791.97	0.373	1409.0	1539.0	1418.0	1404.0	1407.0	1510.0
13	TabDPT-Turbo (default)	Foundation Model	1413.0	2.02	0.183	1383.0	1638.0	1392.0	1377.0	1416.0	1468.0
14	TabM (tuned + ensembled)	Neural Network	1401.0	2462.02	1.988	1404.0	1491.0	1408.0	1414.0	1373.0	1547.0
15	LightGBM (tuned + ensembled)	Tree-based	1396.0	416.63	2.236	1381.0	1542.0	1376.0	1433.0	1359.0	1570.0
16	CatBoost (tuned)	Tree-based	1391.0	1347.32	0.037	1388.0	1494.0	1378.0	1457.0	1354.0	1561.0
17	iLTM (tuned + ensembled)	Foundation Model	1389.0	12741.09	397.882	1388.0	1481.0	1408.0	1337.0	1363.0	1524.0
18	CatBoost (tuned + ensembled)	Tree-based	1388.0	1347.32	0.364	1381.0	1505.0	1370.0	1457.0	1349.0	1570.0
19	TabDPT (tuned)	Foundation Model	1377.0	6155.04	39.452	1321.0	1731.0	1329.0	1317.0	1391.0	1400.0
20	ChimeraBoost (tuned + ensembled)	Tree-based	1367.0	518.46	0.522	1370.0	1440.0	1394.0	1308.0	1304.0	1630.0
21	ModernNCA (tuned + ensembled)	Neural Network	1365.0	4618.5	7.735	1334.0	1582.0	1341.0	1335.0	1297.0	1649.0
22	TabM (tuned)	Neural Network	1364.0	2462.02	0.231	1365.0	1448.0	1361.0	1409.0	1343.0	1482.0
23	LimiX (default)	Foundation Model	1356.0	27.33	6.11	1393.0	1314.0	1375.0	1503.0	1400.0	1289.0
24	XGBoost (tuned + ensembled)	Tree-based	1355.0	700.96	1.438	1359.0	1417.0	1362.0	1372.0	1312.0	1539.0
25	ChimeraBoost (tuned)	Tree-based	1344.0	518.46	0.045	1361.0	1363.0	1381.0	1311.0	1286.0	1579.0
26	LightGBM (tuned)	Tree-based	1341.0	416.63	0.381	1332.0	1451.0	1316.0	1426.0	1300.0	1518.0
27	CatBoost (default)	Tree-based	1340.0	5.81	0.025	1348.0	1390.0	1370.0	1291.0	1296.0	1525.0
28	ModernNCA (tuned)	Neural Network	1337.0	4618.5	0.47	1349.0	1376.0	1363.0	1321.0	1288.0	1540.0
29	XGBoost (tuned)	Tree-based	1332.0	700.96	0.213	1330.0	1414.0	1328.0	1368.0	1296.0	1491.0
30	TabSwift (default)	Foundation Model	1332.0	1.19	0.07	1319.0	1474.0	1354.0	1205.0	1338.0	1371.0
31	xRFM (tuned + ensembled)	Other	1328.0	866.12	2.007	1304.0	1495.0	1296.0	1363.0	1315.0	1414.0
32	TabPFNv2 (tuned + ensembled) [35.29% IMPUTED]	Foundation Model	1312.0	2943.39	17.365	–	–	–	–	–	–
33	iLTM (tuned)	Foundation Model	1294.0	12741.09	60.101	1300.0	1339.0	1313.0	1269.0	1278.0	1386.0
34	Mitra (default) [35.29% IMPUTED]	Foundation Model	1292.0	87.36	2.432	–	–	–	–	–	–
35	ChimeraBoost (default)	Tree-based	1285.0	2.54	0.05	1302.0	1293.0	1319.0	1261.0	1223.0	1518.0
36	xRFM (tuned)	Other	1282.0	866.12	0.097	1258.0	1444.0	1257.0	1284.0	1264.0	1381.0
37	TabDPT (default)	Foundation Model	1278.0	45.42	39.405	1214.0	1620.0	1221.0	1202.0	1295.0	1274.0
38	TabM (default)	Neural Network	1274.0	7.81	0.237	1288.0	1287.0	1290.0	1305.0	1266.0	1340.0
39	TabICL (default) [29.41% IMPUTED]	Foundation Model	1273.0	6.86	1.52	–	–	–	–	–	–
40	EBM (tuned + ensembled)	Tree-based	1255.0	1877.68	0.14	1299.0	1168.0	1301.0	1316.0	1252.0	1310.0
41	TabPFNv2 (tuned) [35.29% IMPUTED]	Foundation Model	1252.0	2943.39	0.262	–	–	–	–	–	–
42	TorchMLP (tuned + ensembled)	Neural Network	1250.0	2832.93	1.801	1266.0	1253.0	1275.0	1250.0	1230.0	1343.0
43	RealMLP (default)	Neural Network	1243.0	10.44	1.714	1257.0	1253.0	1293.0	1130.0	1246.0	1272.0
44	SAP-RPT-OSS (default)	Foundation Model	1239.0	13.96	2.081	1249.0	1272.0	1239.0	1310.0	1278.0	1163.0
45	BetaTabPFN (default) [25.49% IMPUTED]	Foundation Model	1236.0	203.0	1.155	–	–	–	–	–	–
