Learning contact corrections for handle-based subspace dynamics

Abstract

Fig. 1. The left images show a dynamic simulation of an FEM Neo-Hookean jelly with 12,469 triangles. The deformation is rich but slow (20 fps). The central images show the same scene using a linear subspace model built with just 8 point handles. The simulation is fast (420 fps), but it misses all the detail and suffers distortion under moderate forces. The right images show the result with our model, which augments the linear model with nonlinear learning-based corrections. We retain fast dynamics close to the linear model (140 fps), but we recover the detailed contact-driven deformations of the full model.This paper introduces a novel subspace method for the simulation of dynamic deformations. The method augments existing linear handle-based subspace formulations with nonlinear learning-based corrections parameterized by the same subspace. Together, they produce a compact nonlinear model that combines the fast dynamics and overall contact-based interaction of subspace methods, with the highly detailed deformations of learning-based methods. We propose a formulation of the model with nonlinear corrections applied on the local undeformed setting, and decoupling internal and external contactdriven corrections. We define a simple mapping of these corrections to the global setting, an efficient implementation for dynamic simulation, and a training pipeline to generate examples that efficiently cover the interaction space. Altogether, the method achieves unprecedented combination of speed and contact-driven deformation detail.

Neural Jacobian Fields: Learning Intrinsic Mappings of Arbitrary Meshes

“…Many methods focus on a single mesh, or a set of variations of the same mesh [Bogo et al 2014;Osman et al 2020;Varol et al 2017;Zuffi et al 2017], and define an arbitrary fixed correspondence of vertices and/or faces to the entries of a predicted tensor, thereby enabling machine learning algorithms to associate predicted quantities to geometric elements. This enables treating the input and output as general tensors of a homogeneous dataset and applying off-the-shelf tools for data analysis, such as Principal Component Analysis [Anguelov et al 2005], Gaussian Mixture Models [Bogo et al 2016], as well as neural networks, which assign per-vertex coordinates [Shen et al 2021] or offsets from a simpler (e.g., linear) model [Bailey et al 2020[Bailey et al , 2018Romero et al 2021;Yin et al 2021;Zheng et al 2021]. As they are not shape-aware in the sense discussed in Section 1, such methods often need to add additional regularizers such as ARAP [Sun et al 2021] or the Laplacian [Kanazawa et al 2018].…”

“…Learning collision handling. We compare our method to [Romero et al 2021] on collision handling, using their data to train and test. Predictions are overlaid over the ground-truth in the zoom-ins.…”

“…Learning collision handling. [Romero et al 2021] propose an elegant method to train networks to produce non-linear offsets from a linear deformation model so as to account for non-linear behavior due to object collisions, by feeding the network the positions of the collider, along with the handles' positions. We train on their data with the same input as them and optimize for 𝑙 total , without introducing any changes to our architecture.…”

Collision-aware interactive simulation using graph neural networks

“…Deep simulation methods have emerged as popular alternatives to traditional numerical calculation methods owing to the rapid development of deep learning techniques. These methods [ 1 – 4 ] use the ability of neural networks to learn nonlinear functions to propose differentiable models that output deformable objects as functions of the target shape, pose, motion, and other design parameters. However, these methods perform poorly in collision detection and response (CDR), which has a significant impact on visual realism and simulation accuracy.…”

“…For nonlinear elastic deformation, Holden et al [ 1 ] combined subspace simulation techniques with machine learning to support interactions with external objects. Romero et al [ 4 ] used a model formula with nonlinear corrections applied to the local undeformable setting and decoupled internal and external contact-driven corrections.…”