arXiv subjects

Lei Lan

Publications and source records attributed to Lei Lan.

13 recordsLinked to original sources

arXiv2026

Curly Hair Simulation using Curly Finite Elements

Realistic simulation of curly hair is challenging due to the tight coupling between macroscopic strand deformation and high-frequency geometric details such as waves and helices. In this paper, we propose a curly hair model that decomposes each strand into curly elements, consisting of a rod-base configuration and an analytically defined high-frequency wrinkles represented by planar waves or volumetric helices, with deformation governed primarily by bending for wavy hair and twisting for spiral hair. A curvature-energy splitting scheme separates stretching, buckling, and bending contributions, and efficient energy approximations improve numerical robustness and reduce computational cost without degrading visual fidelity. We further introduce a hybrid collision handling strategy that combines coarse collision proxies for the base configuration with analytical treatment of high-frequency details, and adapt guide-strand interpolation to our curly finite-element representation to generate dense hair while preserving fine structure. Experiments demonstrate stable, efficient, and visually faithful simulation of curly hair across diverse scenarios.

cs.GR↗

arXiv2026

Distributed Affine Body Dynamics with Adaptive Consensus

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.

cs.GR↗

arXiv2025

JGS2: Near Second-order Converging Jacobi/Gauss-Seidel for GPU Elastodynamics

In parallel simulation, convergence and parallelism are often seen as inherently conflicting objectives. Improved parallelism typically entails lighter local computation and weaker coupling, which unavoidably slow the global convergence. This paper presents a novel GPU algorithm that achieves convergence rates comparable to fullspace Newton's method while maintaining good parallelizability just like the Jacobi method. Our approach is built on a key insight into the phenomenon of overshoot. Overshoot occurs when a local solver aggressively minimizes its local energy without accounting for the global context, resulting in a local update that undermines global convergence. To address this, we derive a theoretically second-order optimal solution to mitigate overshoot. Furthermore, we adapt this solution into a pre-computable form. Leveraging Cubature sampling, our runtime cost is only marginally higher than the Jacobi method, yet our algorithm converges nearly quadratically as Newton's method. We also introduce a novel full-coordinate formulation for more efficient pre-computation. Our method integrates seamlessly with the incremental potential contact method and achieves second-order convergence for both stiff and soft materials. Experimental results demonstrate that our approach delivers high-quality simulations and outperforms state-of-the-art GPU methods with 50 to 100 times better convergence.

cs.GR↗

arXiv2025

3DGS$^2$: Near Second-order Converging 3D Gaussian Splatting

3D Gaussian Splatting (3DGS) has emerged as a mainstream solution for novel view synthesis and 3D reconstruction. By explicitly encoding a 3D scene using a collection of Gaussian kernels, 3DGS achieves high-quality rendering with superior efficiency. As a learning-based approach, 3DGS training has been dealt with the standard stochastic gradient descent (SGD) method, which offers at most linear convergence. Consequently, training often requires tens of minutes, even with GPU acceleration. This paper introduces a (near) second-order convergent training algorithm for 3DGS, leveraging its unique properties. Our approach is inspired by two key observations. First, the attributes of a Gaussian kernel contribute independently to the image-space loss, which endorses isolated and local optimization algorithms. We exploit this by splitting the optimization at the level of individual kernel attributes, analytically constructing small-size Newton systems for each parameter group, and efficiently solving these systems on GPU threads. This achieves Newton-like convergence per training image without relying on the global Hessian. Second, kernels exhibit sparse and structured coupling across input images. This property allows us to effectively utilize spatial information to mitigate overshoot during stochastic training. Our method converges an order faster than standard GPU-based 3DGS training, requiring over $10\times$ fewer iterations while maintaining or surpassing the quality of the compared with the SGD-based 3DGS reconstructions.

cs.CV↗

arXiv2024

XPBI: Position-Based Dynamics with Smoothing Kernels Handles Continuum Inelasticity

