Deep Fluids: A Generative Network for Parameterized Fluid Simulations

Byungsoo Kim, Vinicius C. Azevedo, Nils Thuerey, Theodore Kim, Markus Gross, Barbara Solenthaler

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.

Deep Fluids: A Generative Network for Parameterized Fluid Simulations

REDMAX: Efficient & Flexible Approach for Articulated Dynamics

Ying Wang, Nicolas J. Weidner, Margaret A. Baxter, Yura Hwang, Danny Kaufman, Shinjiro Sueda

It is well known that the dynamics of articulated rigid bodies can be solved in O(n) time using a recursive method, where n is the number of joints. However, when elasticity is added between the bodies (eg damped springs), with linearly implicit integration, the stiffness matrix in the equations of motion breaks the tree topology of the system, making the recursive O(n) method inapplicable. In such cases, the only alternative has been to form and solve the system matrix, which takes O(n3) time. We propose a new approach that is capable of solving the linearly implicit equations of motion in near linear time. Our method, which we call Red/Max, is built using a combined reduced/maximal coordinate formulation. This hybrid model enables direct flexibility to apply arbitrary combinations of constraints and contact modeling in both reduced and maximal coordinates, as well as mixtures of implicit and explicit forces in either coordinate representation. We highlight Red/Max’s flexibility with seamless integration of deformable objects with two-way coupling, at a standard additional cost. We further highlight its flexibility by constructing an efficient internal (joint) and external (environment) frictional contact solver that can leverage bilateral joint constraints for rapid evaluation of frictional articulated dynamics.

REDMAX: Efficient & Flexible Approach for Articulated Dynamics

An Adaptive Variational Finite Difference Framework for Efficient Symmetric Octree Viscosity

Ryan Goldade, Yipeng Wang, Mridul Aanjaneya, Christopher Batty

While pressure forces are often the bottleneck in (near-)inviscid fluid simulations, viscosity can impose orders of magnitude greater computational costs at lower Reynolds numbers. We propose an implicit octree finite difference discretization that significantly accelerates the solution of the free surface viscosity equations using adaptive staggered grids, while supporting viscous buckling and rotation effects, variable viscosity, and interaction with scripted moving solids. In experimental comparisons against regular grids, our method reduced the number of active velocity degrees of freedom by as much as a factor of 7.7 and reduced linear system solution times by factors between 3.8 and 9.4. We achieve this by developing a novel adaptive variational finite difference methodology for octrees and applying it to the optimization form of the viscosity problem. This yields a linear system that is symmetric positive definite by construction, unlike naive finite difference/volume methods, and much sparser than a hypothetical finite element alternative. Grid refinement studies show spatial convergence at first order in L-infinity and second order in L-1, while the significantly smaller size of the octree linear systems allows for the solution of viscous forces at higher effective resolutions than with regular grids. We demonstrate the practical benefits of our adaptive scheme by replacing the regular grid viscosity step of a commercial liquid simulator (Houdini) to yield large speed-ups, and by incorporating it into an existing inviscid octree simulator to add support for viscous flows. Animations of viscous liquids pouring, bending, stirring, buckling, and melting illustrate that our octree method offers significant computational gains and excellent visual consistency with its regular grid counterpart.

An Adaptive Variational Finite Difference Framework for Efficient Symmetric Octree Viscosity

Latent-space Dynamics for Reduced Deformable Simulation

Lawson Fulton, Vismay Modi, David Duvenaud, David I. W. Levin, Alec Jacobson

We propose the first reduced model simulation framework for deformable solid dynamics using autoencoder neural networks.We provide a data-driven approach to generating nonlinear reduced spaces for deformation dynamics. In contrast to previous methods using machine learning which accelerate simulation by approximating the time-stepping function, we solve the true equations of motion in the latent-space using a variational formulation of implicit integration. Our approach produces drastically smaller reduced spaces than conventional linear model reduction, improving performance and robustness. Furthermore,our method works well with existing force-approximation cubature methods.

