arXiv subjects

David I. W. Levin

Publications and source records attributed to David I. W. Levin.

At least 19 recordsLinked to original sources

arXiv2026

Fluid Control with Localized Spacetime Windows

We present a physics-based fluid control method utilizing localized spacetime windows, extending force-based fluid control to substantially larger simulation scales. In many practical editing scenarios, user-specified objectives affect only a small region of an otherwise satisfactory simulation, resulting in optimal control force distributions that are highly sparse in both space and time. However, existing optimization-based fluid control methods typically solve for control forces over the entire spacetime domain, leading to unnecessarily high computational cost and poor scalability. Motivated by this observation, we restrict optimization to localized spacetime regions surrounding the edit of interest, significantly reducing the dimensionality of the control problem. Within this framework, control forces are parameterized on a coarse "floating" background grid, decoupling control degrees of freedom from simulation resolution and promoting smooth, physically plausible forces. We further analyze spacetime-window selection as a joint spatial-temporal problem. While the full problem can be formulated as a 2D search over spatial and temporal window extents, practical workflows can often leverage user-specified spatial regions and lightweight temporal-window selection strategies to reduce search cost. Our method enables a range of intuitive editing tasks, where sparse user inputs can induce coherent motion in surrounding fluid structures. We demonstrate the effectiveness and efficiency of our method with various 2D and 3D particle-based free-surface simulation examples.

cs.GR↗

arXiv2026

Adaptive Volumetric Mechanical Property Fields Invariant to Resolution

Accurate mechanical properties (or materials) Young's modulus ($E$), Poisson's ratio ($ν$) and density ($ρ$) are essential for reliable physics simulation of digital worlds, but most 3D assets lack this information. We propose AdaVoMP, a method for predicting accurate dense spatially-varying ($E$, $ν$, $ρ$) for input 3D objects across representations, improving the resolution, accuracy, and memory efficiency over the state-of-the-art. The foundation of our technique is a sparse and adaptive voxel structure SAV that efficiently represents both the input 3D shape and the material field output. We replace the fixed-voxel model of the most accurate prior method, VoMP, with a novel sparse transformer encoder-decoder model that learns to generate a unique SAV autoregressively for every input shape to represent its materials, achieving a resolution $16^3\times$ higher than prior art. Experiments show that AdaVoMP estimates more accurate volumetric properties, even with lesser test-time compute than all prior art. This allows us to convert high-resolution complex 3D objects into simulation-ready assets, resulting in realistic deformable simulations.

cs.CV↗

arXiv2026

FreeForm: Reduced-Order Deformable Simulation from Particle-Based Skinning Eigenmodes

We present a novel formulation for mesh-free, reduced-order simulation of deformable hyperelastic objects. Existing work in reduced-order elastodynamic simulation represents the input geometry by either meshes, which can be difficult to obtain due to challenges in scanning and triangulating complex shapes, or by neural fields that require per-shape optimization. We propose to adopt a Reproducing Kernel Particle Method (RKPM) representation, which enables the construction of reduced-order skinning weights by solving a generalized eigensystem on the Hessian matrix of the elastic energy. We demonstrate that this formulation not only leads to a 40x training speedup compared with the per-shape optimization of neural fields, but also achieves lower simulation error when evaluated against the converged results of finite element method. We show our simulation results on a wide variety of objects in different representations including meshes and Gaussian splats, as well as the application of our method in the downstream task of robot simulation.

cs.GR↗

arXiv2026

Differentiable Variable Fonts

Editing and animating text appearance for graphic designs, commercials, etc. remain highly skilled tasks requiring detailed, hands on efforts from artists. Automating these manual workflows requires balancing the competing goals of maintaining legibility and aesthetics of text, while enabling creative expression. Variable fonts, recent parametric extensions to traditional fonts, offer the promise of new ways to ease and automate typographic design and animation. Variable fonts provide custom constructed parameters along which fonts can be smoothly varied. These parameterizations could then potentially serve as high value continuous design spaces, opening the door to automated design optimization tools. However, currently variable fonts are underutilized in creative applications, because artists so far still need to manually tune font parameters. Our work opens the door to intuitive and automated font design and animation workflows with differentiable variable fonts. To do so we distill the current variable font specification to a compact mathematical formulation that differentiably connects the highly non linear, non invertible mapping of variable font parameters to the underlying vector graphics representing the text. This enables us to construct a differentiable framework, with respect to variable font parameters, allowing us to perform gradient based optimization of energies defined on vector graphics control points, and on target rasterized images. We demonstrate the utility of this framework with four applications: direct shape manipulation, overlap aware modeling, physics based text animation, and automated font design optimization. Our work now enables leveraging the carefully designed affordances of variable fonts with differentiability to use modern design optimization technologies, opening new possibilities for easy and intuitive typographic design workflows.

