Simplicits: Mesh-Free, Geometry-Agnostic, Elastic Simulation
This addresses the need for flexible simulators in computer graphics and engineering that can handle multiple geometric representations without conversion, though it is incremental in adapting existing simulation techniques to a broader range of inputs.
The paper tackles the problem of elastic simulation for objects in diverse 3D representations by developing a mesh-free, geometry-agnostic method that uses implicit neural networks as a reduced deformation basis, achieving versatility, accuracy, and speed across various data types and simulation conditions.
The proliferation of 3D representations, from explicit meshes to implicit neural fields and more, motivates the need for simulators agnostic to representation. We present a data-, mesh-, and grid-free solution for elastic simulation for any object in any geometric representation undergoing large, nonlinear deformations. We note that every standard geometric representation can be reduced to an occupancy function queried at any point in space, and we define a simulator atop this common interface. For each object, we fit a small implicit neural network encoding spatially varying weights that act as a reduced deformation basis. These weights are trained to learn physically significant motions in the object via random perturbations. Our loss ensures we find a weight-space basis that best minimizes deformation energy by stochastically evaluating elastic energies through Monte Carlo sampling of the deformation volume. At runtime, we simulate in the reduced basis and sample the deformations back to the original domain. Our experiments demonstrate the versatility, accuracy, and speed of this approach on data including signed distance functions, point clouds, neural primitives, tomography scans, radiance fields, Gaussian splats, surface meshes, and volume meshes, as well as showing a variety of material energies, contact models, and time integration schemes.