Machine learning-based surrogate models have emerged as more efficient alternatives to numerical solvers for physical simulations over complex geometries, such as car bodies. Many existing models incorporate the simulation mesh as an additional input, thereby reducing prediction errors. However, generating a simulation mesh for new geometries is computationally costly. In contrast, mesh-free methods, which do not rely on the simulation mesh, typically incur higher errors. Motivated by these considerations, we introduce SMART, a neural surrogate model that predicts physical quantities at arbitrary query locations using only a point-cloud representation of the geometry, without requiring access to the simulation mesh. The geometry and simulation parameters are encoded into a shared latent space that captures both structural and parametric characteristics of the physical field. A physics decoder then attends to the encoder's intermediate latent representations to map spatial queries to physical quantities. Through this cross-layer interaction, the model jointly updates latent geometric features and the evolving physical field. Extensive experiments show that SMART is competitive with and often outperforms existing methods that rely on the simulation mesh as input, demonstrating its capabilities for industry-level simulations.

翻译：基于机器学习的代理模型已成为复杂几何体（如汽车车身）物理模拟中数值求解器的高效替代方案。许多现有模型将模拟网格作为额外输入，从而降低预测误差。然而，为新几何体生成模拟网格的计算成本高昂。相比之下，不依赖模拟网格的无网格方法通常会产生更高的误差。基于这些考虑，我们提出了SMART——一种神经代理模型，仅使用几何体的点云表示即可预测任意查询位置处的物理量，无需访问模拟网格。几何与模拟参数被编码到共享潜在空间中，该空间同时捕获物理场的结构特征与参数特性。物理解码器随后关注编码器的中间潜在表示，将空间查询映射为物理量。通过这种跨层交互，模型可联合更新潜在几何特征与演化的物理场。大量实验表明，SMART与依赖模拟网格输入的现有方法相比具有竞争力且常表现更优，证明了其在工业级模拟中的应用潜力。