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 700x faster than re-simulating the data with the underlying CPU solver, while achieving compression rates of up to 1300x.Comment: Computer Graphics Forum (Proceedings of EUROGRAPHICS 2019), additional materials: http://www.byungsoo.me/project/deep-fluids

A dimension-reduced pressure solver for liquid simulations

This work presents a method for efficiently simplifying the pressure projection step in a liquid simulation. We first devise a straightforward dimension reduction technique that dramatically reduces the cost of solving the pressure projection. Next, we introduce a novel change of basis that satisfies free-surface boundary conditions exactly, regardless of the accuracy of the pressure solve. When combined, these ideas greatly reduce the computational complexity of the pressure solve without compromising free surface boundary conditions at the highest level of detail. Our techniques are easy to parallelize, and they effectively eliminate the computational bottleneck for large liquid simulations

Reviews on Physically Based Controllable Fluid Animation

In computer graphics animation, animation tools are required for fluid-like motions which are controllable by users or animator, since applying the techniques to commercial animations such as advertisement and film. Many developments have been proposed to model controllable fluid simulation with the need in realistic motion, robustness, adaptation, and support more required control model. Physically based models for different states of substances have been applied in general in order to permit animators to almost effortlessly create interesting, realistic, and sensible animation of natural phenomena such as water flow, smoke spread, etc. In this paper, we introduce the methods for simulation based on physical model and the techniques for control the flow of fluid, especially focus on particle based method. We then discuss the existing control methods within three performances; control ability, realism, and computation time. Finally, we give a brief of the current and trend of the research areas

Learning three-dimensional flow for interactive aerodynamic design

We present a data-driven technique to instantly predict how fluid flows around various three-dimensional objects. Such simulation is useful for computational fabrication and engineering, but is usually computationally expensive since it requires solving the Navier-Stokes equation for many time steps. To accelerate the process, we propose a machine learning framework which predicts aerodynamic forces and velocity and pressure fields given a threedimensional shape input. Handling detailed free-form three-dimensional shapes in a data-driven framework is challenging because machine learning approaches usually require a consistent parametrization of input and output. We present a novel PolyCube maps-based parametrization that can be computed for three-dimensional shapes at interactive rates. This allows us to efficiently learn the nonlinear response of the flow using a Gaussian process regression. We demonstrate the effectiveness of our approach for the interactive design and optimization of a car body

Explicit synchronous partitioned scheme for coupled reduced order models based on composite reduced bases

This paper formulates, analyzes, and demonstrates numerically a method for the partitioned solution of coupled interface problems involving combinations of projection-based reduced order models (ROM) and/or full order methods (FOMs). The method builds on the partitioned scheme developed in [1], which starts from a well-posed formulation of the coupled interface problem and uses its dual Schur complement to obtain an approximation of the interface flux. Explicit time integration of this problem decouples its subdomain equations and enables their independent solution on each subdomain. Extension of this partitioned scheme to coupled ROM-ROM or ROM-FOM problems required formulations with non-singular Schur complements. To obtain these problems, we project a well-posed coupled FOM-FOM problem onto a composite reduced basis comprising separate sets of basis vectors for the interface and interior variables, and use the interface reduced basis as a Lagrange multiplier. Our analysis confirms that the resulting coupled ROM-ROM and ROM-FOM problems have provably non-singular Schur complements, independent of the mesh size and the reduced basis size. In the ROM-FOM case, analysis shows that one can also use the interface FOM space as a Lagrange multiplier. We illustrate the theoretical and computational properties of the partitioned scheme through reproductive and predictive tests for a model advection-diffusion transmission problem

Doctor of Philosophy

dissertationPhysical simulation has become an essential tool in computer animation. As the use of visual effects increases, the need for simulating real-world materials increases. In this dissertation, we consider three problems in physics-based animation: large-scale splashing liquids, elastoplastic material simulation, and dimensionality reduction techniques for fluid simulation. Fluid simulation has been one of the greatest successes of physics-based animation, generating hundreds of research papers and a great many special effects over the last fifteen years. However, the animation of large-scale, splashing liquids remains challenging. We show that a novel combination of unilateral incompressibility, mass-full FLIP, and blurred boundaries is extremely well-suited to the animation of large-scale, violent, splashing liquids. Materials that incorporate both plastic and elastic deformations, also referred to as elastioplastic materials, are frequently encountered in everyday life. Methods for animating such common real-world materials are useful for effects practitioners and have been successfully employed in films. We describe a point-based method for animating elastoplastic materials. Our primary contribution is a simple method for computing the deformation gradient for each particle in the simulation. Given the deformation gradient, we can apply arbitrary constitutive models and compute the resulting elastic forces. Our method has two primary advantages: we do not store or compare to an initial rest configuration and we work directly with the deformation gradient. The first advantage avoids poor numerical conditioning and the second naturally leads to a multiplicative model of deformation appropriate for finite deformations. One of the most significant drawbacks of physics-based animation is that ever-higher fidelity leads to an explosion in the number of degrees of freedom