cs.GR↗

arXiv2026

VoMP: Predicting Volumetric Mechanical Property Fields

Physical simulation relies on spatially-varying mechanical properties, often laboriously hand-crafted. VoMP is a feed-forward method trained to predict Young's modulus ($E$), Poisson's ratio ($ν$), and density ($ρ$) throughout the volume of 3D objects, in any representation that can be rendered and voxelized. VoMP aggregates per-voxel multi-view features and passes them to our trained Geometry Transformer to predict per-voxel material latent codes. These latents reside on a manifold of physically plausible materials, which we learn from a real-world dataset, guaranteeing the validity of decoded per-voxel materials. To obtain object-level training data, we propose an annotation pipeline combining knowledge from segmented 3D datasets, material databases, and a vision-language model, along with a new benchmark. Experiments show that VoMP estimates accurate volumetric properties, far outperforming prior art in accuracy and speed.

cs.CV↗

arXiv2026

High-Performance Moment-Encoded Lattice Boltzmann Method with Stability-Guided Quantization

In this work, we present a memory-efficient, high-performance GPU framework for moment-based lattice Boltzmann methods (LBM) with fluid-solid coupling. We introduce a split-kernel scheme that decouples fluid updates from solid boundary handling, substantially reducing warp divergence and improving utilization on GPUs. We further perform the first von Neumann stability analysis of the high-order moment-encoded LBM (HOME-LBM) formulation, characterizing its spectral behavior and deriving stability bounds for individual moment components. These theoretical insights directly guide a practical 16-bit moment quantization without compromising numerical stability. Our framework achieves up to 6x speedup and reduces GPU memory footprint by up to 50% in fluid-only scenarios and 25% in scenes with complex solid boundaries compared to the state-of-the-art LBM solver, while preserving physical fidelity across a range of large-scale benchmarks and real-time demonstrations. The proposed approach enables scalable, stable, and high-resolution LBM simulation on a single GPU, bridging theoretical stability analysis with practical GPU algorithm design.

cs.GR↗

arXiv2026

SpringTime: Learning Simulatable Models of Cloth with Spatially-varying Constitutive Properties

Materials used in real clothing exhibit remarkable complexity and spatial variation due to common processes such as stitching, hemming, dyeing, printing, padding, and bonding. Simulating these materials, for instance using finite element methods, is often computationally demanding and slow. Worse, such methods can suffer from numerical artifacts called ``membrane locking'' that makes cloth appear artificially stiff. Here we propose a general framework, called SpringTime, for learning a simple yet efficient surrogate model that captures the effects of these complex materials using only motion observations. The cloth is discretized into a mass-spring network with unknown material parameters that are learned directly from the motion data, using a novel force-and-impulse loss function. Our approach demonstrates the ability to accurately model spatially varying material properties from a variety of data sources, and immunity to membrane locking which plagues FEM-based simulations. Compared to graph-based networks and neural ODE-based architectures, our method achieves significantly faster training times, higher reconstruction accuracy, and improved generalization to novel dynamic scenarios. Codebase for the paper can be found at https://github.com/ericchen321/springtime.

cs.GR↗

arXiv2025

Local Surface Parameterizations via Smoothed Geodesic Splines

We present a general method for computing local parameterizations rooted at a point on a surface, where the surface is described only through a signed implicit function and a corresponding projection function. Using a two-stage process, we compute several points radially emanating from the map origin, and interpolate between them with a spline surface. The narrow interface of our method allows it to support several kinds of geometry such as signed distance functions, general analytic implicit functions, triangle meshes, neural implicits, and point clouds. We demonstrate the high quality of our generated parameterizations on a variety of examples, and show applications in local texturing and surface curve drawing.

cs.GR↗

arXiv2025

Sparse, Geometry- and Material-Aware Bases for Multilevel Elastodynamic Simulation