46	TabPFNv2 (default) [35.29% IMPUTED]	Foundation Model	1221.0	3.27	0.315	–	–	–	–	–	–
47	ModernNCA (default)	Neural Network	1217.0	13.74	0.316	1180.0	1398.0	1201.0	1111.0	1206.0	1276.0
48	EBM (tuned)	Tree-based	1207.0	1877.68	0.014	1245.0	1122.0	1248.0	1253.0	1217.0	1214.0
49	ExtraTrees (tuned + ensembled)	Tree-based	1197.0	257.64	0.846	1191.0	1253.0	1167.0	1304.0	1195.0	1225.0
50	EBM (default)	Tree-based	1188.0	6.9	0.015	1242.0	1024.0	1250.0	1230.0	1194.0	1201.0
51	TorchMLP (tuned)	Neural Network	1187.0	2832.93	0.112	1199.0	1204.0	1200.0	1214.0	1181.0	1232.0
52	XGBoost (default)	Tree-based	1184.0	2.06	0.122	1200.0	1167.0	1204.0	1204.0	1128.0	1370.0
53	FastaiMLP (tuned + ensembled)	Neural Network	1169.0	594.95	4.649	1210.0	1048.0	1215.0	1207.0	1179.0	1170.0
54	ExtraTrees (tuned)	Tree-based	1168.0	257.64	0.068	1159.0	1225.0	1144.0	1234.0	1169.0	1178.0
55	Nori-30M (default) [74.51% IMPUTED]	Foundation Model	1164.0	0.53	0.077	–	–	–	–	–	–
56	RandomForest (tuned + ensembled)	Tree-based	1161.0	377.14	0.747	1167.0	1158.0	1140.0	1288.0	1141.0	1238.0
57	Nori (default) [74.51% IMPUTED]	Foundation Model	1156.0	0.53	0.077	–	–	–	–	–	–
58	LightGBM (default)	Tree-based	1154.0	2.2	0.171	1150.0	1200.0	1141.0	1201.0	1134.0	1228.0
59	RandomForest (tuned)	Tree-based	1124.0	377.14	0.091	1130.0	1117.0	1109.0	1224.0	1098.0	1206.0
60	FastaiMLP (tuned)	Neural Network	1104.0	594.95	0.336	1134.0	1014.0	1143.0	1109.0	1127.0	1053.0
61	PerpetualBooster (tuned + ensembled)	Tree-based	1082.0	176.26	0.499	1060.0	1177.0	1106.0	817.0	1091.0	1060.0
62	iLTM (default)	Foundation Model	1080.0	301.0	65.827	1135.0	860.0	1163.0	1019.0	1058.0	1156.0
63	TabSTAR (tuned)	Foundation Model	1075.0	39935.25	4.288	1115.0	939.0	1143.0	1000.0	1115.0	958.0
64	TabSTAR (tuned + ensembled)	Foundation Model	1072.0	39935.25	20.166	1105.0	976.0	1133.0	988.0	1114.0	950.0
65	OrionMSP (default) [25.49% IMPUTED]	Foundation Model	1050.0	12.4	2.558	–	–	–	–	–	–
66	TorchMLP (default)	Neural Network	1040.0	8.96	0.129	1045.0	1024.0	1052.0	1019.0	1023.0	1087.0
67	PerpetualBooster (tuned)	Tree-based	1036.0	176.26	0.191	1009.0	1133.0	1057.0	740.0	1049.0	998.0
68	xRFM (default)	Other	1030.0	3.14	0.741	978.0	1203.0	939.0	1111.0	1043.0	1006.0
69	ExtraTrees (default)	Tree-based	1007.0	1.97	0.251	987.0	1074.0	997.0	942.0	1036.0	929.0
70	RandomForest (default)	Tree-based	1000.0	0.43	0.053	1000.0	1000.0	1000.0	1000.0	1000.0	1000.0
71	TabFlex (default) [25.49% IMPUTED]	Foundation Model	982.0	0.8	0.119	–	–	–	–	–	–
72	FastaiMLP (default)	Neural Network	979.0	3.12	0.312	1003.0	881.0	1021.0	926.0	988.0	962.0
73	TabSTAR (default)	Foundation Model	976.0	398.79	4.645	1018.0	789.0	1059.0	808.0	1019.0	827.0
74	KNN (tuned + ensembled)	Baseline	970.0	129.17	1.627	1000.0	854.0	995.0	1021.0	968.0	972.0
75	PerpetualBooster (default)	Tree-based	940.0	22.76	0.025	933.0	952.0	978.0	672.0	962.0	876.0
76	Linear (tuned + ensembled)	Baseline	903.0	240.78	0.308	968.0	468.0	981.0	912.0	899.0	907.0
77	Linear (tuned)	Baseline	880.0	240.78	0.068	946.0	409.0	958.0	890.0	880.0	871.0
78	KNN (tuned)	Baseline	822.0	129.17	0.103	842.0	722.0	846.0	805.0	820.0	807.0
79	Linear (default)	Baseline	821.0	1.23	0.115	887.0	271.0	919.0	718.0	837.0	757.0
80	KNN (default)	Baseline	606.0	0.19	0.037	566.0	625.0	612.0	214.0	623.0	559.0

