Physics-Based Animation

Pranav Jain, Peter Yichen Chen, Ziyin Qu, Oded Stein

The idea of using a neural network to represent continuous vector fields (i.e., neural fields) has become popular for solving PDEs arising from physics simulations. Here, the classical spatial discretization (e.g., finite difference) of PDE solvers is replaced with a neural network that models a differentiable function, so the spatial gradients of the PDEs can be readily computed via autodifferentiation. When used in fluid simulation, however, neural fields fail to capture many important phenomena, such as the vortex shedding experienced in the von Kármán vortex street experiment. We present a novel neural network representation for fluid simulation that augments neural fields with explicitly enforced boundary conditions as well as a Monte Carlo pressure solver to get rid of all weakly enforced boundary conditions. Our method, the Neural Monte Carlo method (NMC), is completely mesh-free, i.e., it doesn’t depend on any grid-based discretization. While NMC does not achieve the state-of-the-art accuracy of the well-established gridbased methods, it significantly outperforms previous mesh-free neural fluid methods on fluid flows involving intricate boundaries and turbulence regimes.

Neural Monte Carlo Fluid Simulation

Ryusuke Sugimoto, Christopher Batty, Toshiya Hachisuka

We present a velocity-based Monte Carlo fluid solver that overcomes the limitations of its existing vorticity-based counterpart. Because the velocity-based formulation is more commonly used in graphics, our Monte Carlo solver can be readily extended with various techniques from the fluid simulation literature. We derive our method by solving the Navier-Stokes equations via operator splitting and designing a pointwise Monte Carlo estimator for each substep. We reformulate the projection and diffusion steps as integration problems based on the recently introduced walk-on-boundary technique [Sugimoto et al. 2023]. We transform the volume integral arising from the source term of the pressure Poisson equation into a form more amenable to practical numerical evaluation. Our resulting velocity-based formulation allows for the proper simulation of scenes that the prior vorticity-based Monte Carlo method [Rioux-Lavoie and Sugimoto et al. 2022] either simulates incorrectly or cannot support. We demonstrate that our method can easily incorporate advancements drawn from conventional non-Monte Carlo methods by showing how one can straightforwardly add buoyancy effects, divergence control capabilities, and numerical dissipation reduction methods, such as advection-reflection and PIC/FLIP methods.

Velocity-Based Monte Carlo Fluids

Wei Li, Kui Wu, Mathieu Desbrun

Despite its visual appeal, the simulation of separated multiphase flows (i.e., streams of fluids separated by interfaces) faces numerous challenges in accurately reproducing complex behaviors such as guggling, wetting, or bubbling. These difficulties are especially pronounced for high Reynolds numbers and large density variations between fluids, most likely explaining why they have received comparatively little attention in Computer Graphics compared to single- or two-phase flows. In this paper, we present a full LBM solver for multifluid simulation. We derive a conservative phase field model with which the spatial presence of each fluid or phase is encoded to allow for the simulation of miscible, immiscible and even partially-miscible fluids, while the temporal evolution of the phases is performed using a D3Q7 lattice-Boltzmann discretization. The velocity field, handled through the recent high-order moment-encoded LBM (HOME-LBM) framework to minimize its memory footprint, is simulated via a velocity-based distribution stored on a D3Q27 or D3Q19 discretization to offer accuracy and stability to large density ratios even in turbulent scenarios, while coupling with the phases through pressure, viscosity, and interfacial forces is achieved by leveraging the diffuse encoding of interfaces. The resulting solver addresses a number of limitations of kinetic methods in both computational fluid dynamics and computer graphics: it offers a fast, accurate, and low-memory fluid solver enabling efficient turbulent multiphase simulations free of the typical oscillatory pressure behavior near boundaries. We present several numerical benchmarks, examples and comparisons of multiphase flows to demonstrate our solver’s visual complexity, accuracy, and realism.

Kinetic Simulation of Turbulent Multifluid Flows

Jiong Chen, Florian Schäfer, Mathieu Desbrun

The method of fundamental solutions (MFS) and its associated boundary element method (BEM) have gained popularity in computer graphics due to the reduced dimensionality they offer: for three-dimensional linear problems, they only require variables on the domain boundary to solve and evaluate the solution throughout space, making them a valuable tool in a wide variety of applications. However, MFS and BEM have poor computational scalability and huge memory requirements for large-scale problems, limiting their applicability and efficiency in practice. By leveraging connections with Gaussian Processes and exploiting the sparse structure of the inverses of boundary integral matrices, we introduce a variational preconditioner that can be computed via a sparse inverse-Cholesky factorization in a massively parallel manner. We show that applying our preconditioner to the Preconditioned Conjugate Gradient algorithm greatly improves the efficiency of MFS or BEM solves, up to four orders of magnitude in our series of tests.

