Neural Stress Fields for Reduced-order Elastoplasticity and Fracture
Zeshun Zong Xuan Li Minchen Li Maurizio M. Chiaramonte Wojciech Matusik Eitan Grinspun Kevin Carlberg Chenfanfu Jiang Peter Yichen Chen
We propose a hybrid neural network and physics framework for reduced-order
modeling of elastoplasticity and fracture. State-of-the-art scientific
computing models like the Material Point Method (MPM) faithfully simulate
large-deformation elastoplasticity and fracture mechanics. However, their long
runtime and large memory consumption render them unsuitable for applications
constrained by computation time and memory usage, e.g., virtual reality. To
overcome these barriers, we propose a reduced-order framework. Our key
innovation is training a low-dimensional manifold for the Kirchhoff stress
field via an implicit neural representation. This low-dimensional neural stress
field (NSF) enables efficient evaluations of stress values and,
correspondingly, internal forces at arbitrary spatial locations. In addition,
we also train neural deformation and affine fields to build low-dimensional
manifolds for the deformation and affine momentum fields. These neural stress,
deformation, and affine fields share the same low-dimensional latent space,
which uniquely embeds the high-dimensional simulation state. After training, we
run new simulations by evolving in this single latent space, which drastically
reduces the computation time and memory consumption. Our general
continuum-mechanics-based reduced-order framework is applicable to any
phenomena governed by the elastodynamics equation. To showcase the versatility
of our framework, we simulate a wide range of material behaviors, including
elastica, sand, metal, non-Newtonian fluids, fracture, contact, and collision.
We demonstrate dimension reduction by up to 100,000X and time savings by up to
10X.