5. TALENT-300

We compare DIM-GP with TALENT’s published methods and with three additional tabular foundation models evaluated in our own runs.

5.1 Comparison with TALENT’s published methods

TALENT publishes results for 28 regression methods and 31 classification methods, including XGBoost, CatBoost, LightGBM, TabPFN, TabR, ModernNCA and RealMLP.

DIM-GP has the lowest average rank in each task type within this published comparison field.

5.2 Additional foundation-model comparison

Our additional comparison evaluates TabPFN-3, TabICLv2 and LimiX on the TALENT datasets. Average ranks use the common set completed by all four methods, with lower values indicating better performance:

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DIM-GP has the lowest average rank in all three task types. Section 5.3 reports completion counts for these models and for Mitra, which was excluded from the rank comparison because of its lower completion rate.

5.3 Running on one consumer GPU

The comparison uses one RTX 4090 with 24 GB of physical memory. DIM-GP’s allocation is limited to less than 8 GB. Completion counts for the tested implementations and settings are:

DIM-GP completed all 300 datasets with GPU memory below 8 GB. The baseline evaluation allows caps on the in-context sample count and ensemble size to manage resource use. The accuracy comparison in §5.2 uses the common completed datasets under those settings.

5.4 How to read these two tables

The DIM-GP and additional foundation-model evaluations use a single seed and fixed splits; TALENT’s published tables average multiple seeds. Classification is scored by accuracy, including threshold selection for binary tasks; TabPFN-3’s reported TALENT result uses AUC. Average ranks and win counts permit comparison across datasets with different target scales.

6. Beyond tabular data: physics surrogates

The physics evaluation covers particle dynamics, contact and large deformation, aerodynamic fields and transient structural response.

6.1 What is being evaluated

Two members of the STOCHOS model family are evaluated:

• DIM-GP Particle — predicts the evolution of particle and mesh-node states (§§7–9).
• DIM-GP — the surrogate for fields on unstructured meshes, evaluated in §§10–17.

6.2 Why these particular benchmarks

The benchmarks cover the following physical regimes and comparison fields:

PLAID sections report the archived board state of 4 September 2026, except for 2D_profile, which uses the 7 September snapshot. Submissions from commercial vendors are identified by their entry names, so each comparison refers to a specific submission in that snapshot.

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7. LagrangeBench — verified against the benchmark’s own evaluator

LagrangeBench [33] is a Lagrangian-simulation benchmark: seven SPH datasets (2D and 3D Taylor–Green vortex, reverse Poiseuille flow, lid-driven cavity, and 2D dam break), a fixed protocol, and published baselines. It supports comparison across three published methods: GNS [34], SEGNN [35] and CoRGI [36] all publish numbers on the same cells under the same rules.

7.1 Protocol

Scoring follows the benchmark exactly: 26-frame windows made of 6 seed frames and 20 predicted steps, with RPF-2D scored over 384 and RPF-3D over 192 test windows. Three metrics per dataset — MSE20 (position error over the 20 predicted steps, per dimension), Sinkhorn (a distributional divergence, blind to particle identity) and Ekin (squared error of total kinetic energy).

7.2 Result — lower error in 19 of 21 comparisons

Each DIM-GP result is compared with the lowest published error for that dataset and metric across GNS, SEGNN and CoRGI.

Compared with each method individually, DIM-GP has lower error than GNS on all 21 cells, lower error than SEGNN on 20 with one parity, and lower error than CoRGI on 19.

DIM-GP has the lowest error on all three metrics for DAM-2D, LDC-2D, TGV-2D, LDC-3D and TGV-3D.

Under the Neural-SPH 400-step protocol [37] on DAM-2D, evaluated over all 25 trajectories, the corresponding values are 3.12e-2 / 4.90e-4 / 1.99e-4 against a published best of 8.4e-2 / 7.5e-3 / 2.1e-3, a factor of 2.7 / 15 / 10.6. Since the 20-step protocol is comparatively short, this establishes that the margin persists at twenty times the horizon.

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7.3 The remaining two comparisons

RPF-3D Ekin — parity. DIM-GP records 1.263e-6 against SEGNN’s 1.34e-6 and is reported as parity.

RPF-2D Ekin — higher error than CoRGI. DIM-GP has 3.9-fold lower error than GNS and 2.5-fold lower error than SEGNN on this cell, while CoRGI reports the lowest error.

7.4 Cost

Each reported model was trained on a single RTX 4090, at roughly 20–90 seconds per epoch depending on dataset and resolution.

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8. DeepMind Water-3D — measured against the published GNS result

Water-3D is the 3D fluid dataset from Learning to Simulate Complex Physics with Graph Networks [34]: approximately 14,000 particles over 800 timesteps. It tests prediction over a much longer rollout than the 20-step LagrangeBench evaluation.

