Abstract:We present ElastoGen, a knowledge-driven model that generates physically accurate and coherent 4D elastodynamics. Instead of relying on petabyte-scale data-driven learning, ElastoGen leverages the principles of physics-in-the-loop and learns from established physical knowledge, such as partial differential equations and their numerical solutions. The core idea of ElastoGen is converting the global differential operator, corresponding to the nonlinear elastodynamic equations, into iterative local convolution-like operations, which naturally fit modern neural networks. Each network module is specifically designed to support this goal rather than functioning as a black box. As a result, ElastoGen is exceptionally lightweight in terms of both training requirements and network scale. Additionally, due to its alignment with physical procedures, ElastoGen efficiently generates accurate dynamics for a wide range of hyperelastic materials and can be easily integrated with upstream and downstream deep modules to enable end-to-end 4D generation.
Abstract:We demonstrate the feasibility of integrating physics-based animations of solids and fluids with 3D Gaussian Splatting (3DGS) to create novel effects in virtual scenes reconstructed using 3DGS. Leveraging the coherence of the Gaussian splatting and position-based dynamics (PBD) in the underlying representation, we manage rendering, view synthesis, and the dynamics of solids and fluids in a cohesive manner. Similar to Gaussian shader, we enhance each Gaussian kernel with an added normal, aligning the kernel's orientation with the surface normal to refine the PBD simulation. This approach effectively eliminates spiky noises that arise from rotational deformation in solids. It also allows us to integrate physically based rendering to augment the dynamic surface reflections on fluids. Consequently, our framework is capable of realistically reproducing surface highlights on dynamic fluids and facilitating interactions between scene objects and fluids from new views. For more information, please visit our project page at \url{https://amysteriouscat.github.io/GaussianSplashing/}.
Abstract:We show that physics-based simulations can be seamlessly integrated with NeRF to generate high-quality elastodynamics of real-world objects. Unlike existing methods, we discretize nonlinear hyperelasticity in a meshless way, obviating the necessity for intermediate auxiliary shape proxies like a tetrahedral mesh or voxel grid. A quadratic generalized moving least square (Q-GMLS) is employed to capture nonlinear dynamics and large deformation on the implicit model. Such meshless integration enables versatile simulations of complex and codimensional shapes. We adaptively place the least-square kernels according to the NeRF density field to significantly reduce the complexity of the nonlinear simulation. As a result, physically realistic animations can be conveniently synthesized using our method for a wide range of hyperelastic materials at an interactive rate. For more information, please visit our project page at https://fytalon.github.io/pienerf/.