industrial simulation teams

Abstract: Neural solvers offer efficient surrogates for numerical simulation of partial differential equations (PDEs). For time-dependent problems, strong one-step accuracy does not necessarily translate into reliable autoregressive rollout. We observe that a solver based only on physical-state modeling can achieve lower one-step error, whereas its spectral-only counterpart can become more accurate at later rollout steps. Motivated by this observation, we present Transolver-$σ$, a neural PDE solver based on joint spectral--physical subspace modeling. Within each block, adaptive physical-state interactions and spectral transformations are modeled in dedicated latent subspaces, whose responses are recomposed to enable information exchange between the two representations. Within the physical subspace, we introduce Slice-Residual Physics-Attention (SRPA), which preserves an explicit slice-space identity path while retaining learnable cross-slice interaction. In parallel, an axis-factorized Fourier operator captures global spectral structure. Across five well-established PDE benchmarks spanning steady-state prediction and time-dependent dynamics, Transolver-$σ$ achieves state-of-the-art with a benchmark-averaged relative error reduction of 33.4% over the strongest baseline for each metric, while consistently improving autoregressive rollout over single-operator counterparts. Transolver-$σ$ further delivers strong gains on coupled multiphysics systems and real-world fluid and combustion measurements from RealPDEBench, demonstrating its effectiveness beyond standard simulation benchmarks.

Abstract: We present CADSplat, a framework that reconstructs photorealistic, geometrically accurate digital twins from sparse ($<15$ views), wide-baseline posed images of an object by regularizing 3D Gaussian Splatting (3DGS) with an explicit CAD shape prior. Using such a prior requires finding a CAD model whose shape resembles the object depicted in the images and determining the pose of each camera relative to the object. We obtain both by matching segmented object silhouettes against silhouettes rendered from a CAD library and keeping the camera-to-object poses of the best-matching model. We then anchor 3D Gaussian primitives to the surface of the retrieved model and jointly optimize the 3DGS parameters, the camera-to-object registration, and a non-rigid deformation field to account for shape differences between the physical object and the CAD model. Across two real-world datasets, CADSplat outperforms unconstrained, few-shot, and mesh-texturing baselines and degrades gracefully to as few as 3 views. Our experiments show that most of the gain in rendering quality comes from how the splats are constrained---a fixed set of splats tied to a surface and moved by a single smooth deformation field---rather than from the CAD shape itself. The CAD model adds shape knowledge where views are scarcest, in the sparsest captures and on strongly self-occluded objects, and it places every camera in the object's own frame. This enables applications beyond novel-view synthesis, such as markerless augmented reality registration, per-image object pose estimation, physical simulations, and the transfer of part labels from the design to the reconstruction.