ABSTRACT The mass‐spring model is popular for representing the dynamics of distance‐based systems. In particular, elastic materials can be easily simulated using the mass‐spring model, thanks to the simplicity of its spring‐length constraint. The model is commonly defined in a typical simulation domain, that is, 2D or 3D Euclidean space. If the elastic body is heavily deformed, however, its mass‐spring configuration easily becomes hard or impossible to resolve in the typical domain. In order to tackle the challenge, we propose a dimension expansion method, which utilizes auxiliary coordinates for defining the model. By solving the problem in such an expanded domain, the solver can untangle complex spring configurations that are otherwise locked in local minima. Our study demonstrates the potential of the dimension expansion method for mass‐spring‐based elastic‐body simulations and for different applications such as multi‐dimensional data embedding problems.

Abstract This paper proposes a novel method that enhances the optimization‐based elastic body solver. The proposed method tackles the element inversion problem, which is prevalent in the prediction‐projection approach for numerical simulation of elastic bodies. At the prediction stage, our method alleviates inversions such that the subsequent projection solver can benefit in stability and efficiency. To prevent excessive suppression of predicted inertial motion when alleviating, we introduce a velocity decomposition method and adapt only the non‐rigid motion while preserving the rigid motion, that is, linear and angular momenta. Thanks to the respected inertial motion in the prediction stage, our method produces lively motions while keeping the entire simulation more stable. The experiments demonstrate that our alleviation method successfully stabilizes the simulation and improves the efficiency particularly when large deformations hamper the solver.

Abstract This paper proposes a novel method for simulating hyperelastic solids with Smoothed Particle Hydrodynamics (SPH). The proposed method extends the coverage of the state‐of‐the‐art elastic SPH solid method to include different types of hyperelastic materials, such as the Neo‐Hookean and the St. Venant‐Kirchoff models. To this end, we reformulate an implicit integration scheme for SPH elastic solids into an optimization problem and solve the problem using a general‐purpose quasi‐Newton method. Our experiments show that the Limited‐memory BFGS (L‐BFGS) algorithm can be employed to efficiently solve our optimization problem in the SPH framework and demonstrate its stable and efficient simulations for complex materials in the SPH framework. Thanks to the nature of our unified representation for both solids and fluids, the SPH formulation simplifies coupling between different materials and handling collisions.

Abstract In general, it is not easy to simulate an elastic body that undergoes large deformations. Especially when its elements are inverted or tangled, that is, when its vertices penetrate its polygons, simulation often fails. In this paper, we propose a simple yet highly effective method for alleviating the inversion problems of elastic bodies. Our experiments made with typical optimization‐based solvers demonstrate that the proposed method successfully stabilizes the solvers and produces visually plausible motions. We believe that our method can be widely adopted by a variety of state‐of‐the‐art elastic‐body simulators thanks to its simplicity.

Comparative evaluation lies at the heart of science, and determining the accuracy of a computational method is crucial for evaluating its potential as well as for guiding future efforts. However, metrics that are typically used have inherent shortcomings when faced with the under-resolved solutions of real-world simulation problems. We show how to leverage the human visual system in conjunction with crowd-sourced user studies to address the fundamental problems of widely used classical evaluation metrics. We demonstrate that such user studies driven by visual perception yield a very robust metric and consistent answers for complex phenomena without any requirements for proficiency regarding the physics at hand. This holds even for cases away from convergence where traditional metrics often end up with inconclusive results. More specifically, we evaluate results of different essentially non-oscillatory (ENO) schemes in different fluid flow settings. Our methodology represents a novel and practical approach for scientific evaluations that can give answers for previously unsolved problems.

This paper proposes a novel energy-momentum conserving integration method. Adopting Projective Dynamics, the proposed method extends its unconstrained minimization for time integration into the constrained form with the position-based energy-momentum constraints. This resolves the well-known problem of unwanted dissipation of energy and momenta without compromising the real-time performance and simulation stability. The proposed method also enables users to directly control the energy and momenta so as to easily create the vivid deformable and global motions they want, which is a fascinating feature for many real-time applications such as virtual/augmented reality and games.

