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 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.CCS Concepts: • Computing methodologies → Physical simulation; Dimensionality reduction and manifold learning.

Simulating stiff materials in applications where deformations are either not significant or else can safely be ignored is a fundamental task across fields. Rigid body modeling has thus long remained a critical tool and is, by far, the most popular simulation strategy currently employed for modeling stiff solids. At the same time, rigid body methods continue to pose a number of well known challenges and trade-offs including intersections, instabilities, inaccuracies, and/or slow performances that grow with contact-problem complexity. In this paper we revisit the stiff body problem and present ABD, a simple and highly effective affine body dynamics framework, which significantly improves state-of-the-art for simulating stiff-body dynamics. We trace the challenges in rigid-body methods to the necessity of linearizing piecewise-rigid trajectories and subsequent constraints. ABD instead relaxes the unnecessary (and unrealistic) constraint that each body's motion be exactly rigid with a stiff orthogonality potential, while preserving the rigid body model's key feature of a small coordinate representation. In doing so ABD replaces piecewise linearization with piecewise linear trajectories. This, in turn, combines the best of both worlds: compact coordinates ensure small, sparse system solves, while piecewise-linear trajectories enable efficient and accurate constraint (contact and joint) evaluations. Beginning with this simple foundation, ABD preserves all guarantees of the underlying IPC model we build it upon, e.g., solution convergence, guaranteed non-intersection, and accurate frictional contact. Over a wide range and scale of simulation problems we demonstrate that ABD brings orders of magnitude performance gains (two- to three-orders on the CPU and an order more when utilizing the GPU, obtaining 10, 000× speedups) over prior IPC-based methods, while maintaining simulation quality and nonintersection of trajectories. At the same time ABD has comparable or faster timings when compared to state-of-the-art rigid body libraries optimized for performance without guarantees, and successfully and efficiently solves challenging simulation problems where both classes of prior rigid body simulation methods fail altogether.

In recent years, the research into automatic aided detection systems for pulmonary nodules has been extremely active. Most of the existing studies are based on 2D convolution neural networks, which cannot make full use of computed tomography’s (CT) 3D spatial information. To address this problem, a computer-aided detection (CAD) system for lung nodules based on a 3D residual network (3D-ResNet) inspired by cognitive science is proposed in this paper. In this system, we feed the slice information extracted from three different axis planes into the U-NET network set, and make the joint decision to generate a candidate nodule set, which is the input of the proposed 3D residual network after extraction. We extracted 3D samples with 40, 44, 48, 52, and 56 mm sides from each candidate nodule in the candidate set and feed them into the trained residual network to get the probability of positive nodule after re-sampling the 3D sample to 48 × 48 × 48 mm 3 . Finally, a joint judgment is made based on the probabilities of five 3D samples of different sizes to obtain the final result. Random rotation and translation and data amplification technology are used to prevent overfitting during network training. The detection intensity on the largest public data set (i.e., the Lung Image Database Consortium and Image Database Resource Initiative—LIDC-IDRI) reached 86.5% and 92.3% at 1 frame per second (FPs) and 4 FPs respectively using our algorithm, which is better than most CAD systems using 2D convolutional neural networks. In addition, a 3D residual network and a multi-section 2D convolution neural network were tested on the unrelated Tianchi dataset. The results indicate that 3D-ResNet has better feature extraction ability than multi-section 2D-ConvNet and is more suitable for reduction of false positive nodules.

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 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.