JGS2 is a Jacobi-like GPU simulation algorithm. It avoids the overshooting issue by augmenting each subproblem with a perturbation subspace that predicts the global influence of the local solve. The efficiency of JGS2 is due to Cubature-based subspace integration at each subproblem. Being a data-driven method, Cubature requires a set of representative deformed poses that cover deformations likely to occur in the simulation. This requirement is unlikely for high-resolution deformation with rich local details. Therefore, simulation performance and convergence degenerate when Cubature extrapolates. This paper proposes a training-free subspace integration algorithm based on classic Gaussian quadrature (GQ). We leverage the fact that the subproblem's subspace bases can be well-approximated by a low-degree multivariable polynomial, which suggests GQ an excellent candidate for Cubature substitute. To this end, we introduce a novel algorithm that adaptively generates the integration region for each subproblem. As a result, GQ integration can be analytically retrieved without cumbersome data generation and training. We also show how to handle frictional contact by modifying the pre-computed perturbation subspace. The resulting JGS2-GQ framework is more versatile than the vanilla JGS2 method. It is more stable for large and novel deformations, and is free of data generation and expensive training, while maintaining a near second-order convergence that is comparable to Newton. Performance-wise, JGS2-GQ is as efficient as JGS2, which is three orders faster than classic CPU methods and up to two orders faster than classic GPU algorithms. When novel deformation occurs, JGS2-GQ outperforms JGS2 over 50%.

Simulating heterogeneous multibody systems with both deformable and stiff components remains a challenge for GPU solvers. While Newton-Krylov methods are popular for their matrix-free nature and good GPU compatibility, they often suffer from severe ill-conditioning and slow convergence when handling stiff contacts and material disparities in deformable multibody systems. In this paper, we present Heterogeneous Subspace Corrections (HSC), a novel Newton-CG variant to efficiently simulate such complex systems. HSC decouples the system into two Krylov iterations: a Newton-CG procedure for deformable bodies and a Neumann-based iteration for the affine subsystem. We introduce a GPU-based Adaptive Cross Approximation (ACA) algorithm to exploit the low-rank nature of the coupling matrices, which manages to reduce the overhead of sparse matrix-vector multiplications substantially on the GPU. For the affine subsystem, we propose a dedicated data structure for fast assembling contact Hessians in parallel. A variety of experimental results demonstrate that our framework consistently outperforms existing GPU simulators, achieving convergence rates comparable to direct solvers even in scenes with high-resolution models and extensive stiff contacts.

Simulating large-scale articulated assemblies poses a significant challenge due to the numerical stiffness and geometric complexity of jointed structures. Conventional rigid body solvers struggle with the high nonlinearity induced by rotation parameterization. This difficulty becomes more pronounced for multiple two-way-coupled bodies. This paper introduces a novel framework that leverages the linear kinematic mapping of Affine Body Dynamics (ABD). As ABD targets near-rigid objects, the constitutive variations of different materials become negligible, which justifies a co-rotational approach to isolate geometric nonlinearities of the system. This insight enables the use of constant system matrices that can be pre-factorized throughout the simulation, even with fully implicit integration schemes. To manage the high DOF counts of large-scale systems, we map primal body coordinates onto a compact dual space defined by minimal joint degrees of freedom. By solving the resulting KKT systems, our method ensures exact constraint enforcement and physically accurate motion propagation. We provide a suite of specialized solvers tailored for diverse joint topologies, including chains, trees, closed loops, and irregular networks. Experimental results show that our approach achieves interactive rates for systems with hundreds of thousands of bodies on a single CPU core, while maintaining excellent stability at large time steps.

While yarn-level garments offer rich dynamic details and compelling visual realism compared to triangle-based models, their wide adoption is hindered by the immense computational cost due to the presence of a large number of degrees of freedom (DOFs). This paper proposes a novel simulation framework designed to enhance the performance and stability for numerical simulation of nonlinear, non-convex, and high-resolution knitwear. Our method generalizes the Douglas-Rachford Splitting (DRS) scheme to resolve the non-convex coupling between stretching, shearing, bending, twisting, and contacting at each yarn thread. A key contribution is a nested decomposition strategy that decouples the non-convex variational energy into independent and convex sub-problems. Such convexification improves solver robustness and removes the necessity for frequent line searches. We provide a theoretically grounded strategy for metric selection for each sub-problem, derived from an analysis of the convergence guarantee of DRS. Consequently, our method achieves close-to-optimal convergence along the nonlinear iterations rather than relying on ad-hoc parameter tuning. The paper also clarifies a formal connection between our generalized DRS and the ADMM (Alternating Direction Method of Multipliers) framework, extending the applicability of our analysis to a broader set of constrained dynamics problems. Experimental results demonstrate that our method robustly handles complex knitwear simulation scenes with superior efficiency, stability, and physical fidelity compared to existing methods. With a matrix-free GPU parallelization, our method allows an interactive simulation rate of knitwear of multi-million DOFs.