We present a multi-level elastodynamics timestep solver for accelerating incremental potential contact (IPC) simulations. Our method retains the robustness of gold standard IPC in the face of intricate geometry, complex heterogeneous material distributions and high resolution input data without sacrificing visual fidelity (per-timestep relative displacement error of $\approx1\%$). The success of our method is enabled by a novel, sparse, geometry- and material-aware basis construction method which allows for the use of fast preconditioned conjugate gradient solvers (in place of a sparse direct solver), but without suffering convergence issues due to stiff or heterogeneous materials. The end result is a solver that produces results visually indistinguishable and quantitatively very close to gold-standard IPC methods but up to $13\times$ faster on identical hardware.

cs.GR↗

arXiv2025

Adaptive Algebraic Reuse of Reordering in Cholesky Factorization with Dynamic Sparsity Pattern

Cholesky linear solvers are a critical bottleneck in challenging applications within computer graphics and scientific computing. These applications include but are not limited to elastodynamic barrier methods such as Incremental Potential Contact (IPC), and geometric operations such as remeshing and morphology. In these contexts, the sparsity patterns of the linear systems frequently change across successive calls to the Cholesky solver, necessitating repeated symbolic analyses that dominate the overall solver runtime. To address this bottleneck, we evaluate our method on over 150,000 linear systems generated from diverse nonlinear problems with dynamic sparsity changes in Incremental Potential Contact (IPC) and patch remeshing on a wide range of triangular meshes of various sizes. Our analysis using three leading sparse Cholesky libraries, Intel MKL Pardiso, SuiteSparse CHOLMOD, and Apple Accelerate, reveals that the primary performance constraint lies in the symbolic re-ordering phase of the solver. Recognizing this, we introduce Parth, an innovative re-ordering method designed to update ordering vectors only where local connectivity changes occur adaptively. Parth employs a novel hierarchical graph decomposition algorithm to break down the dual graph of the input matrix into fine-grained subgraphs, facilitating the selective reuse of fill-reducing orderings when sparsity patterns exhibit temporal coherence. Our extensive evaluation demonstrates that Parth achieves up to a 255x and 13x speedup in fill-reducing ordering for our IPC and remeshing benchmark and a 6.85x and 10.7x acceleration in symbolic analysis. These enhancements translate to up to 2.95x and 5.89x reduction in overall solver runtime. Additionally, Parth's integration requires only three lines of code, resulting in significant computational savings without the requirement of changes to the computational stack.

math.NA↗

arXiv2025

Stochastic Barnes-Hut Approximation for Fast Summation on the GPU

We present a novel stochastic version of the Barnes-Hut approximation. Regarding the level-of-detail (LOD) family of approximations as control variates, we construct an unbiased estimator of the kernel sum being approximated. Through several examples in graphics applications such as winding number computation and smooth distance evaluation, we demonstrate that our method is well-suited for GPU computation, capable of outperforming a GPU-optimized implementation of the deterministic Barnes-Hut approximation by achieving equal median error in up to 9.4x less time.

cs.GR↗

arXiv2025

Neurally Integrated Finite Elements for Differentiable Elasticity on Evolving Domains

We present an elastic simulator for domains defined as evolving implicit functions, which is efficient, robust, and differentiable with respect to both shape and material. This simulator is motivated by applications in 3D reconstruction: it is increasingly effective to recover geometry from observed images as implicit functions, but physical applications require accurately simulating and optimizing-for the behavior of such shapes under deformation, which has remained challenging. Our key technical innovation is to train a small neural network to fit quadrature points for robust numerical integration on implicit grid cells. When coupled with a Mixed Finite Element formulation, this yields a smooth, fully differentiable simulation model connecting the evolution of the underlying implicit surface to its elastic response. We demonstrate the efficacy of our approach on forward simulation of implicits, direct simulation of 3D shapes during editing, and novel physics-based shape and topology optimizations in conjunction with differentiable rendering.

cs.GR↗

arXiv2025

Rigid Body Adversarial Attacks

Due to their performance and simplicity, rigid body simulators are often used in applications where the objects of interest can considered very stiff. However, no material has infinite stiffness, which means there are potentially cases where the non-zero compliance of the seemingly rigid object can cause a significant difference between its trajectories when simulated in a rigid body or deformable simulator. Similarly to how adversarial attacks are developed against image classifiers, we propose an adversarial attack against rigid body simulators. In this adversarial attack, we solve an optimization problem to construct perceptually rigid adversarial objects that have the same collision geometry and moments of mass to a reference object, so that they behave identically in rigid body simulations but maximally different in more accurate deformable simulations. We demonstrate the validity of our method by comparing simulations of several examples in commercially available simulators.

