Simplicits：无网格、几何无关的弹性模拟
Simplicits: Mesh-Free, Geometry-Agnostic, Elastic Simulation
AI总结：
该研究提出无网格、几何无关的弹性模拟方法Simplicits，以占据函数为通用接口，通过小型隐式神经网络构建降维形变基，可适配多种3D表示与物理模拟设置，兼具通用性、准确性和速度优势。
摘要：
从显式网格到隐式神经场等各类3D表示的涌现，催生了对不受表示形式限制的模拟器的需求。我们提出了一种无数据、无网格、无网格格点的弹性模拟方案，适用于任意几何表示的、发生大尺度非线性形变的任意物体。我们指出，每一种标准几何表示都可简化为能在空间任意点查询的占据函数，并在此通用接口之上定义了模拟器。针对每个物体，我们拟合一个小型隐式神经网络，用于编码充当降维形变基的空间变化权重。这些权重通过随机扰动训练，以学习物体中具有物理意义的运动。我们的损失函数通过对形变量进行蒙特卡洛采样来随机评估弹性能，确保找到能最小化形变能的权重空间基。运行时，我们在降维基中进行模拟，再将形变采样回原始域。我们的实验在有符号距离函数、点云、神经基元、断层扫描、辐射场、高斯溅射、表面网格和体网格等数据上验证了该方法的通用性、准确性和速度，同时还展示了其适配多种材料能量、接触模型和时间积分方案的能力。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