Principal Geodesic Dynamics

International audienceThis paper presents a new integration of a data-driven approach using dimension reduction and a physically-based simulation for real-time character animation. We exploit Lie group statistical analysis techniques (Principal Geodesic Analysis, PGA) to approximate the pose manifold of a motion capture sequence by a reduced set of pose geodesics. We integrate this kinematic parametrization into a physically-based animation approach of virtual characters, by using the PGA-reduced parametrization directly as generalized coordinates of a Lagrangian formulation of mechanics. In order to achieve real-time without sacrificing stability, we derive an explicit time integrator by approximating existing variational integrators. Finally, we test our approach in task-space motion control. By formulating both physical simulation and inverse kinematics time stepping schemes as two quadratic programs, we propose a features-based control algorithm that interpolates between the two metrics. This allows for an intuitive trade-off between realistic physical simulation and controllable kinematic manipulation

Doctor of Philosophy

dissertationReal-time global illumination is the next frontier in real-time rendering. In an attempt to generate realistic images, games have followed the film industry into physically based shading and will soon begin integrating global illumination techniques. Traditional methods require too much memory and too much time to compute for real-time use. With Modular and Delta Radiance Transfer we precompute a scene-independent, low-frequency basis that allows us to calculate complex indirect lighting calculations in a much lower dimensional subspace with a reduced memory footprint and real-time execution. The results are then applied as a light map on many different scenes. To improve the low frequency results, we also introduce a novel screen space ambient occlusion technique that allows us to generate a smoother result with fewer samples. These three techniques, low and high frequency used together, provide a viable indirect lighting solution that can be run in milliseconds on today's hardware, providing a useful new technique for indirect lighting in real-time graphics

Constraint bubbles and affine regions: reduced fluid models for efficient immersed bubbles and flexible spatial coarsening

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]. © 2020 Copyright held by the owner/author(s). Publication rights licensed to ACM. 0730-0301/2020/7-ART43 $15.00 https://doi.org/10.1145/3386569.3392455We propose to enhance the capability of standard free-surface flow simulators with efficient support for immersed bubbles through two new models: constraint-based bubbles and affine fluid regions. Unlike its predecessors, our constraint-based model entirely dispenses with the need for advection or projection inside zero-density bubbles, with extremely modest additional computational overhead that is proportional to the surface area of all bubbles. This surface-only approach is easy to implement, realistically captures many familiar bubble behaviors, and even allows two or more distinct liquid bodies to correctly interact across completely unsimulated air. We augment this model with a per-bubble volume-tracking and correction framework to minimize the cumulative effects of gradual volume drift. To support bubbles with non-zero densities, we propose a novel reduced model for an irregular fluid region with a single pointwise incompressible affine vector field. This model requires only 11 interior velocity degrees of freedom per affine fluid region in 3D, and correctly reproduces buoyant, stationary, and sinking behaviors of a secondary fluid phase with non-zero density immersed in water. Since the pressure projection step in both the above schemes is a slightly modified Poisson-style system, we propose novel Multigrid-based preconditioners for Conjugate Gradients for fast numerical solutions of our new discretizations. Furthermore, we observe that by enforcing an incompressible affine vector field over a coalesced set of grid cells, our reduced model is effectively an irregular coarse super-cell. This offers a convenient and flexible adaptive coarsening strategy that integrates readily with the standard staggered grid approach for fluid simulation, yet supports coarsened regions that are arbitrary voxelized shapes, and provides an analytically divergence-free interior. We demonstrate its effectiveness with a new adaptive liquid simulator whose interior regions are coarsened into a mix of tiles with regular and irregular shapes.This work was supported in part by the Natural Sciences and En- gineering Research Council of Canada (RGPIN-04360-2014), the Rutgers University start-up grant, and the Ralph E. Powe Junior Fac- ulty Enhancement Award. We would like to thank Cristin Barghiel and SideFX for their generous software donation and Ryoichi Ando for his insightful discussion on comparing our constraint method with stream functions