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arxiv: 2602.20399 · v2 · pith:4JN6FELGnew · submitted 2026-02-23 · 💻 cs.LG

GeoPT: Scaling Physics Simulation via Lifted Geometric Pre-Training

Haixu Wu , Minghao Guo , Zongyi Li , Zhiyang Dou , Mingsheng Long , Kaiming He , Wojciech Matusik This is my paper

Pith reviewed 2026-05-21 12:11 UTC · model grok-4.3

classification 💻 cs.LG
keywords neural physics simulationgeometric pre-trainingsynthetic dynamicsself-supervised learningfluid mechanicssolid mechanicsdata-efficient trainingsurrogate modeling
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The pith

Augmenting static geometries with synthetic dynamics enables pre-training that transfers to real physics simulation tasks.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper aims to show that neural simulators for physics can be scaled by pre-training on abundant geometric data rather than scarce high-fidelity simulations. The central challenge is that static shapes alone provide no information about motion or forces, which risks harming performance when the model later faces actual dynamics. By adding synthetic dynamics to the geometries during pre-training, the model learns features that capture both shape and plausible motion without any real physics labels. This pre-trained model then requires far less labeled data when fine-tuned on industrial tasks such as car airflow, aircraft flow, ship hydrodynamics, and vehicle crash tests. If correct, the approach would let researchers train useful simulators with 20 to 60 percent fewer expensive simulations and reach target accuracy roughly twice as fast.

Core claim

GeoPT is a unified pre-trained model for general physics simulation that rests on lifted geometric pre-training. The method augments each static geometry with synthetic dynamics to create dynamics-aware self-supervision signals, closing the gap between pure geometry and full physics without requiring labeled simulation data. After pre-training on more than one million such augmented samples, the model is fine-tuned on downstream benchmarks in fluid mechanics and solid mechanics. It consistently lowers the amount of labeled data needed by 20-60 percent and halves the number of training steps required to reach a given accuracy level.

What carries the argument

Lifted geometric pre-training: the addition of synthetic dynamics to static 3D geometries so that self-supervised objectives can encode both shape and plausible motion.

If this is right

  • The pre-trained model improves accuracy on fluid-flow benchmarks for cars, aircraft, and ships as well as on solid-mechanics crash simulations.
  • Downstream training converges roughly twice as fast on the same industrial tasks.
  • Labeled data requirements for reaching target accuracy drop by 20 to 60 percent across the tested domains.
  • The same pre-training recipe can be applied to other geometry-based simulation problems that currently suffer from scarce labeled data.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same lifting strategy might reduce data costs in neighboring scientific domains such as molecular dynamics or structural engineering where static geometries are plentiful but full simulations are costly.
  • If synthetic dynamics prove broadly useful, future pre-training pipelines could generate even larger and more diverse augmentation sets to push scaling further.
  • Architectures that already handle 3D geometry well could be swapped into the same pre-training loop to test whether the benefit is model-agnostic.

Load-bearing premise

Adding synthetic dynamics to static geometries supplies supervision that transfers usefully to real physics problems and does not produce negative transfer.

What would settle it

A controlled experiment in which the pre-trained GeoPT model, after fine-tuning on a fixed budget of real physics labels, reaches lower accuracy than an identical model trained from scratch on the same labels.

Figures

Figures reproduced from arXiv: 2602.20399 by Haixu Wu, Kaiming He, Minghao Guo, Mingsheng Long, Wojciech Matusik, Zhiyang Dou, Zongyi Li.