8.1 Result

Scored under the paper’s own protocol — 100 test sequences, full 800-step rollouts, seed frames excluded:

The accuracy setting has a mean rollout MSE 8.5% above the published GNS value, with approximately one tenth as many gradient updates. The update count describes the training schedule; wall-clock time also depends on the cost of each update.

The second setting improves the physical diagnostics, reaching 90% of reference fluid-column thickness and 106% of characteristic speed, compared with 82% and 87% for the accuracy setting. The two configurations illustrate the choice between minimizing position error and preserving bulk fluid behaviour.

8.2 Comparison scope

The comparison uses the published GNS result on Water-3D under the full 800-step protocol. LagrangeBench reports a different quantity, MSE over 20 predicted steps, while NeuralMPM [38] reports full-rollout results on 2D fluid datasets. Those results belong to their respective datasets and protocols and are evaluated separately from Water-3D.

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9. DeepMind DeformingPlate — comparison under the canonical protocol

DeformingPlate is the solid-mechanics case of the MeshGraphNets suite [48]: a rigid actuator with a prescribed motion is pressed into a hyperelastic plate that is clamped along one edge, and the plate’s node positions are to be predicted over 400 quasi-static steps on a tetrahedral mesh of 700–2,200 nodes. The task includes contact and large deformation, and every trajectory has its own plate geometry, actuator shape and path. 1,200 trajectories are used for training, 100 for validation and 100 for the test score.

9.1 Protocol

The score follows the original paper: RMSE of world positions in metres over all nodes and all 399 predicted steps of the 100 test trajectories, with errors pooled before taking the square root and reported . The seed frame is excluded. The checkpoint was selected on the validation split, and the test split was scored once.

9.2 Result

DIM-GP reports RMSE of 6.45 versus 15.1 for MeshGraphNets, a 57% reduction, and ranks second among the three canonical-protocol entries. M4GN reports the lowest value, 2.65. The remaining rows use different data, splits or error conventions and are listed separately.

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9.3 Cost

Training completed in less than one day on a single RTX 4090, with peak GPU memory below 8 GB.

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10. AhmedML — internal evaluation against published baselines

AhmedML [39] is a 500-geometry CFD dataset over the Ahmed body, a standard automotive bluff-body. The published comparison in AB-UPT [40] provides the external baseline values used below.

10.1 Protocol and metric

The metric follows that comparison: per design, the Frobenius relative error , averaged over designs, reported as a percentage. Five channels are scored — surface pressure and wall shear stress ; volume velocity , vorticity and total pressure . Evaluation uses raw full-resolution clouds from the 50 test designs in AB-UPT’s published split.

10.2 Result

AhmedML test geometry run_241 (official test split): surface pressure of the reference simulation and of the DIM-GP prediction, displayed on a decimated surface mesh. Drag to orbit, scroll to zoom, right-drag to pan.

¹ Measured for AB-UPT’s 200K-update schedule on the same RTX 4090 (§10.3). Both models use the same training data, including surface and volume fields. Other methods have no timing on this hardware.

DIM-GP places first of ten on all five channels in the comparison with published baselines [40]. Relative to AB-UPT, error is lower by 1.3% on surface pressure, 1.8% on wall shear, 2.6% on volume velocity, 3.4% on vorticity and 6.6% on total pressure.

The DIM-GP row reports our internal evaluation as of 7 September 2026. Baseline values come from the published comparison [40]. The ranking is based on point estimates.

10.3 Cost — measured on identical hardware

DIM-GP trains in 6.7 h on one RTX 4090 under an 8 GB cap. We executed AB-UPT’s released code on the same hardware and measured ~77 h for its 200K-update training schedule. Both training times are validated on our hardware, with the same data and split, surface and volume together. DIM-GP therefore requires approximately 91% less training time in this configuration.

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11. DrivAerML — internal evaluation against published baselines

DrivAerML [43] comprises 484 usable variants of the DrivAer notchback vehicle, each solved by hybrid RANS–LES (SA- -DDES, OpenFOAM) on a ~160M-cell mesh at a cost of roughly 40 hours on 1,536 CPU cores per design — on the order of 61,000 core-hours per geometry. The learning task is steady: one geometry in, the time-averaged surface pressure and wall-shear-stress fields out (~8.8M surface cells). Evaluation follows AB-UPT [40]: its published 400/34/50 split and per-design relative L2 error, using the Frobenius norm over the three shear components and averaging over the 50 test designs.

DrivAerML test car run_11: surface pressure of the reference simulation and of the DIM-GP prediction, displayed on a decimated surface mesh. Drag to orbit, scroll to zoom, right-drag to pan.

² Schedule estimate from measured throughput of the released implementation in a surface-only configuration on our RTX 4090 (§11.1). The published AB-UPT accuracy uses surface and volume data.

DIM-GP places 1st of 10 on both channels, with 2.1% less surface-pressure error and 1.9% less wall-shear error than runner-up AB-UPT. The DIM-GP values report our internal evaluation as of 7 September 2026. Baseline values come from the published comparison [40]. The ranking is based on point estimates.