PBD and its extension, XPBD, have been predominantly applied to compliant constrained elastodynamics, with their potential in finite strain (visco-) elastoplasticity remaining underexplored. XPBD is often perceived to stand in contrast to other meshless methods, such as the MPM. MPM is based on discretizing the weak form of governing partial differential equations within a continuum domain, coupled with a hybrid Lagrangian-Eulerian method for tracking deformation gradients. In contrast, XPBD formulates specific constraints, whether hard or compliant, to positional degrees of freedom. We revisit this perception by investigating the potential of XPBD in handling inelastic materials that are described with classical continuum mechanics-based yield surfaces and elastoplastic flow rules. Our inspiration is that a robust estimation of the velocity gradient is a sufficiently useful key to effectively tracking deformation gradients in XPBD simulations. By further incorporating implicit inelastic constitutive relationships, we introduce a plasticity in-the-loop updated Lagrangian augmentation to XPBD. This enhancement enables the simulation of elastoplastic, viscoplastic, and granular substances following their standard constitutive laws. We demonstrate the effectiveness of our method through high-resolution and real-time simulations of diverse materials such as snow, sand, and plasticine, and its integration with standard XPBD simulations of cloth and water.

cs.GR↗

arXiv2024

ElastoGen: 4D Generative Elastodynamics

We present ElastoGen, a knowledge-driven AI model that generates physically accurate 4D elastodynamics. Unlike deep models that learn from video- or image-based observations, ElastoGen leverages the principles of physics and learns from established mathematical and optimization procedures. The core idea of ElastoGen is converting the differential equation, corresponding to the nonlinear force equilibrium, into a series of iterative local convolution-like operations, which naturally fit deep architectures. We carefully build our network module following this overarching design philosophy. ElastoGen is much more lightweight in terms of both training requirements and network scale than deep generative models. Because of its alignment with actual physical procedures, ElastoGen efficiently generates accurate dynamics for a wide range of hyperelastic materials and can be easily integrated with upstream and downstream deep modules to enable end-to-end 4D generation.

cs.LG↗

arXiv2024

Volumetric Homogenization for Knitwear Simulation

This paper presents volumetric homogenization, a spatially varying homogenization scheme for knitwear simulation. We are motivated by the observation that macro-scale fabric dynamics is strongly correlated with its underlying knitting patterns. Therefore, homogenization towards a single material is less effective when the knitting is complex and non-repetitive. Our method tackles this challenge by homogenizing the yarn-level material locally at volumetric elements. Assigning a virtual volume of a knitting structure enables us to model bending and twisting effects via a simple volume-preserving penalty and thus effectively alleviates the material nonlinearity. We employ an adjoint Gauss-Newton formulation to battle the dimensionality challenge of such per-element material optimization. This intuitive material model makes the forward simulation GPU-friendly. To this end, our pipeline also equips a novel domain-decomposed subspace solver crafted for GPU projective dynamics, which makes our simulator hundreds of times faster than the yarn-level simulator. Experiments validate the capability and effectiveness of volumetric homogenization. Our method produces realistic animations of knitwear matching the quality of full-scale yarn-level simulations. It is also orders of magnitude faster than existing homogenization techniques in both the training and simulation stages.

cs.GR↗

arXiv2024

Efficient GPU Cloth Simulation with Non-distance Barriers and Subspace Reuse

This paper pushes the performance of cloth simulation, making the simulation interactive even for high-resolution garment models while keeping every triangle untangled. The penetration-free guarantee is inspired by the interior point method, which converts the inequality constraints to barrier potentials. We propose a major overhaul of this modality within the projective dynamics framework by leveraging an adaptive weighting mechanism inspired by barrier formulation. This approach does not depend on the distance between mesh primitives, but on the virtual life span of a collision event and thus keeps all the vertices within feasible region. Such a non-distance barrier model allows a new way to integrate collision resolution into the simulation pipeline. Another contributor to the performance boost comes from the subspace reuse strategy. This is based on the observation that low-frequency strain propagation is near orthogonal to the deformation induced by collisions or self-collisions, often of high frequency. Subspace reuse then takes care of low-frequency residuals, while high-frequency residuals can also be effectively smoothed by GPU-based iterative solvers. We show that our method outperforms existing fast cloth simulators by at least one order while producing high-quality animations of high-resolution models.

cs.GR↗

arXiv2022

Affine Body Dynamics: Fast, Stable & Intersection-free Simulation of Stiff Materials

Simulating stiff materials in applications where deformations are either not significant or can safely be ignored is a pivotal task across fields. Rigid body modeling has thus long remained a fundamental tool and is, by far, the most popular simulation strategy currently employed for modeling stiff solids. At the same time, numerical models of a rigid body continue to pose a number of known challenges and trade-offs including intersections, instabilities, inaccuracies, and/or slow performances that grow with contact-problem complexity. In this paper we revisit this problem and present ABD, a simple and highly effective affine body dynamics framework, which significantly improves state-of-the-art stiff simulations. We trace the challenges in the rigid-body IPC (incremental potential contact) method to the necessity of linearizing piecewise-rigid (SE(3)) 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 from both parties: 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 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-order on the CPU and an order more utilizing the GPU, which is 10,000x speedups) over prior IPC-based methods with a similar or higher simulation quality.

