Deep Fluids: A Generative Network for Parameterized Fluid Simulations

This paper presents a novel generative model to synthesize fluid simulations from a set of reduced parameters. A convolutional neural network is trained on a collection of discrete, parameterizable fluid simulation velocity fields. Due to the capability of deep learning architectures to learn representative features of the data, our generative model is able to accurately approximate the training data set, while providing plausible interpolated in‐betweens. The proposed generative model is optimized for fluids by a novel loss function that guarantees divergence‐free velocity fields at all times. In addition, we demonstrate that we can handle complex parameterizations in reduced spaces, and advance simulations in time by integrating in the latent space with a second network. Our method models a wide variety of fluid behaviors, thus enabling applications such as fast construction of simulations, interpolation of fluids with different parameters, time re‐sampling, latent space simulations, and compression of fluid simulation data. Reconstructed velocity fields are generated up to 700× faster than re‐simulating the data with the underlying CPU solver, while achieving compression rates of up to 1300×.     

Strain Rate Dissipation for Elastic Deformations

Damping determines how the energy in dynamic deformations is dissipated. The design of damping requires models where the behavior along deformation modes is easily controlled, while other motions are left unaffected. In this paper, we propose a framework for the design of damping using dissipation potentials formulated as functions of strain rate. We study simple parameterizations of the models, the application to continuum and discrete deformation models, and practical implications for implementation. We also study previous simple damping models, in particular we demonstrate limitations of Rayleigh damping. We analyze in detail the application of strain rate dissipation potentials to two highly different deformation models, StVK hyperlasticity and yarn‐level cloth with sliding persistent contacts. These deformation models are representative of the range of applicability of the damping model.     

Time‐Domain Parallelization for Accelerating Cloth Simulation

Cloth simulations, widely used in computer animation and apparel design, can be computationally expensive for real‐time applications. Some parallelization techniques have been proposed for visual simulation of cloth using CPU or GPU clusters and often rely on parallelization using spatial domain decomposition techniques that have a large communication overhead. In this paper, we propose a novel time‐domain parallelization technique that makes use of the two‐level mesh representation to resolve the time‐dependency issue and develop a practical algorithm to smooth the state transition from the corresponding coarse to fine meshes. A load estimation and a load balancing technique used in online partitioning are also proposed to maximize the performance acceleration. Our method achieves a nearly linear performance scaling on manycore clusters and outperforms spatial‐domain parallelization on a diverse set of benchmarks.     

A Physically Consistent Implicit Viscosity Solver for SPH Fluids

In this paper, we present a novel physically consistent implicit solver for the simulation of highly viscous fluids using the Smoothed Particle Hydrodynamics (SPH) formalism. Our method is the result of a theoretical and practical in‐depth analysis of the most recent implicit SPH solvers for viscous materials. Based on our findings, we developed a list of requirements that are vital to produce a realistic motion of a viscous fluid. These essential requirements include momentum conservation, a physically meaningful behavior under temporal and spatial refinement, the absence of ghost forces induced by spurious viscosities and the ability to reproduce complex physical effects that can be observed in nature. On the basis of several theoretical analyses, quantitative academic comparisons and complex visual experiments we show that none of the recent approaches is able to satisfy all requirements. In contrast, our proposed method meets all demands and therefore produces realistic animations in highly complex scenarios. We demonstrate that our solver outperforms former approaches in terms of physical accuracy and memory consumption while it is comparable in terms of computational performance. In addition to the implicit viscosity solver, we present a method to simulate melting objects. Therefore, we generalize the viscosity model to a spatially varying viscosity field and provide an SPH discretization of the heat equation.     

Cable Joints

Robustly and efficiently simulating cables and ropes that are part of a larger system such as cable driven machines, cable cars or tendons in a human or robot is a challenging task. To be able to adapt to the environment, cables are typically modeled as a large number of small segments that are connected via joints. The two main difficulties with this approach are to satisfy the inextensibility constraint and to handle the typically large mass ratio between the small segments and the larger objects they connect. In this paper we present a new approach which solves these problems in a simple and effective way. Our method is based on the idea to simulate the effect of the cables instead of the cables themselves. To this end we propose a new special type of distance constraint we call cable joint that changes both its attachment points and its rest length dynamically. A cable connecting a series of objects is then modeled as a sequence of cable joints which reduces the complexity of the simulation from the order of the number of segments to just the number of connected objects. This makes simulations both faster and more robust as we will demonstrate on a variety of examples.     