With the rise of digital fashion, reusing high-quality garment assets to assemble new outfits has become increasingly important for improving design efficiency and reducing production costs. However, combining multiple garments often introduces complex inter-garment intersections that are difficult to resolve. In this paper, we propose a novel framework that introduces a midsurface representation to simplify multilayered garments for intersection-free outfit assembly. Each garment is approximated by a watertight tetrahedral enclosure, enabling efficient resolution of inter-garment collisions on the midsurface level. To assemble an outfit, our method progressively untangles pairs of single-layer midsurfaces and incrementally constructs a merged midsurface. To recover the intersection-free full geometry from these deformed midsurfaces and enable instantaneous transfer across different poses, we uses embedded anchors to drive inversion-free deformation of enclosing tetrahedral cages. Through various examples, we demonstrate that our method provides a scalable and automated solution for virtual outfit coordination, enabling the direct reuse of garment assets in high-fidelity, collision-free digital fashion workflows.

To bridge the gap between artists and non-specialists, we present a unified framework, Neural-Polyptych, to facilitate the creation of expansive, high-resolution paintings by seamlessly incorporating interactive hand-drawn sketches with fragments from original paintings. We have designed a multi-scale GAN-based architecture to decompose the generation process into two parts, each responsible for identifying global and local features. To enhance the fidelity of semantic details generated from users' sketched outlines, we introduce a Correspondence Attention module utilizing our Reference Bank strategy. This ensures the creation of high-quality, intricately detailed elements within the artwork. The final result is achieved by carefully blending these local elements while preserving coherent global consistency. Consequently, this methodology enables the production of digital paintings at megapixel scale, accommodating diverse artistic expressions and enabling users to recreate content in a controlled manner. We validate our approach to diverse genres of both Eastern and Western paintings. Applications such as large painting extension, texture shuffling, genre switching, mural art restoration, and recomposition can be successfully based on our framework.

Meshless simulation of elasticity is important for deformable simulation in computer graphics. While shape matching is a popular meshless solution, it is limited to a subset of elastic constitutive models, challenging the simulation of generic elastic constitutive models using meshless integration. In contrast, peridynamics offers a more versatile capacity and can describe various material behavior through non-local interactions between vertices. However, the size of each stencil Hessian matrix varies with the number of nearby integration points, leading to inefficiency and accuracy loss. To address these challenges, we present an efficient and robust solver for generic elastic models based on peridynamics. We propose an efficient first-order Hessian proxy derived from the positive-negative decomposition of the stress tensor. The proposed symmetric positive definite proxies ensure convergence within a reasonable number of iterations while also being easy to parallelize on GPU. To further enhance stability, particularly for hyperelastic models, we propose enforcing strain limiting between peridynamics bonds to prevent tensile instability in meshless integration. Our algorithm includes two iteration loops of strain limiting and elastic Jacobis, and the pipeline is well-suited for GPU implementation. We evaluated the performance of our approach with a wide range of elastic constitutive models in diverse testing scenarios against the alternative numerical solvers. Our method features superior efficiency and faster convergence compared to existing numerical solvers. These compelling results underscore the practicality and effectiveness of our method for simulating elasticity via meshless integration.

We propose a GPU-based iterative method for accelerated elastodynamic simulation with the log-barrier-based contact model. While Newton's method is a conventional choice for solving the interior-point system, the presence of ill-conditioned log barriers often necessitates a direct solution at each linearized substep and costs substantial storage and computational overhead. Moreover, constraint sets that vary in each iteration present additional challenges in algorithm convergence. Our method employs a novel barrier-augmented Lagrangian method to improve system conditioning and solver efficiency by adaptively updating an augmentation constraint sets. This enables the utilization of a scalable, inexact Newton-PCG solver with sparse GPU storage, eliminating the need for direct factorization. We further enhance PCG convergence speed with a domain-decomposed warm start strategy based on an eigenvalue spectrum approximated through our in-time assembly. Demonstrating significant scalability improvements, our method makes simulations previously impractical on 128 GB of CPU memory feasible with only 8 GB of GPU memory and orders-of-magnitude faster. Additionally, our method adeptly handles stiff problems, surpassing the capabilities of existing GPU-based interior-point methods. Our results, validated across various complex collision scenarios involving intricate geometries and large deformations, highlight the exceptional performance of our approach.

Crowd counting is widely used in real-time congestion monitoring and public security. Due to the limited data, many methods have little ability to be generalized because the differences between feature domains are not taken into consideration. We propose VGG-embedded adaptive layer normalization (VadaLN) to filter the features that irrelevant to the counting tasks in order that the counting results should not be affected by the image quality, color or illumination. VadaLN is implemented on the pretrained VGG-16 backbone. There is no additional learning parameters required through our method. VadaLN incoporates the proposed scale-shuffling modules (SSM) to relax the distortions in upsampling operations. Besides, nonaligned training methdology for the estimation of density maps is leveraged by an adversarial contextual loss (ACL) to improve the counting performance. Based on the proposed method, we construct an end-to-end trainable baseline model without bells and whistles, namely VadaLNet, which outperforms several recent state-of-the-art methods on commonly used challenging standard benchmarks. The intermediate scale-shuffled results are combined to formulate a scale-complementary strategy as a more powerful network, namely as VadaLNeSt. We implement VadaLNeSt on standard benchmarks, e.g. ShanghaiTech (Part A & Part B), UCF_CC_50, and UCF_QNRF, to show the superiority of our method.