We propose a neural network-based approach that computes a stable and generalizing metric (LSiM) to compare data from a variety of numerical simulation sources. We focus on scalar time-dependent 2D data that commonly arises from motion and transport-based partial differential equations (PDEs). Our method employs a Siamese network architecture that is motivated by the mathematical properties of a metric. We leverage a controllable data generation setup with PDE solvers to create increasingly different outputs from a reference simulation in a controlled environment. A central component of our learned metric is a specialized loss function that introduces knowledge about the correlation between single data samples into the training process. To demonstrate that the proposed approach outperforms existing metrics for vector spaces and other learned, image-based metrics, we evaluate the different methods on a large range of test data. Additionally, we analyze generalization benefits of an adjustable training data difficulty and demonstrate the robustness of LSiM via an evaluation on three real-world data sets.

Finding accurate solutions to partial differential equations (PDEs) is a crucial task in all scientific and engineering disciplines. It has recently been shown that machine learning methods can improve the solution accuracy by correcting for effects not captured by the discretized PDE. We target the problem of reducing numerical errors of iterative PDE solvers and compare different learning approaches for finding complex correction functions. We find that previously used learning approaches are significantly outperformed by methods that integrate the solver into the training loop and thereby allow the model to interact with the PDE during training. This provides the model with realistic input distributions that take previous corrections into account, yielding improvements in accuracy with stable rollouts of several hundred recurrent evaluation steps and surpassing even tailored supervised variants. We highlight the performance of the differentiable physics networks for a wide variety of PDEs, from non-linear advection-diffusion systems to three-dimensional Navier-Stokes flows.

In this paper, we present ScalarFlow , a first large-scale data set of reconstructions of real-world smoke plumes. In addition, we propose a framework for accurate physics-based reconstructions from a small number of video streams. Central components of our framework are a novel estimation of unseen inflow regions and an efficient optimization scheme constrained by a simulation to capture real-world fluids. Our data set includes a large number of complex natural buoyancy-driven flows. The flows transition to turbulence and contain observable scalar transport processes. As such, the ScalarFlow data set is tailored towards computer graphics, vision, and learning applications. The published data set contains volumetric reconstructions of velocity and density as well as the corresponding input image sequences with calibration data, code, and instructions how to reproduce the commodity hardware capture setup. We further demonstrate one of the many potential applications: a first perceptual evaluation study, which reveals that the complexity of the reconstructed flows would require large simulation resolutions for regular solvers in order to recreate at least parts of the natural complexity contained in the captured data.

Abstract 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.

This paper proposes a novel framework to evaluate fluid simulation methods based on crowd-sourced user studies in order to robustly gather large numbers of opinions. The key idea for a robust and reliable evaluation is to use a reference video from a carefully selected real-world setup in the user study. By conducting a series of controlled user studies and comparing their evaluation results, we observe various factors that affect the perceptual evaluation. Our data show that the availability of a reference video makes the evaluation consistent. We introduce this approach for computing scores of simulation methods as visual accuracy metric. As an application of the proposed framework, a variety of popular simulation methods are evaluated.

Abstract Muddy water is an example of suspension, which is a mixture containing particles that separate into distinct layers if left undisturbed. When stirred, however, the mud substance flows like a liquid and again begins settling out. Mud is composed of various sized particles, and they produce different effects when it is blended with water. This paper classifies the mud particles into three types and proposes different simulation methods for the types. The experimental results demonstrate that the proposed methods effectively produce visually plausible muddy water effects. Copyright © 2015 John Wiley & Sons, Ltd.

Abstract This paper proposes a novel hybrid particle‐grid approach to liquid simulation, which uses the fluid‐implicit‐particle (FLIP) method to resolve the liquid motion and a grid‐based particle correction method to complement FLIP. The correction process addresses the high‐frequency errors in FLIP ensuring that the particles are properly distributed. The proposed approach enables the corrective procedure to avoid directly processing the particle relationships and supports flexible corrective forces. The proposed technique effectively and efficiently improves the distribution of the particles and therefore enhances the overall simulation quality. The experimental results confirm that the technique is able to conserve the liquid volume and to produce dynamic surface motions, thin liquid sheets, and smooth surfaces without disturbing artifacts such as bumpy noise.

ABSTRACT This paper proposes a method for simulating the dynamics of porous deformable shells in the presence of water that floats on the surface or is absorbed into the interior. The proposed method enables various effects such as surface flow, capillary flow involving absorption and saturation of water, changes of the material properties caused by water saturation, and the deformable body dynamics including tearing. The experiments demonstrate that the proposed method produces promising results.Copyright © 2013 John Wiley & Sons, Ltd.