MPM simulation of interacting fluids and solids

The material point method (MPM) has attracted increasing attention from the graphics community, as it combines the strengths of both particle‐ and grid‐based solvers. Like the smoothed particle hydrodynamics (SPH) scheme, MPM uses particles to discretize the simulation domain and represent the fundamental unknowns. This makes it insensitive to geometric and topological changes, and readily parallelizable on a GPU. Like grid‐based solvers, MPM uses a background mesh for calculating spatial derivatives, providing more accurate and more stable results than a purely particle‐based scheme. MPM has been very successful in simulating both fluid flow and solid deformation, but less so in dealing with multiple fluids and solids, where the dynamic fluid‐solid interaction poses a major challenge. To address this shortcoming of MPM, we propose a new set of mathematical and computational schemes which enable efficient and robust fluid‐solid interaction within the MPM framework. These versatile schemes support simulation of both multiphase flow and fully‐coupled solid‐fluid systems. A series of examples is presented to demonstrate their capabilities and performance in the presence of various interacting fluids and solids, including multiphase flow, fluid‐solid interaction, and dissolution.     

Fast Corotated FEM using Operator Splitting

In this paper we present a novel operator splitting approach for corotated FEM simulations. The deformation energy of the corotated linear material model consists of two additive terms. The first term models stretching in the individual spatial directions and the second term describes resistance to volume changes. By formulating the backward Euler time integration scheme as an optimization problem, we show that the first term is invariant to rotations. This allows us to use an operator splitting approach and to solve both terms individually with different numerical methods. The stretching part is solved accurately with an optimization integrator, which can be done very efficiently because the system matrix is constant over time such that its Cholesky factorization can be precomputed. The volume term is solved approximately by using the compliant constraints method and Gauss‐Seidel iterations. Further, we introduce the analytic polar decomposition which allows us to speed up the extraction of the rotational part of the deformation gradient and to recover inverted elements. Finally, this results in an extremely fast and robust simulation method with high visual quality that outperforms standard corotated FEMs by more than two orders of magnitude and even the fast but inaccurate PBD and shape matching methods by more than one order of magnitude without having their typical drawbacks. This enables a very efficient simulation of complex scenes containing more than a million elements.     

Position‐Based Simulation of Elastic Models on the GPU with Energy Aware Gauss‐Seidel Algorithm

In this paper, we provide a smooth extension of the energy aware Gauss‐Seidel iteration to the Position‐Based Dynamics (PBD) method. This extension is inspired by the kinetic and potential energy changes equalization and uses the foundations of the recent extended version of PBD algorithm (XPBD). The proposed method is not meant to conserve the total energy of the system and modifies each position constraint based on the equality of the kinetic and potential energy changes within the Gauss‐Seidel process of the XPBD algorithm. Our extension provides an implicit solution for relatively better stiffness during the simulation of elastic objects. We apply our solution directly within each Gauss‐Seidel iteration and it is independent of both simulation step‐size and integration methods. To demonstrate the benefits of our proposed extension with higher frame rates, we develop an efficient and practical mesh coloring algorithm for the XPBD method which provides parallel processing on a GPU. During the initialization phase, all mesh primitives are grouped according to their connectivity. Afterwards, all these groups are computed simultaneously on a GPU during the simulation phase. We demonstrate the benefits of our method with many spring potential and strain‐based continuous material constraints. Our proposed algorithm is easy to implement and seamlessly fits into the existing position‐based frameworks.     

A Geometrically Consistent Viscous Fluid Solver with Two‐Way Fluid‐Solid Coupling

We present a grid‐based fluid solver for simulating viscous materials and their interactions with solid objects. Our method formulates the implicit viscosity integration as a minimization problem with consistently estimated volume fractions to account for the sub‐grid details of free surfaces and solid boundaries. To handle the interplay between fluids and solid objects with viscosity forces, we also formulate the two‐way fluid‐solid coupling as a unified minimization problem based on the variational principle, which naturally enforces the boundary conditions. Our formulation leads to a symmetric positive definite linear system with a sparse matrix regardless of the monolithically coupled solid objects. Additionally, we present a position‐correction method using density constraints to enforce the uniform distributions of fluid particles and thus prevent the loss of fluid volumes. We demonstrate the effectiveness of our method in a wide range of viscous fluid scenarios.     

A Temporally Adaptive Material Point Method with Regional Time Stepping

Spatially and temporally adaptive algorithms can substantially improve the computational efficiency of many numerical schemes in computational mechanics and physics‐based animation. Recently, a crucial need for temporal adaptivity in the Material Point Method (MPM) is emerging due to the potentially substantial variation of material stiffness and velocities in multi‐material scenes. In this work, we propose a novel temporally adaptive symplectic Euler scheme for MPM with regional time stepping (RTS), where different time steps are used in different regions. We design a time stepping scheduler operating at the granularity of small blocks to maintain a natural consistency with the hybrid particle/grid nature of MPM. Our method utilizes the Sparse Paged Grid (SPGrid) data structure and simultaneously offers high efficiency and notable ease of implementation with a practical multi‐threaded particle‐grid transfer strategy. We demonstrate the efficacy of our asynchronous MPM method on various examples including elastic objects, granular media, and fluids.     