Figure 1
Figure 1. Figure 1: Neural aerodynamics simulation on DrivAerML (Ash￾ton et al., 2024) based on Transolver (Wu et al., 2024) backbone. Geometry-only pre-training and conditioning refer to pre-training by predicting vector distance (Faugeras & Gomes, 2000) of given positions and utilizing geometry representation extracted by Hun￾yuan3D (Tencent, 2025) as auxiliary feature, respectively. hinges on scaling model capacity and tra… view at source ↗
Figure 2
Figure 2. Figure 2: GeoPT offers a way to scale up neural simulators with off-the-shelf geometries and enables fast fine-tuning for various physics. of the pre-training data, such as learning to reconstruct from masked images (He et al., 2022) or learning to identify sim￾ilar samples from augmentations (Chen et al., 2020), where the model input will not exceed the original information of pre-training data. This paradigm succe… view at source ↗
Figure 3
Figure 3. Figure 3: Geometry-physics analysis. (a) Visualization of learned correlations on DrivAerML (Ashton et al., 2024). We train Tran￾solver (Wu et al., 2024) using different supervisions and visualize the spatial distribution of learned aggregation weights in four tokens. Brighter colors indicate higher token assignment likelihood, revealing correlations captured by the model. See Appendix G full results. (b) We lift th… view at source ↗
Figure 4
Figure 4. Figure 4: Overall design of GeoPT. (a) To ensure the pre-training diversity, we pre-train the model with geometry randomly sampled from the public repository (Chang et al., 2015) and generate the supervision for random tracking points under random dynamics. (b) Through a dynamics-lifted framework, we can configure the dynamics condition to “prompt” the corresponding pre-training capability of GeoPT. mass-conservatio… view at source ↗
Figure 5
Figure 5. Figure 5: Performance comparison across fine-tuning epochs and physics samples. We show detailed curves at 200 epochs and 100 samples for clarity. Here, geometry-only pre-training adopts vector distance, which is better than SDF. See Appendix D for full results. (ii) Improving geometry generalization. GeoPT yields larger improvements in simulations involving a greater diversity of geometries. For instance, GeoPT bri… view at source ↗
Figure 6
Figure 6. Figure 6: GeoPT scaling tests. (a) Gradually increase model layers from 8 to 32 and record the performance change of training from scratch and with GeoPT. (b) Reduce the pre-training diversity of both geometries and dynamics. See Appendix G for full results. the model hypothesis space to alleviate potential overfitting, thereby consistently benefiting from increasing model size. (ii) Data diversity. In GeoPT, we con… view at source ↗
Figure 7
Figure 7. Figure 7: Simulation results and learned representations from GeoPT, including (a) visualization of the prediction results with the worst relative L2 performance in DrivAerML, (b) the error map of surface pressure and surrounding velocity, (c) correlations learned by pre-trained GeoPT under varied dynamics information, such as different directions and speeds of VS. See Appendix E for more results. Relative L2 Benchm… view at source ↗
Figure 8
Figure 8. Figure 8: (a) Analysis for the geometry usage, including the com￾parison between geometry-only and dynamics-lifted spaces, as well as pre-training v.s. conditioning. (b) Backbone comparison. 5.2. Model Analysis Geometry usage. We provide a detailed ablation of how geometric information is utilized in [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: reveals that GeoPT captures high-frequency shadow boundaries more accurately, particularly in regions with complex light-geometry interactions. Notably, neither the Cornell box geometry nor any light transport physics was seen during pre-training. This result highlights GeoPT’s potential as a general-purpose prior for diverse simulation tasks. Ground Truth Training from Scratch GeoPT Ground Truth Training … view at source ↗
Figure 10
Figure 10. Figure 10: Ablations for the pre-training choices in GeoPT, including the comparison among (a) pre-training with a single subset or mixed data from ShapeNet-V1, -V2, (b) discretizing the dynamics into various step numbers τ , and (c) pre-training with different geometry information, such as SDF and vector distance. All the experiments are based on GeoPT-Based under the full-data-full-training setting. Test MSE Epoch… view at source ↗
Figure 11
Figure 11. Figure 11: The pre-training process of GeoPT. (a) We plot the test MSE change during 200 pre-training epochs, which is calculated on 300 leave-out geometries. The initial unstable stage is caused by learning rate warm up. (b) Prediction case of the pre-trained GeoPT-Base. For clarity, we only plot 35 points under 3 dynamic steps, where the prediction is in blue and the ground truth is in orange. Ablation 2: ShapeNet… view at source ↗
Figure 12
Figure 12. Figure 12: GeoPT-Base performance change w.r.t. the direction shifted (by 0◦ to 40◦ ) from the correct configuration. Zero shift refers to configuring the dynamics field direction along the incoming flow or impact angle, which is our default setting. For clarity, we adopt the same y-axis range of 0.75 among different benchmarks in visualization. All the experiments are under the full-data-full-training setting. Rela… view at source ↗
Figure 13
Figure 13. Figure 13: GeoPT-Base performance change w.r.t. the configured velocity norm in VS, which is sampled from [0, 2] during pre-training. For real-world low-speed cases, such as car and watercraft simulations, we explore the choices within less than 1.0. As for high-speed cases, such as aircraft, we explore a larger range [0.2, 2.6]. Since both NASA-CRM and AirCraft involve varying simulation speeds, we normalize the re… view at source ↗
Figure 14
Figure 14. Figure 14: Test loss (relative L2) change during fine-tuning. Note that these test losses are calculated from the downsampled physics field to ensure training efficiency, which is proportional to the final performance, but may be shifted w.r.t. the full mesh results. among different samples for the model, it will cause performance degradation since it will inform the pre-trained with incorrect correlations, as visua… view at source ↗
Figure 15
Figure 15. Figure 15: Showcase of NASA-CRM. (a) The pressure coefficient field of the airplane flying under 0.7219 Mach and 3.46◦ angle of attack. (b) Error map and the relative L2 of different models for this case. For clarity, we zoom in on high-error zones. (a) Physics Field Visualization (b) Error Map Visualization 7 Mach 0.00 125. 250. 375. 500. pred X Y Z 0 5 Ground Truth GeoPT-Base Prediction Transolver rL2 = 0.0823 Geo… view at source ↗
Figure 16
Figure 16. Figure 16: Showcase of AirCraft. We plot the Z-force coefficient field for aircraft flying under 7 Mach, 7◦ angle of attack and 2◦ sideslip. (a) Physics Field Visualization (b) Error Map Visualization 0.00 125. 250. 375. 500. pred X Y Z 0 2 Ground Truth GeoPT-Base Prediction Galerkin rL2 = 0.2570 Transolver rL2 = 0.1921 GeoPT-Base rL2 = 0.1399 GeoPT-Huge rL2 = 0.1321 Yaw Angle 11° -200. -100. 0.00 100. 200. pred X Y… view at source ↗
Figure 17
Figure 17. Figure 17: Showcase of DTCHull. (a) We plot the hydrostatic pressure–corrected pressure and surrounding velocity streamlines for a ship moving under 11◦ yaw angle. (b) We highlight the surrounding velocity error in the streamline and the pressure error in underside view. 0.00 125. 250. 375. 500. X pred Y Z -200. -100. 0.00 100. 200. X pred Y Z -200. -100. 0.00 100. 200. X pred Y Z -200. -100. 0.00 100. 200. X pred Y… view at source ↗
Figure 18
Figure 18. Figure 18: Showcase of Car-Crash. We plot the element-wise maximum 2D Von Mises stress during the crash with 26.93◦ impact angle. (a) DTCHull Geometry Examples (b) Car-Crash Geometry Deformation Examples Time Impact Angle -39.71° Impact Angle -31.39° [PITH_FULL_IMAGE:figures/full_fig_p017_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Examples from DTCHull and Car-Crash benchmarks, which involve diverse geometries and deformations, respectively. 17 [PITH_FULL_IMAGE:figures/full_fig_p017_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Reconstruction examples of latent tokens extracted by Hunyuan3D. (i) Geometry-only pre-training. In this type of baseline, we only adopt the geometry-only feature as supervision. Specifically, we train the model to pre￾dict SDF or vector distance (Faugeras & Gomes, 2000) based on given positions. (ii) Geometry-only conditioning. The prior work (Zhang et al., 2025) has explored using frozen geometry repres… view at source ↗
Figure 21
Figure 21. Figure 21: Visualization of physical states learned from different supervision signals, including (a) pre-training by learning to predict vector distance, (b) directly training with DrivAerML physics supervision and (c) pre-training with the dynamic process proposed by GeoPT. Here, we visualize the last layer. The visualizations from other layers can differ in absolute value but share a similar distribution. 23 [PI… view at source ↗
Figure 22
Figure 22. Figure 22: Visualization of DrivAerML physical states in GeoPT “prompted” from different dynamics configurations, including varied (a-c) direction and (d-e) velocity norm (speed) configurations. Here, we visualize the fourth layer as a supplement to the last layer visualization in [PITH_FULL_IMAGE:figures/full_fig_p024_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Visualization of NASA-CRM physical states in GeoPT “prompted” from different dynamics configurations, including varied (a-c) direction and (d-e) speed configurations. Here, we visualize the physical states in the last layer. Similar to DrivAerML, changing the angle of attack in the y-z plane will affect the state distribution and increasing speed will lead to a more concentrated state distribution. 25 [P… view at source ↗
Figure 24
Figure 24. Figure 24: Visualization of DTCHull physical states in GeoPT “prompted” from different dynamics configurations, including varied (a-c) direction and (d-e) speed configurations. Here, we visualize the physical states in the last layer. Notably, to ensure a clear presentation of the inside ship surface, we downsample the mesh by 10 times for visualization. 26 [PITH_FULL_IMAGE:figures/full_fig_p026_24.png] view at source ↗
read the original abstract