Lightning-fast Method of Fundamental Solutions

• Lightning-Fast Method of Fundamental Solutions
• Kinetic Simulation of Turbulent Multifluid Flows
• Velocity-based Monte Carlo Fluids
• Neural Monte Carlo Fluid Simulation
• Going with the Flow
• VR-GS: A Physical Dynamics-Aware Interactive Gaussian Splatting System in Virtual Reality
• Differentiable solver for time-dependent deformation problems with contact
• Real-time Wing Deformation Simulation for Flying Insects
• Cyclogenesis: Simulating Hurricanes and Tornadoes
• Scintilla: Simulating Combustible Vegetation for Wildfires
• GIPC: Fast and stable Gauss-Newton optimization of IPC barrier energy
• Vertex Block Descent
• Primal-Dual Non-Smooth Friction for Rigid Body Animation
• Multi-Material Mesh-Based Surface Tracking with Implicit Topology Changes
• Real-time Physically Guided Hair Interpolation
• Proxy Asset Generation for Cloth Simulation in Games
• A Dynamic Duo of Finite Elements and Material Points
• …

Petros Tzathas, Boris Gailleton, Philippe Steer, Guillaume Cordonnier

Terrain generation methods have long been divided between procedural and physically-based. Procedural methods build upon the fast evaluation of a mathematical function but suffer from a lack of geological consistency, while physically-based simulation enforces this consistency at the cost of thousands of iterations unraveling the history of the landscape. In particular, the simulation of the competition between tectonic uplift and fluvial erosion expressed by the stream power law raised recent interest in computer graphics as this allows the generation and control of consistent large-scale mountain ranges, albeit at the cost of a lengthy simulation. In this paper, we explore the analytical solutions of the stream power law and propose a method that is both physically-based and procedural, allowing fast and consistent large-scale terrain generation. In our approach, time is no longer the stopping criterion of an iterative process but acts as the parameter of a mathematical function, a slider that controls the aging of the input terrain from a subtle erosion to the complete replacement by a fully formed mountain range. While analytical solutions have been proposed by the geomorphology community for the 1D case, extending them to a 2D heightmap proves challenging. We propose an efficient implementation of the analytical solutions with a multigrid accelerated iterative process and solutions to incorporate landslides and hillslope processes – two erosion factors that complement the stream power law.

Physically-based analytical erosion for fast terrain generation

Peizhuo Li, Tuanfeng Y. Wang, Timur Levent Kesdogan, Duygu Ceylan, Olga Sorkine-Hornung

Data driven and learning based solutions for modeling dynamic garments have significantly advanced, especially in the context of digital humans. However, existing approaches often focus on modeling garments with respect to a fixed parametric human body model and are limited to garment geometries that were seen during training. In this work, we take a different approach and model the dynamics of a garment by exploiting its local interactions with the underlying human body. Specifically, as the body moves, we detect local garment-body collisions, which drive the deformation of the garment. At the core of our approach is a mesh-agnostic garment representation and a manifold-aware transformer network design, which together enable our method to generalize to unseen garment and body geometries. We evaluate our approach on a wide variety of garment types and motion sequences and provide competitive qualitative and quantitative results with respect to the state of the art.

Neural Garment Dynamics via Manifold-Aware Transformers

Xingyu Ye, Xiaokun Wang, Yanrui Xu, Jirí Kosinka, Alexandru C. Telea, Lihua You, Jian Jun Zhang, Jian Chang

For vortex particle methods relying on SPH-based simulations, the direct approach of iterating all fluid particles to capture velocity from vorticity can lead to a significant computational overhead during the Biot-Savart summation process. To address this challenge, we present a Monte Carlo vortical smoothed particle hydrodynamics (MCVSPH) method for efficiently simulating turbulent flows within an SPH framework. Our approach harnesses a Monte Carlo estimator and operates exclusively within a pre-sampled particle subset, thus eliminating the need for costly global iterations over all fluid particles. Our algorithm is decoupled from various projection loops which enforce incompressibility, independently handles the recovery of turbulent details, and seamlessly integrates with state-of-the-art SPH-based incompressibility solvers. Our approach rectifies the velocity of all fluid particles based on vorticity loss to respect the evolution of vorticity, effectively enforcing vortex motions. We demonstrate, by several experiments, that our MCVSPH method effectively preserves vorticity and creates visually prominent vortical motions.

Monte Carlo Vortical Smoothed Particle Hydrodynamics for Simulating Turbulent Flows

Sergio Sancho, Jingwei Tang, Christopher Batty, Vinicius Azevedo

An ongoing challenge in fluid animation is the faithful preservation of vortical details, which impacts the visual depiction of flows. We propose the Impulse Particle-In-Cell (IPIC) method, a novel extension of the popular Affine Particle-In-Cell (APIC) method that makes use of the impulse gauge formulation of the fluid equations. Our approach performs a coupled advection-stretching during particle-based advection to better preserve circulation and vortical details. The associated algorithmic changes are simple and straightforward to implement, and our results demonstrate that the proposed method is able to achieve more energetic and visually appealing smoke and liquid flows than APIC.

The Impulse Particle-In-Cell Method

• Estimating Cloth Simulation Parameters From Tag Information and Cusick Drape Test
• Neural Garment Dynamics via Manifold-Aware Transformers
• Practical Method to Estimate Fabric Mechanics from Metadata
• The Impulse Particle-In-Cell Method
• Wavelet Potentials: An Efficient Potential Recovery Technique for Pointwise Incompressible Fluids
• Monte Carlo Vortical Smoothed Particle Hydrodynamics for Simulating Turbulent Flows
• Physically-based analytical erosion for fast terrain generation
• Volcanic Skies: coupling ejection with atmospheric simulation to create consistent skyscapes