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GeoPT: Scaling Physics Simulation via Lifted Geometric Pre-Training

Haixu Wu, Minghao Guo, Zongyi Li, Zhiyang Dou, Mingsheng Long, Kaiming He, Wojciech Matusik

TL;DR

The results show that lifting with synthetic dynamics bridges the geometry-physics gap, unlocking a scalable path for neural simulation and potentially beyond.

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.

GeoPT: Scaling Physics Simulation via Lifted Geometric Pre-Training

TL;DR

The results show that lifting with synthetic dynamics bridges the geometry-physics gap, unlocking a scalable path for neural simulation and potentially beyond.

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. 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.
Paper Structure (44 sections, 1 theorem, 12 equations, 26 figures, 10 tables, 1 algorithm)

This paper contains 44 sections, 1 theorem, 12 equations, 26 figures, 10 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Neural Simulators
  4. Self-Supervised Pre-Training
  5. Problem Setup
  6. Method
  7. Lifting Geometry to Physics
  8. Lifted Geometric Pre-Training
  9. Implementation Details
  10. Experiments
  11. Main Results
  12. Model Analysis
  13. Conclusion
  14. Extension to Radiosity
  15. Theoretical Understanding of GeoPT Pre-Training
  16. ...and 29 more sections

Key Result

Proposition 2.1

The phase-space transport equation in Eq. eq:phase_space_transport is conservative. In the absence of sticking, the phase-space flow $(x,v) \mapsto (x+t v, v)$ is divergence-free. With sticking boundaries, mass is not destroyed but transferred from the interior to the boundary. Specifically, the tot Here $dS(x)$ denotes the surface measure on $G=\partial\Omega$. Thus, the dynamics conserve the tot

Figures (26)

  • Figure 1: Neural aerodynamics simulation on DrivAerML ashton2024drivaerml based on Transolver wu2024Transolver backbone. Geometry-only pre-training and conditioning refer to pre-training by predicting vector distance faugeras2000dynamic of given positions and utilizing geometry representation extracted by Hunyuan3D hunyuan3d22025tencent as auxiliary feature, respectively.
  • Figure 2: GeoPT offers a way to scale up neural simulators with off-the-shelf geometries and enables fast fine-tuning for various physics.
  • Figure 3: Geometry-physics analysis. (a) Visualization of learned correlations on DrivAerML ashton2024drivaerml. We train Transolver wu2024Transolver 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 \ref{['appdix:full_results']} full results. (b) We lift the geometry space by augmenting it with synthetic velocity fields, which further derive a dynamics-aware supervision.
  • 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 chang2015shapenet 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.
  • 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 \ref{['appdix:rep']} for full results.
  • ...and 21 more figures

Theorems & Definitions (5)

  • Remark 4.1: Theoretical interpretation
  • Proposition 2.1: Mass conservation
  • Remark 2.2: Connect between GeoPT pre-training and solving collisionless transport equation in Eq. \ref{['eq:phase_space_transport']}
  • Remark 2.3: Generalizability of theoretical framework
  • Remark 4.1: Distinguishable configurations