We propose accelerating the simulation of Lagrangian dynamics, such as fluid flows, granular flows, and elastoplasticity, with neural-operator-based reduced-order modeling. While full-order approaches simulate the physics of every particle within the system, incurring high computation time for dense inputs, we propose to simulate the physics on sparse graphs constructed by sampling from the spatially discretized system. Our discretization-invariant reduced-order framework trains on any spatial discretizations and computes temporal dynamics on any sparse sampling of these discretizations through neural operators. Our proposed approach is termed Graph Informed Optimized Reduced-Order Modeling or \textit{GIOROM}. Through reduced order modeling, we ensure lower computation time by sparsifying the system by 6.6-32.0$\times$, while ensuring high-fidelity full-order inference via neural fields. We show that our model generalizes to a range of initial conditions, resolutions, and materials. The code and the demos are provided at \url{https://github.com/HrishikeshVish/GIOROM}
With the help of Score Distillation Sampling (SDS) and the rapid development of neural 3D representations, some methods have been proposed to perform 3D editing such as adding additional geometries, or overwriting textures. However, generalized 3D non-rigid editing task, which requires changing both the structure (posture or composition) and appearance (texture) of the original object, remains to be challenging in 3D editing field. In this paper, we propose Plasticine3D, a novel text-guided fine-grained controlled 3D editing pipeline that can perform 3D non-rigid editing with large structure deformations. Our work divides the editing process into a geometry editing stage and a texture editing stage to achieve separate control of structure and appearance. In order to maintain the details of the original object from different viewpoints, we propose a Multi-View-Embedding (MVE) Optimization strategy to ensure that the guidance model learns the features of the original object from various viewpoints. For the purpose of fine-grained control, we propose Embedding-Fusion (EF) to blend the original characteristics with the editing objectives in the embedding space, and control the extent of editing by adjusting the fusion rate. Furthermore, in order to address the issue of gradual loss of details during the generation process under high editing intensity, as well as the problem of insignificant editing effects in some scenarios, we propose Score Projection Sampling (SPS) as a replacement of score distillation sampling, which introduces additional optimization phases for editing target enhancement and original detail maintenance, leading to better editing quality. Extensive experiments demonstrate the effectiveness of our method on 3D non-rigid editing tasks