A Rigging‐Skinning Scheme to Control Fluid Simulation

Inspired by skeletal animation, a novel rigging‐skinning flow control scheme is proposed to animate fluids intuitively and efficiently. The new animation pipeline creates fluid animation via two steps: fluid rigging and fluid skinning. The fluid rig is defined by a point cloud with rigid‐body movement and incompressible deformation, whose time series can be intuitively specified by a rigid body motion and a constrained free‐form deformation, respectively. The fluid skin generates plausible fluid flows by virtually fluidizing the point‐cloud fluid rig with adjustable zero‐ and first‐order flow features and at fixed computational cost. Fluid rigging allows the animator to conveniently specify the desired low‐frequency flow motion through intuitive manipulations of a point cloud, while fluid skinning truthfully and efficiently converts the motion specified on the fluid rig into plausible flows of the animation fluid, with adjustable fine‐scale effects. Besides being intuitive, the rigging‐skinning scheme for fluid animation is robust and highly efficient, avoiding completely iterative trials or time‐consuming nonlinear optimization. It is also versatile, supporting both particle‐ and grid‐ based fluid solvers. A series of examples including liquid, gas and mixed scenes are presented to demonstrate the performance of the new animation pipeline.     

Collision‐Aware and Online Compression of Rigid Body Simulations via Integrated Error Minimization

Methods to compress simulation data are invaluable as they facilitate efficient transmission along the visual effects pipeline, fast and efficient replay of simulations for visualization and enable storage of scientific data. However, all current approaches to compressing simulation data require access to the entire dynamic simulation, leading to large memory requirements and additional computational burden. In this paper we perform compression of contact‐dominated, rigid body simulations in an online, error‐bounded fashion. This has the advantage of requiring access to only a narrow window of simulation data at a time while still achieving good agreement with the original simulation. Our approach is simulator agnostic allowing us to compress data from a variety of sources. We demonstrate the efficacy of our algorithm by compressing contact‐dominated rigid body simulations from a number of sources, achieving compression rates of up to 360 times over raw data size.     

Liquid Splash Modeling with Neural Networks

This paper proposes a new data‐driven approach to model detailed splashes for liquid simulations with neural networks. Our model learns to generate small‐scale splash detail for the fluid‐implicit‐particle method using training data acquired from physically parametrized, high resolution simulations. We use neural networks to model the regression of splash formation using a classifier together with a velocity modifier. For the velocity modification, we employ a heteroscedastic model. We evaluate our method for different spatial scales, simulation setups, and solvers. Our simulation results demonstrate that our model significantly improves visual fidelity with a large amount of realistic droplet formation and yields splash detail much more efficiently than finer discretizations.     

Distributing and Load Balancing Sparse Fluid Simulations

This paper describes a general algorithm and a system for load balancing sparse fluid simulations. Automatically distributing sparse fluid simulations efficiently is challenging because the computational load varies across the simulation domain and time. A key challenge with load balancing is that optimal decision making requires knowing the fluid distribution across partitions for future time steps, but computing this state for an arbitrary simulation requires running the simulation itself. The key insight of this paper is that it is possible to predict future load by running a speculative low resolution simulation in parallel. We mathematically formulate the problem of load balancing over multiple time steps and present a polynomial time algorithm to compute an approximate solution to it. Our experimental results show that distributing and speculatively load balancing sparse FLIP simulations over 8 nodes speeds them up by 5.3× to 7.9×, and that speculative load balancing generates assignments that perform within 20% of optimal.     

Fast Penetration Volume for Rigid Bodies

Handling collisions among a large number of bodies can be a performance bottleneck in video games and many other real‐time applications. We present a new framework for detecting and resolving collisions using the penetration volume as an interpenetration measure. Given two non‐convex polyhedral bodies, a new sampling paradigm locates their near‐contact configurations in advance, and stores associated contact information in a compact database. At runtime, we retrieve a given configuration's nearest neighbors. By taking advantage of the penetration volume's continuity, cheap geometric methods can use the neighbors to estimate contact information as well as a translational gradient. This results in an extremely fast, geometry‐independent, and trivially parallelizable computation, which constitutes the first global volume‐based collision resolution. When processing multiple collisions simultaneously on a 4‐core processor, the average running cost is as low as 5 μs. Furthermore, no additional proximity or contact‐regions queries are required. These results are orders of magnitude faster than previous penetration volume approaches.     