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11.1 Computational cost on identical hardware

The released AB-UPT implementation (Noether, Emmi AI, v2026.4.0) was executed on the same RTX 4090 workstation and 400-design split in a surface-only configuration. Its measured update time of 1.21 seconds implies approximately 67 hours for 200,000 updates. This is a schedule estimate derived from measured throughput, compared with under 15 hours of DIM-GP wall-clock training, including evaluation checkpointing.

The timing was measured in our Windows environment with the available kernels. The published AB-UPT accuracy uses surface and volume data, whereas the timed configuration uses surface data alone and omits domain-branched cross-attention.

12. PLAID Rotor37 — live leaderboard, third placeboard state as of 4 September 2026

Rotor37 [41] is part of the PLAID benchmark suite (Safran, CC-BY-SA): 1,000 training and 200 test designs of a transonic axial compressor blade, 29,773 surface nodes each, with two operating scalars (rotational speed , inlet pressure ) as input and three surface fields (density, pressure, temperature) plus three global quantities (mass flow, compression ratio, isentropic efficiency) as output. All six are scored by a server-side leaderboard.

In the 4 September 2026 snapshot, DIM-GP ranks 3rd of 16 at a total error of 0.000488 (displayed 0.0005), behind NPco (~0.00043) and PXTransolver (~0.00047) and ahead of Super-MARIO (~0.00077). The gap to NPco is approximately 0.00006 in aggregate RRMSE, or 0.006 percentage points when expressed as percentages (approximately 0.049% versus 0.043%).

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13. PLAID VKI-LS59 — live leaderboard, first placeboard state as of 4 September 2026

VKI-LS59 [41] is the suite’s 2D transonic turbine cascade: 671 training and 168 test profiles of a linear cascade (Safran, CC-BY-SA), 36,421 nodes each, solved by compressible RANS (Spalart–Allmaras) with the passage reaching Mach 1.78. Inputs are two operating scalars (inlet angle, outlet Mach number) and the mesh; the competition scores two nodal fields (Mach number and turbulent viscosity ) and six global quantities ( , power, the pressure and temperature ratios and , the isentropic efficiency and the outlet angle).

The entry holds first place of 21 at 0.0093, approximately 8% lower aggregate error than PXTransolver. It leads the efficiency column and maintains competitive errors across the other scored outputs.

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14. PLAID 2D Multiscale Hyperelasticity — live leaderboard, first placeboard state as of 4 September 2026

This benchmark [41] is the suite’s variable-topology case: 764 training and 376 test representative volume elements of a porous hyperelastic material, each a different microstructure with five to eight holes (constant total porosity, node counts from 4,100 to 7,100), solved by FEniCS at finite strain. Inputs are three macroscopic strain components and the mesh; the competition scores seven nodal fields — the displacements , the four components of the first Piola–Kirchhoff stress, and the strain-energy density — together with the homogenised effective energy. Every design has its own mesh topology.

The entry ranks first of 22 at 0.010093 (displayed 0.0101), approximately 6% below PXTransolver in aggregate error. The four stress errors are comparable to PXTransolver’s. DIM-GP has the lowest effective-energy error, 0.0020, followed by NPco at 0.0037 and PXTransolver at 0.0074.

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15. PLAID Tensile2d — live leaderboard, second place behind a declared solverboard state as of 4 September 2026

Tensile2d [41] is the suite’s entry-level structural case: a 2D plane-strain, quasi-static, small-strain elastoplastic specimen under a uniform top traction, meshed once per design with 6,000–10,000 nodes (Safran, Z-set solver). Inputs are six scalars — the load , four parameters of the isotropic hardening law and the Young’s modulus — and the mesh; the competition scores five nodal fields ( , , , , ) and three scalars (the maximum von Mises stress, and the maximum and on the top edge). 500 designs carry labels, 200 form the test set.

DIM-GP ranks second of 22 at a displayed aggregate error of 0.0007. In its article How an AI Agent Cracked an Industry Benchmark, PhysicsX reports that AI agents reconstructed the reference simulator by inferring the constitutive law and simulation setup from the supplied training data [44]. Its entry ranks first with zero error at the leaderboard’s displayed precision.

The DIM-GP workflow runs on the CPU in minutes.

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16. PLAID 2D ElastoPlastoDynamics — live leaderboard, first placeboard state as of 4 September 2026

This is a transient solid-mechanics case [41]: a 200 × 100 mm steel plate with up to four holes and edge notches, clamped on the left and pulled at 500 mm/s on the right, computed by the benchmark’s authors with an explicit finite-element solver, a non-linear, non-local constitutive law and element erosion, and delivered as 41 time steps of the two displacement fields on 19,000–30,000 nodes per design. There are no input scalars: the geometry is the only variable, 1,000 designs are labelled and 18 form the test set. The competition scores the full and trajectories.

Transient field prediction substantially increases the scale of the learning problem. Each design contains a sequence of complete mesh fields rather than a single steady-state solution. Here, 41 time steps across 19,000–30,000 nodes produce approximately 0.8–1.2 million node-time states per design and output field. Memory use and training cost therefore grow rapidly with both spatial resolution and sequence length, particularly for architectures that represent mesh states as large token sequences. This makes the benchmark a demanding test of an architecture’s ability to model high-resolution spatial fields and their evolution over time.