cs.CV↗

arXiv2024

Trust-Region Eigenvalue Filtering for Projected Newton

We introduce a novel adaptive eigenvalue filtering strategy to stabilize and accelerate the optimization of Neo-Hookean energy and its variants under the Projected Newton framework. For the first time, we show that Newton's method, Projected Newton with eigenvalue clamping and Projected Newton with absolute eigenvalue filtering can be unified using ideas from the generalized trust region method. Based on the trust-region fit, our model adaptively chooses the correct eigenvalue filtering strategy to apply during the optimization. Our method is simple but effective, requiring only two lines of code change in the existing Projected Newton framework. We validate our model outperforms stand-alone variants across a number of experiments on quasistatic simulation of deformable solids over a large dataset.

cs.GR↗

arXiv2024

A Differentiable Material Point Method Framework for Shape Morphing

We present a novel, physically-based morphing technique for elastic shapes, leveraging the differentiable material point method (MPM) with space-time control through per-particle deformation gradients to accommodate complex topology changes. This approach, grounded in MPM's natural handling of dynamic topologies, is enhanced by a chained iterative optimization technique, allowing for the creation of both succinct and extended morphing sequences that maintain coherence over time. Demonstrated across various challenging scenarios, our method is able to produce detailed elastic deformation and topology transitions, all grounded within our physics-based simulation framework.

cs.GR↗

arXiv2024

Automatic Skinning using the Mixed Finite Element Method

In this work, we show that exploiting additional variables in a mixed finite element formulation of deformation leads to an efficient physics-based character skinning algorithm. Taking as input, a user-defined rig, we show how to efficiently compute deformations of the character mesh which respect artist-supplied handle positions and orientations, but without requiring complicated constraints on the physics solver, which can cause poor performance. Rather we demonstrate an efficient, user controllable skinning pipeline that can generate compelling character deformations, using a variety of physics material models.

cs.GR↗

arXiv2024

Stabler Neo-Hookean Simulation: Absolute Eigenvalue Filtering for Projected Newton

Volume-preserving hyperelastic materials are widely used to model near-incompressible materials such as rubber and soft tissues. However, the numerical simulation of volume-preserving hyperelastic materials is notoriously challenging within this regime due to the non-convexity of the energy function. In this work, we identify the pitfalls of the popular eigenvalue clamping strategy for projecting Hessian matrices to positive semi-definiteness during Newton's method. We introduce a novel eigenvalue filtering strategy for projected Newton's method to stabilize the optimization of Neo-Hookean energy and other volume-preserving variants under high Poisson's ratio (near 0.5) and large initial volume change. Our method only requires a single line of code change in the existing projected Newton framework, while achieving significant improvement in both stability and convergence speed. We demonstrate the effectiveness and efficiency of our eigenvalue projection scheme on a variety of challenging examples and over different deformations on a large dataset.

cs.GR↗

arXiv2024

Simplicits: Mesh-Free, Geometry-Agnostic, Elastic Simulation

The proliferation of 3D representations, from explicit meshes to implicit neural fields and more, motivates the need for simulators agnostic to representation. We present a data-, mesh-, and grid-free solution for elastic simulation for any object in any geometric representation undergoing large, nonlinear deformations. We note that every standard geometric representation can be reduced to an occupancy function queried at any point in space, and we define a simulator atop this common interface. For each object, we fit a small implicit neural network encoding spatially varying weights that act as a reduced deformation basis. These weights are trained to learn physically significant motions in the object via random perturbations. Our loss ensures we find a weight-space basis that best minimizes deformation energy by stochastically evaluating elastic energies through Monte Carlo sampling of the deformation volume. At runtime, we simulate in the reduced basis and sample the deformations back to the original domain. Our experiments demonstrate the versatility, accuracy, and speed of this approach on data including signed distance functions, point clouds, neural primitives, tomography scans, radiance fields, Gaussian splats, surface meshes, and volume meshes, as well as showing a variety of material energies, contact models, and time integration schemes.

cs.CV↗