Learning Contact Corrections for Handle-Based Subspace Dynamics

Cristian Romero, Dan Casas, Jesús Pérez and Miguel A. Otaduy
ACM Transactions on Graphics (Proc. of SIGGRAPH), 2021


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 contact-driven 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.


@article {romero2021subspacelearning,
    author  = {Romero, Cristian and Casas, Dan and Pérez, Jesús and Otaduy, Miguel A.},
    title   = {{Learning Contact Corrections for Handle-Based Subspace Dynamics}},
    number  = "4",
    volume  = "40",
    journal = {ACM Transactions on Graphics (Proc. of ACM SIGGRAPH)},
    year    = {2021}


We introduce a novel subspace method for the simulation of dynamic deformations.

Subspace simulation models define a compact space for animating complex objects, without the constraints of mesh resolution. Solving the equations of motion in a reduced deformation subspace they have demonstrated the ability to produce expressive simulations under low computational cost. However, these methods are not free of limitations, as they suffer to produce high-frequency details, e.g., resulting from contact.

As an improvement, we augment handle-based linear subspace formulations with nonlinear learned corrections parameterized by the same subspace. Combining the features of subspace and learning models, we achieve dynamic simulations with unprecedented combination of speed and contact-driven deformation detail.

Our nonlinear corrections are learned in the local undeformed configuration, defining an efficient subspace dependent mapping to the global setting. This decision, along with a compact parametrization of subspace handles and external interactions, results in a model with improved generalization capabilities. Internal and external contact-driven corrections are independently learned and aggregated, resulting in smaller and more specialized learning architectures. Relying on this separation, we have also designed an efficient data-generation pipeline, simplifying considerably the sampling of representative training data.


For additional results and comparisons, check the supplementary video.


We wish to thank the anonymous reviewers for their helpful comments. We also thank Igor Santesteban for help with the comparisons, and Jorge López for the artwork in the worm and jelly examples. This work was funded in part by the European Research Council (ERC Consolidator Grant 772738 TouchDesign) and the Spanish Ministry of Science (grant RTI2018-098694-B-I00 VizLearning).


Cristian Romero – crisrom002@gmail.com
Dan Casas – dan.casas@urjc.es
Jesús Pérez – jesus.prod@gmail.com
Miguel A. Otaduy – miguel.otaduy@urjc.es