The entry holds first place of eight at 0.008605, with the lowest displayed and errors in the archived table. The displayed values are 0.0005 for DIM-GP and 0.0008 for the next entry.

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The board metric normalises each field by its maximum over the whole test set, with constants of roughly 340 mm ( ) and 25 mm ( ).

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17. PLAID 2D_profile — live leaderboard, third placeboard state as of 7 September 2026

2D_profile [41] is the suite’s shape-only aerodynamics case: 300 training and 100 test airfoil profiles in a transonic flow, each with its own triangular mesh of 35,000–39,000 nodes cut close to the profile, and no input scalars at all — the geometry is the whole input, with the effective angle of attack baked into the shape. The competition scores four nodal fields (Mach number, pressure and the two velocity components). The test cases include transonic shocks.

DIM-GP ranks third of 22 in the 7 September 2026 snapshot, with an aggregate error of 0.0152 versus PXTransolver’s 0.0134. The numerical gap is 0.0018, equivalent to 0.18 percentage points when these relative errors are expressed as percentages (1.52% versus 1.34%). DIM-GP’s Velocity-y error of 0.0134 is the lowest displayed value on the board; its pressure error of 0.011 is joint-third.

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18. Bayesian optimization — concrete mix design, six approaches, one virtual problem

Bayesian optimization uses predictions and uncertainty estimates to select the next design to evaluate. Here, STOCHOS searches for concrete recipes that combine high 28-day compressive strength with low cradle-to-gate CO and material cost. Seven ingredient masses per cubic metre are varied, subject to a total mass of 2,195–2,551 kg.

The study uses a fixed virtual test bench fitted to the 1,022 usable rows of the public Concrete Compressive Strength dataset (UCI, 1,030 laboratory recipes) [45]. It predicts strength; CO and cost follow from the ingredient quantities, sourced emission factors and an indicative price basket. Six approaches receive the same starting recipes and a budget of 60 evaluations: STOCHOS, BoTorch’s qNEHVI [46], BayBE’s desirability approach [47], a random-forest optimizer, D-optimal design of experiments and random search.

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Part A — reaching a specification. Five levels of increasing difficulty each demand a minimum strength together with a CO and a cost ceiling on the same recipe; difficulty is characterized by an estimated probability that a random valid recipe qualifies (1 in 9 for S1 down to 1 in 66,667 for S4.5), and an unreachable sixth level serves as a control that no method passes. Ten repeated runs per level, at round sizes of one, three and six recipes. The table counts, per level, how many of the 10 runs at one recipe per round found a qualifying recipe.

Choose the difficulty level to see how many runs met the strength, CO₂ and cost requirements as the experiment budget increased.

Over all five levels and all three round sizes STOCHOS reaches the specification in 149 of 150 runs, against 137 for BoTorch, 111 for BayBE, 87 for the random forest, 78 for classical DoE and 66 for random search; it is the only method that solves the extreme level in every sequential run. Among runs in which both STOCHOS and BoTorch succeeded, STOCHOS reached the target sooner in 99 of 136 comparisons, later in 16 and at the same experiment in 21 (reported two-sided sign test ).

Part B — discovering the trade-off set. With no single target, a method is scored on how much of the achievable trade-off region it discovers: the hypervolume of its evaluated recipes against a frozen reference point, averaged over 30 repeated runs; the table gives the coverage after 60 experiments at round sizes of one, five and ten.

Higher coverage means a broader set of useful trade-offs. Hover for exact values; error bars show the standard error across 30 runs.

STOCHOS leads at round sizes one and five and is second at ten, where the batch of ten commits a sixth of the budget before any result returns. Choosing one recipe at a time, it reaches 80% coverage in a median of 32 experiments and 90% in 46 (on 20 of 30 runs, the most of any method); random forest, classical DoE and random search never reach 80% inside the budget. The extended-budget study of the classical design makes the gap concrete: a D-optimal plan needs 180 experiments to reach the 70% coverage that STOCHOS passes at 21.

Choose two objectives to compare the best trade-offs each method found across 30 runs. Higher strength, lower CO₂ and lower cost are preferred: towards the lower right in the strength views and towards the lower left in the CO₂–cost view.

Compare how many experiments each method needs to reach a given level of trade-off coverage. Higher curves indicate broader coverage at the same experiment budget.

Cost of the decisions. Part B’s sequential runs have median elapsed times of 26.7 minutes for STOCHOS, 50.2 minutes for BoTorch and 147.6 minutes for BayBE over 30 runs per method, each with a 60-experiment budget. STOCHOS uses approximately 47% less elapsed time than BoTorch in this comparison, measured for model fitting and proposal generation in the virtual benchmark. The methods with the lowest computational overhead, classical DoE and random search, have lower reported coverage.

Hover to see the time spent fitting models and proposing recipes. Compare the median computational time per campaign with the trade-off coverage above.