cs.GR↗

arXiv2021

High-order Differentiable Autoencoder for Nonlinear Model Reduction

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.

cs.LG↗

arXiv2019

Neptune's resonances in the Scattered Disk

The Scattered Disk Objects (SDOs) are thought to be a small fraction of the ancient population of leftover planetesimals in the outer solar system that were gravitationally scattered by the giant planets and have managed to survive primarily by capture and sticking in Neptune's exterior mean motion resonances (MMRs). In order to advance understanding of the role of MMRs in the dynamics of the SDOs, we investigate the phase space structure of a large number of Neptune's MMRs in the semi-major axis range 33--140~au by use of Poincaré sections of the circular planar restricted three body model for the full range of particle eccentricity pertinent to SDOs. We find that, for eccentricities corresponding to perihelion distances near Neptune's orbit, distant MMRs have stable regions with widths that are surprisingly large and of similar size to those of the closer-in MMRs. We identify a phase-shifted second resonance zone that exists in the phase space at planet-crossing eccentricities but not at lower eccentricities; this second resonance zone plays an important role in the dynamics of SDOs in lengthening their dynamical lifetimes. Our non-perturbative measurements of the sizes of the stable resonance zones confirm previous results and provide an additional explanation for the prominence of the $N$:1 sequence of MMRs over the $N$:2, $N$:3 sequences and other MMRs in the population statistics of SDOs; our results also provide a tool to more easily identify resonant objects.

astro-ph.EP↗

arXiv2018

Neptune's 5:2 Resonance in the Kuiper Belt

Observations of Kuiper belt objects (KBOs) in Neptune's 5:2 resonance present two puzzles: this third order resonance hosts a surprisingly large population, comparable to the prominent populations of Plutinos and Twotinos in the first order 3:2 and 2:1 resonances, respectively; secondly, their eccentricities are concentrated near $0.4$. To shed light on these puzzles, we investigate the phase space near this resonance with use of Poincaré sections of the circular planar restricted three body model. We find several transitions in the phase space structure with increasing eccentricity, which we explain with the properties of the resonant orbit relative to Neptune's. The resonance width is narrow for very small eccentricities, but widens dramatically for $e\gtrsim0.2$, reaching a maximum near $e\approx0.4$, where it is similar to the maximum widths of the 2:1 and 3:2 resonances. We confirm these results with N-body numerical simulations, including the effects of all four giant planets and a wide range of orbital inclinations of the KBOs. We find that the boundaries of the stable resonance zone are not strongly sensitive to inclination and remain very similar to those found with the simplified three body model, with the caveat that orbits of eccentricity above $\sim0.53$ are unstable; higher eccentricity orbits are phase-protected from destabilizing encounters with Neptune but not with Uranus. These results show that the 5:2 resonant KBOs are not more puzzling than the Plutinos and Twotinos; however, detailed understanding of the origins of eccentric, inclined resonant KBOs remains a challenge.

astro-ph.EP↗

arXiv2015

Debris Engine: A Potential Thruster for Space Debris Removal

We present a design concept for a space engine that can continuously remove the orbit debris by using the debris as a propellant. Space robotic cleaner is adopted to capture the targeting debris and to transfer them into the engine. Debris with larger size is first disintegrated into small pieces by using a mechanical method. The planetary ball mill is then adopted to grind the pieces into micrometer or smaller powder. The energy needed in this process is get from the nuclear and solar power. By the effect of gamma-ray photoelectric or the behavior of tangently rub of tungsten needles, the debris powered is charged. This behavior can be used to speed up the movement of powder in a tandem electrostatic particle accelerator. By ejecting the high-temperture and high-pressure charged powered from the nozzle of the engine,the continuously thrust is obtained. This thrust can be used to perform orbital maneuver and debris rendezvous for the spacecraft and robotic cleaner. The ejected charged particle will be blown away from the circumterrestrial orbit by the solar wind. By digesting the space debris, we obtain not only the previous thrust but also the clean space. In the near future, start trek will not just a dream, human exploration will extend to deep universe. The analysis shown, the magnitude of the specific impulse for debris engine is determined by the accelerating electrostatic potential and the charge-to-mass ratio of the powder.

astro-ph.IM↗