Fast Fluid Simulations with Sparse Volumes on the GPU

We introduce efficient, large scale fluid simulation on GPU hardware using the fluid‐implicit particle (FLIP) method over a sparse hierarchy of grids represented in NVIDIA^® GVDB Voxels. Our approach handles tens of millions of particles within a virtually unbounded simulation domain. We describe novel techniques for parallel sparse grid hierarchy construction and fast incremental updates on the GPU for moving particles. In addition, our FLIP technique introduces sparse, work efficient parallel data gathering from particle to voxel, and a matrix‐free GPU‐based conjugate gradient solver optimized for sparse grids. Our results show that our method can achieve up to an order of magnitude faster simulations on the GPU as compared to FLIP simulations running on the CPU.     

Learning‐Based Animation of Clothing for Virtual Try‐On

This paper presents a learning‐based clothing animation method for highly efficient virtual try‐on simulation. Given a garment, we preprocess a rich database of physically‐based dressed character simulations, for multiple body shapes and animations. Then, using this database, we train a learning‐based model of cloth drape and wrinkles, as a function of body shape and dynamics. We propose a model that separates global garment fit, due to body shape, from local garment wrinkles, due to both pose dynamics and body shape. We use a recurrent neural network to regress garment wrinkles, and we achieve highly plausible nonlinear effects, in contrast to the blending artifacts suffered by previous methods. At runtime, dynamic virtual try‐on animations are produced in just a few milliseconds for garments with thousands of triangles. We show qualitative and quantitative analysis of results.     

A CNN‐based Flow Correction Method for Fast Preview

Eulerian‐based smoke simulations are sensitive to the initial parameters and grid resolutions. Due to the numerical dissipation on different levels of the grid and the nonlinearity of the governing equations, the differences in simulation resolutions will result in different results. This makes it challenging for artists to preview the animation results based on low‐resolution simulations. In this paper, we propose a learning‐based flow correction method for fast previewing based on low‐resolution smoke simulations. The main components of our approach lie in a deep convolutional neural network, a grid‐layer feature vector and a special loss function. We provide a novel matching model to represent the relationship between low‐resolution and high‐resolution smoke simulations and correct the overall shape of a low‐resolution simulation to closely follow the shape of a high‐resolution down‐sampled version. We introduce the grid‐layer concept to effectively represent the 3D fluid shape, which can also reduce the input and output dimensions. We design a special loss function for the fluid divergence‐free constraint in the neural network training process. We have demonstrated the efficacy and the generality of our approach by simulating a diversity of animations deviating from the original training set. In addition, we have integrated our approach into an existing fluid simulation framework to showcase its wide applications.     

Controllable Dendritic Crystal Simulation Using Orientation Field

Real world dendritic growths show charming structures by their exquisite balance between the symmetry and randomness in the crystal formation. Other than the variety in the natural crystals, richer visual appearance of crystals can benefit from artificially controlling of the crystal growth on its growing directions and shapes. In this paper, by introducing one extra dimension of freedom, i.e. the orientation field, into the simulation, we propose an efficient algorithm for dendritic crystal simulation that is able to reproduce arbitrary symmetry patterns with different levels of asymmetry breaking effect on general grids or meshes, including spreading on curved surfaces and growth in 3D. Flexible artistic control is also enabled in a unified manner by exploiting and guiding the orientation field in the visual simulation. We show the effectiveness of our approach by various demonstrations of simulation results.     

An Efficient Solver for Two‐way Coupling Rigid Bodies with Incompressible Flow

We present an efficient solver for monolithic two‐way coupled simulation of rigid bodies with incompressible fluids that is robust to poor conditioning of the coupled system in the presence of large density ratios between the solid and the fluid. Our method leverages ideas from the theory of Domain Decomposition, and uses a hybrid combination of direct and iterative solvers that exploits the low‐dimensional nature of the solid equations. We observe that a single Multigrid V‐cycle for the fluid equations serves as a very effective preconditioner for solving the Schur‐complement system using Conjugate Gradients, which is the main computational bottleneck in our pipeline. We use spectral analysis to give some theoretical insights behind this observation. Our method is simple to implement, is entirely assembly‐free besides the solid equations, allows for the use of large time steps because of the monolithic formulation, and remains stable even when the iterative solver is terminated early. We demonstrate the efficacy of our method on several challenging examples of two‐way coupled simulation of smoke and water with rigid bodies. To illustrate that our method is applicable to other problems, we also show an example of underwater bubble simulation.