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Appendix A. Sources and authorship

Public leaderboard rows, published baseline values and internal experiments are distinguished in the relevant sections. Numerical ranks refer to the stated comparison fields and snapshot dates. PLAID scores are computed by the benchmark platform; STOCHOS training and timing measurements are reported by the authors.

This report is authored by PI Probaligence GmbH, the developer of STOCHOS. References link to the benchmark datasets, published methods and evaluation protocols used in the comparisons.

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References

References identify benchmark datasets, evaluation procedures, methods and author descriptions. For tabular entries, registered TabArena references were used where available.

Benchmarks

[1] TabArena: a living benchmark for tabular machine learning. Leaderboard https://huggingface.co/spaces/TabArena/leaderboard, code https://github.com/autogluon/tabrepo. Results accessed 18 August 2026 (42 registered methods).

[2] TALENT: a tabular analytics and learning toolbox. https://github.com/LAMDA-Tabular/TALENT.

Pretrained tabular models

[3] TabFM. Google Research, released 30 June 2026. https://github.com/google-research/tabfm. Released configuration: 1,639,444,298 parameters (§3). Consult the repository for license terms.

[4] EXAONE-Tabular. LG AI Research, released 31 July 2026. https://github.com/LGAI-Research/EXAONE-Tabular. Consult the repository for code and model-license terms.

[5] Prior Labs. TabPFN-3: Technical Report. arXiv:2605.13986. https://priorlabs.ai/technical-reports/tabpfn-3. Consult the model release for license terms.

[6] TabPFN-2.6 and RealTabPFN-2.5. arXiv:2511.08667.

[7] TabICL: a tabular foundation model for in-context learning on large data. arXiv:2502.05564. TabICLv2: arXiv:2602.11139. BSD-3-Clause.

[8] LimiX. arXiv:2509.03505.

[9] TabDPT. arXiv:2410.18164.

[10] Mitra. arXiv:2510.21204.

[11] TabPFN-Wide. arXiv:2510.06162.

[12] TabSTAR. arXiv:2505.18125.

[13] SAP-RPT-OSS. arXiv:2506.10707.

[14] OrionMSP. arXiv:2511.02818.

[15] iLTM. arXiv:2511.15941.

[16] Nori / Nori-30M. https://github.com/Synthefy/synthefy-nori.

[17] TabSwift. https://github.com/LAMDA-Tabular/TabSwift.

Trees, networks and classical baselines

[18] LightGBM: a highly efficient gradient boosting decision tree. NeurIPS 2017. https://papers.nips.cc/paper_files/paper/2017/hash/6449f44a102fde848669bdd9eb6b76fa-Abstract.html

[19] CatBoost: unbiased boosting with categorical features. arXiv:1706.09516.

[20] XGBoost: a scalable tree boosting system. arXiv:1603.02754.

[21] RealMLP — Better by default: strong pre-tuned MLPs and boosted trees on tabular data. arXiv:2407.04491.

[22] TabM. arXiv:2410.24210.

[23] ModernNCA. arXiv:2407.03257.

[24] xRFM. arXiv:2508.10053.

[25] Explainable Boosting Machine (EBM), Lou et al., KDD 2013.

[26] Random Forests, Breiman (2001), and Extremely Randomized Trees, Geurts et al. (2006).

[27] TorchMLP / FastaiMLP. arXiv:2003.06505.

[28] PerpetualBooster. https://perpetual-ml.com/.

Statistical methods used in this document

[29] R. A. Bradley and M. E. Terry. Rank analysis of incomplete block designs: I. The method of paired comparisons. Biometrika 39(3/4), 324–345 (1952). The model underlying the Elo ratings defined in §2.0.

[30] H. Theil (1950); P. K. Sen. Estimates of the regression coefficient based on Kendall’s tau. JASA 63(324), 1379–1389 (1968). The robust slope estimator used in §4.5.

[31] F. Wilcoxon. Individual comparisons by ranking methods. Biometrics Bulletin 1(6), 80–83 (1945). The paired test used in §4.2.

[32] J. Demšar. Statistical comparisons of classifiers over multiple data sets. JMLR 7, 1–30 (2006). On why paired, non-parametric tests are the appropriate instrument for benchmark comparisons of this shape.

Physics benchmarks and surrogate models (§§6–17)

[33] LagrangeBench: a Lagrangian fluid mechanics benchmarking suite. A. P. Toshev, G. Galletti, F. Fritz, S. Adami, N. A. Adams. NeurIPS 2023 Datasets & Benchmarks. arXiv:2309.16342. Datasets on Zenodo, CC-BY.

[34] Learning to simulate complex physics with graph networks (GNS). A. Sanchez-Gonzalez, J. Godwin, T. Pfaff, R. Ying, J. Leskovec, P. W. Battaglia. ICML 2020. arXiv:2002.09405. Source of the Water-3D dataset and protocol used in §8.

[35] Geometric and physical quantities improve E(3) equivariant message passing (SEGNN). J. Brandstetter, R. Hesselink, E. van der Pol, E. J. Bekkers, M. Welling. ICLR 2022 (spotlight). arXiv:2110.02905. Baseline in [33].