Neural simulators promise efficient surrogates for physics simulation, but scaling them is bottlenecked by the prohibitive cost of generating high-fidelity training data. Pre-training on abundant off-the-shelf geometries offers a natural alternative, yet faces a fundamental gap: supervision on static geometry alone ignores dynamics and can lead to negative transfer on physics tasks. We present GeoPT, a unified pre-trained model for general physics simulation based on lifted geometric pre-training. The core idea is to augment geometry with synthetic dynamics, enabling dynamics-aware self-supervision without physics labels. Pre-trained on over one million samples, GeoPT consistently improves industrial-fidelity benchmarks spanning fluid mechanics for cars, aircraft, and ships, and solid mechanics in crash simulation, reducing labeled data requirements by 20-60% and accelerating convergence by 2$\times$. These results show that lifting with synthetic dynamics bridges the geometry-physics gap, unlocking a scalable path for neural simulation and potentially beyond. Code is available at https://github.com/Physics-Scaling/GeoPT.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper introduces GeoPT, a unified pre-trained model for general physics simulation based on lifted geometric pre-training. Static geometries are augmented with synthetic dynamics to enable dynamics-aware self-supervision without physics labels. Pre-trained on over one million samples, the model is evaluated on industrial-fidelity benchmarks in fluid mechanics (cars, aircraft, ships) and solid mechanics (crash simulation), where it reduces labeled-data requirements by 20-60% and accelerates convergence by 2×. The central claim is that this lifting bridges the geometry-physics gap and provides a scalable path for neural simulators.

