Lei Lan

Jiafeng Liu, Wenhui Zhou, Xinming Pei et al.

Affine Body Dynamics (ABD) within the Incremental Potential Contact (IPC) framework provides accurate simulation of extremely stiff solids exhibiting near-rigid behavior, with strict non-penetration guarantees. However, IPC's globally coupled barrier constraints hinder scalable execution across multiple GPUs and compute nodes. We propose a distributed formulation of ABD using a consensus-based ADMM scheme. Each compute node solves its local ABD subproblem in parallel, followed by a global consensus step that enforces consistency among shared boundary bodies. The proposed method preserves IPC-level robustness and global consistency under distributed execution. Experiments demonstrate stable convergence, non-penetration, and efficient scaling on large-scale scenes across multiple nodes.

Siyuan Shen, Yang Yin, Tianjia Shao et al.

This paper provides a new avenue for exploiting deep neural networks to improve physics-based simulation. Specifically, we integrate the classic Lagrangian mechanics with a deep autoencoder to accelerate elastic simulation of deformable solids. Due to the inertia effect, the dynamic equilibrium cannot be established without evaluating the second-order derivatives of the deep autoencoder network. This is beyond the capability of off-the-shelf automatic differentiation packages and algorithms, which mainly focus on the gradient evaluation. Solving the nonlinear force equilibrium is even more challenging if the standard Newton's method is to be used. This is because we need to compute a third-order derivative of the network to obtain the variational Hessian. We attack those difficulties by exploiting complex-step finite difference, coupled with reverse automatic differentiation. This strategy allows us to enjoy the convenience and accuracy of complex-step finite difference and in the meantime, to deploy complex-value perturbations as collectively as possible to save excessive network passes. With a GPU-based implementation, we are able to wield deep autoencoders (e.g., $10+$ layers) with a relatively high-dimension latent space in real-time. Along this pipeline, we also design a sampling network and a weighting network to enable \emph{weight-varying} Cubature integration in order to incorporate nonlinearity in the model reduction. We believe this work will inspire and benefit future research efforts in nonlinearly reduced physical simulation problems.