[36] CoRGI: convolutional residual global interactions. KDD 2026. arXiv:2511.22938. The strongest published per-cell numbers on most of the board in §7.2.

[37] Neural-SPH. arXiv:2402.06275. Source of the 400-step long-horizon protocol used in the supplement to §7.2.

[38] NeuralMPM. TMLR. arXiv:2408.15753. The only surveyed method reporting full-rollout MSE in the same convention as [34] (§8.2).

[39] AhmedML. N. Ashton et al. High-fidelity CFD dataset over the Ahmed body, 500 geometries. https://huggingface.co/datasets/neashton/ahmedml.

[40] AB-UPT: anchored-branched universal physics transformers. arXiv:2502.09692. Source of the baseline tables used in §§10.2 and 11. https://arxiv.org/abs/2502.09692.

[41] PLAID: a benchmark suite of physics-learning datasets. Safran. arXiv:2505.02974. Rotor37 leaderboard hosted at https://huggingface.co/PLAIDcompetitions. CC-BY-SA 4.0.

[42] EqGINO: equivariant geometry-informed Fourier neural operators for 3D PDEs. S. Kim, J. Song, S. Shin, G. Cho, S. Kim, C. Park. arXiv:2606.03260.

[43] DrivAerML: high-fidelity computational fluid dynamics dataset for road-car external aerodynamics. N. Ashton et al. arXiv:2408.11969. 500 morphed DrivAer variants, SA-sigma-DDES, ~160M cells; source of the solver-cost figures quoted in §11.

[44] Douglas Boubert. How an AI Agent Cracked an Industry Benchmark. PhysicsX, 11 August 2026. https://www.physicsx.ai/newsroom/how-an-ai-agent-cracked-an-industry-benchmark. Author description of the solver-based Tensile2d entry (§15).

[45] I-C. Yeh. Modeling of strength of high-performance concrete using artificial neural networks. Cement and Concrete Research 28(12), 1998. Dataset: UCI Machine Learning Repository, Concrete Compressive Strength (1,030 recipes).

[46] M. Balandat et al. BoTorch: A framework for efficient Monte-Carlo Bayesian optimization. NeurIPS 2020. botorch.org — qNEHVI acquisition, version 0.18.1 in §18.

[47] BayBE — Bayesian back end, Merck KGaA. emdgroup.github.io/baybe — version 0.15.0 in §18.

[48] T. Pfaff, M. Fortunato, A. Sanchez-Gonzalez, P. W. Battaglia. Learning mesh-based simulation with graph networks (MeshGraphNets). ICLR 2021. arXiv:2010.03409. Source of the DeformingPlate data and protocol of §9.

[49] M4GN: mesh-based multi-segment hierarchical graph network. Transactions on Machine Learning Research, 2025 (openreview.net/forum?id=R3vDbqWa1v). Reported 2.65 on DeformingPlate; no code released.

[50] MGN-T: MeshGraphNet-Transformer for solid mechanics. arXiv:2601.23177. DeformingPlate data regenerated with COMSOL.

[51] Y.-Y. Yu et al. Learning Flexible Body Collision Dynamics with Hierarchical Contact Mesh Transformer. ICLR 2024. https://arxiv.org/abs/2312.12467.

[52] Diffusion-Based Hierarchical Graph Neural Networks for Simulating Nonlinear Solid Mechanics (ROBIN). NeurIPS 2025. https://arxiv.org/abs/2506.06045.

[53] EvoMesh: Adaptive Physical Simulation with Hierarchical Graph Evolutions. ICML 2025. https://hbell99.github.io/evo-mesh/.

[54] Y. Cao, M. Chai, M. Li and C. Jiang. Efficient Learning of Mesh-Based Physical Simulation with Bi-Stride Multi-Scale Graph Neural Network. ICML 2023. https://proceedings.mlr.press/v202/cao23a.html.

[55] A. Vaswani et al. Attention Is All You Need. NeurIPS 2017. https://arxiv.org/abs/1706.03762.

[56] H. Wu et al. Transolver: A Fast Transformer Solver for PDEs on General Geometries. ICML 2024. https://arxiv.org/abs/2402.02366.

[57] Z. Li et al. Transformer for Partial Differential Equations’ Operator Learning. ICLR 2023. https://arxiv.org/abs/2205.13671.

[58] B. Alkin et al. Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operators. NeurIPS 2024. https://arxiv.org/abs/2402.12365.

[59] H. Gao and S. Ji. Graph U-Nets. ICML 2019. https://arxiv.org/abs/1905.05178.

[60] Z. Li et al. Geometry-Informed Neural Operator for Large-Scale 3D PDEs. NeurIPS 2023. https://arxiv.org/abs/2309.00583.

[61] C. R. Qi et al. PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation. CVPR 2017. https://arxiv.org/abs/1612.00593.

[62] T. Wang and C. Wang. Latent Neural Operator for Solving Forward and Inverse PDE Problems. NeurIPS 2024. https://arxiv.org/abs/2406.03923.

[63] PI Probaligence. How STOCHOS Works: The DIM-GP Algorithm. Technical description (not a peer-reviewed method paper). https://probaligence.com/how-stochos-works/.