Significance. If the empirical gains hold under rigorous validation, the work could meaningfully advance scalable neural physics simulation by leveraging abundant geometric data plus synthetic dynamics, thereby lowering the barrier of expensive high-fidelity labeled data. The public release of code at https://github.com/Physics-Scaling/GeoPT is a positive contribution to reproducibility. The approach is potentially extensible beyond the tested fluid and solid mechanics domains.

major comments (3)
  1. [Abstract] Abstract: performance improvements are stated (20-60% reduction in labeled data, 2× faster convergence) without any description of experimental setup, baselines, statistical significance testing, error bars, number of runs, or data exclusion criteria. This information is load-bearing for the central empirical claim and must be supplied in §4.
  2. [§3] §3 (Lifted Geometric Pre-Training): the procedure for generating the synthetic dynamics used to augment geometry is not specified in sufficient detail to determine whether the resulting signals respect conservation laws, boundary conditions, or constitutive relations of the target domains. Without this, it is impossible to assess the risk of negative transfer versus genuine transfer of dynamics-aware representations.
  3. [§4] §4 (Experiments): the manuscript must include an ablation that isolates the contribution of the synthetic-dynamics component from the effects of model scale, architecture, or geometry encoding alone. Current results do not rule out the possibility that gains arise from pre-training scale rather than the claimed geometry-physics bridging mechanism.
minor comments (2)
  1. [§2] Clarify the precise definition of the 'lifted' representation and the loss used for self-supervision on synthetic dynamics; the current notation is ambiguous between geometry-only and dynamics-augmented terms.
  2. [Figure 2] Figure 2 (or equivalent architecture diagram) should explicitly annotate the synthetic-dynamics augmentation step and the downstream fine-tuning pathway.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough and constructive review of our manuscript. We address each major comment point by point below and have incorporated revisions where appropriate to improve clarity and rigor.

read point-by-point responses

  1. Referee: [Abstract] Abstract: performance improvements are stated (20-60% reduction in labeled data, 2× faster convergence) without any description of experimental setup, baselines, statistical significance testing, error bars, number of runs, or data exclusion criteria. This information is load-bearing for the central empirical claim and must be supplied in §4.

    Authors: We agree that the abstract claims require supporting experimental details in the main text. In the revised manuscript, Section 4 has been expanded with a dedicated subsection on experimental protocol. This includes descriptions of all baselines (MeshGraphNets, standard GNNs, and non-pretrained variants), the number of independent runs (five runs per configuration with distinct random seeds), statistical significance via paired t-tests (p-values reported), error bars as standard deviation across runs, and data exclusion criteria (no exclusions applied; all runs completed successfully within compute limits). A summary table has been added for transparency. revision: yes

  2. Referee: [§3] §3 (Lifted Geometric Pre-Training): the procedure for generating the synthetic dynamics used to augment geometry is not specified in sufficient detail to determine whether the resulting signals respect conservation laws, boundary conditions, or constitutive relations of the target domains. Without this, it is impossible to assess the risk of negative transfer versus genuine transfer of dynamics-aware representations.

    Authors: We appreciate the referee's emphasis on this detail. The original Section 3.2 outlines the high-level augmentation using random velocity and force perturbations derived from geometry, but we acknowledge the need for greater specificity. The revised manuscript adds Appendix B with the exact algorithmic steps and equations for generating the synthetic fields. These perturbations are constructed to weakly respect mass and momentum conservation in an integral sense but deliberately avoid strict enforcement of domain-specific boundary conditions or constitutive laws to preserve scalability and label-free generality. We have also added a short discussion of negative-transfer risks, noting that our downstream results show no performance degradation and consistent gains across fluid and solid mechanics tasks. revision: partial

  3. Referee: [§4] §4 (Experiments): the manuscript must include an ablation that isolates the contribution of the synthetic-dynamics component from the effects of model scale, architecture, or geometry encoding alone. Current results do not rule out the possibility that gains arise from pre-training scale rather than the claimed geometry-physics bridging mechanism.

    Authors: We agree that an explicit ablation isolating the synthetic-dynamics contribution is necessary to substantiate the central claim. The revised Section 4.4 now contains a controlled ablation study in which model architecture, parameter count, and geometry encoding are held fixed while varying only the presence of synthetic dynamics during pre-training. We compare (i) geometry-only pre-training, (ii) lifted synthetic-dynamics pre-training, and (iii) training from scratch. Results indicate that the dynamics component yields an additional 20–25 % reduction in labeled-data requirements and roughly 1.5× faster convergence beyond scale or architecture effects. We further report performance across two model sizes to control for scale. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical pre-training gains measured on held-out benchmarks

full rationale

The paper's central claim rests on an empirical pipeline: pre-train a model on over one million geometry samples augmented with synthetic dynamics, then fine-tune and evaluate on separate industrial physics benchmarks (fluids for cars/aircraft/ships, solid crash simulation). Reported gains in labeled-data reduction (20-60%) and convergence speed (2×) are presented as experimental outcomes, not as quantities derived by construction from the pre-training inputs or via self-referential definitions. No equations, uniqueness theorems, or fitted parameters are shown to reduce tautologically to the synthetic augmentation itself; the geometry-physics gap is treated as an empirical hypothesis tested externally rather than assumed or renamed. The derivation chain is therefore self-contained against the benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, the central claim rests on the domain assumption that synthetic dynamics can bridge static geometry to dynamic physics without negative transfer. No free parameters or invented entities are explicitly described in the available text.

axioms (1)
  • domain assumption Neural networks trained on geometry augmented with synthetic dynamics can learn representations that transfer positively to real physics simulation tasks.
    This underpins the claim that the pre-training improves downstream performance and reduces labeled data needs.

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Forward citations

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Reference graph

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    to extract the static geometry representation for comparison. Specifically, we adopt the pre-trained V AE model4 encoder, which can receive a set of points sampled from a mesh geometry as input and encode it into 3,072 geometry tokens with 64 hidden channels. Then we integrate the extracted token sequence into Transolver based on an additional cross-atten...

    work page 2025

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    and Transolver++ (Luo et al., 2025), to further benchmark GeoPT. As shown in Table 4, in the two largest 3https://github.com/thuml/Neural-Solver-Library 4https://huggingface.co/tencent/Hunyuan3D-2/tree/main/hunyuan3d-vae-v2-0-withencoder 20 GeoPT: Scaling Physics Simulation via Lifted Geometric Pre-Training Table 4.Comparison between GeoPT and the previou...

    work page 2025

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    w/o GeoPT

    It is also observed that pre-training with GeoPT can help avoid potential overfitting, especially in industrial design tasks where only limited data is available. Besides, GeoPT can also take advantage of diverse geometry and dynamics conditions, highlighting the value of rich 3D geometry assets. Table 5.Quantitative results for scaling performance and su...

    work page 1977

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    prompted

    We color some results to highlight GeoPT’s capability in improving performance, convergence and reducing data requirements: (i) Improving performance:We color results that outperform Transolver under the same samples and epochs as bright blue. (ii) Accelerating convergence:Under the same training samples, the results surpass the best performance achieved ...

    work page arXiv 2024

  25. [25]

    prompted

    Notably, the states in the fourth layer are less distinguishable in the middle layers when compared with the last layer. This can be viewed as an architectural feature of Transolver, which can enable better global interaction among different states. 24 GeoPT: Scaling Physics Simulation via Lifted Geometric Pre-Training (a) GeoPT with +x direction, 1.2 nor...

    work page 2023