Latent-space Dynamics for Reduced Deformable Simulation

Procedural Tectonic Plates

Y. Cortial, A. Peytavie, E. Galin, E. Guérin

We present a procedural method for authoring synthetic tectonic planets. Instead of relying on computationally demanding physically-based simulations, we capture the fundamental phenomena into a procedural method that faithfully reproduces large-scale planetary features generated by the movement and collision of the tectonic plates. We approximate complex phenomena such as plate subduction or collisions to deform the lithosphere, including the continental and oceanic crusts. The user can control the movement of the plates, which dynamically evolve and generate a variety of landforms such as continents, oceanic ridges, large scale mountain ranges or island arcs. Finally, we amplify the large-scale planet model with either procedurally-defined or real-world elevation data to synthesize coherent detailed reliefs. Our method allows the user to control the evolutionof an entire planet interactively, and to trigger specific events such as catastrophic plate rifting.

Procedural Tectonic Plates

Learning-Based Animation of Clothing for Virtual Try-On

Igor Santesteban, Miguel A. Otaduy, Dan Casas

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.

Learning-Based Animation of Clothing for Virtual Try-On

Latent-space Physics: Towards Learning the Temporal Evolution of Fluid Flow

Steffen Wiewel, Moritz Becher, Nils Thuerey

We propose a method for the data-driven inference of temporal evolutions of physical functions with deep learning. More specifically, we target fluid flows, i.e. Navier-Stokes problems, and we propose a novel LSTM-based approach to predict the changes of pressure fields over time. The central challenge in this context is the high dimensionality of Eulerian space-time data sets. We demonstrate for the first time that dense 3D+time functions of physics system can be predicted within the latent spaces of neural networks, and we arrive at a neural-network based simulation algorithm with significant practical speed-ups. We highlight the capabilities of our method with a series of complex liquid simulations, and with a set of single-phase buoyancy simulations. With a set of trained networks, our method is more than two orders of magnitudes faster than a traditional pressure solver. Additionally, we present and discuss a series of detailed evaluations for the different components of our algorithm.

Latent-space Physics: Towards Learning the Temporal Evolution of Fluid Flow

Eurographics 2019

Efficient and Conservative Fluids Using Bidirectional Mapping

Ziyin Qu*, Xinxin Zhang* (joint 1st authors), Ming Gao, Chenfanfu Jiang, Baoquan Chen

In this paper, we introduce BiMocq2, an unconditionally stable, pure Eulerian-based advection scheme to efficiently preserve the advection accuracy of all physical quantities for long-term fluid simulations. Our approach is built upon the method of characteristic mapping (MCM). Instead of the costly evaluation of the temporal characteristic integral, we evolve the mapping function itself by solving an advection equation for the mappings. Dual mesh characteristics (DMC) method is adopted to more accurately update the mapping. Furthermore, to avoid visual artifacts like instant blur and temporal inconsistency introduced by reinitialization, we introduce multi-level mapping and back and forth error compensation. We conduct comprehensive 2D and 3D benchmark experiments to compare against alternative advection schemes. In particular, for the vortical flow and level set experiments, our method outperforms almost all state-of-art hybrid schemes, including FLIP, PolyPic and Particle Level Set, at the cost of only two Semi-Lagrangian advections. Additionally, our method does not rely on the particle-grid transfer operations, leading to a highly parallelizable pipeline. As a result, more than 45× performance acceleration can be achieved via even a straightforward porting of the code from CPU to GPU.

Efficient and Conservative Fluids Using Bidirectional Mapping

Decomposed Optimization Time Integrator for Large-Step Elastodynamics

Minchen Li, Ming Gao, Timothy Langlois, Chenfanfu Jiang, Danny M. Kaufman

Simulation methods are rapidly advancing the accuracy, consistency and controllability of elastodynamic modeling and animation. Critical to these advances, we require efficient time step solvers that reliably solve all implicit time integration problems for elastica. While available time step solvers succeed admirably in some regimes, they become impractically slow, inaccurate, unstable, or even divergent in others — as we show here. Towards addressing these needs we present the Decomposed Optimization Time Integrator(DOT), a new domain-decomposed optimization method for solving the per time step, nonlinear problems of implicit numerical time integration. DOT is especially suitable for large time step simulations of deformable bodies with nonlinear materials and high-speed dynamics. It is efficient, automated, and robust at large, fixed-size time steps, thus ensuring stable, continued progress of high-quality simulation output. Across a broad range of extreme and mild deformation dynamics, using frame-rate size time steps with widely varying object shapes and mesh resolutions, we show that DOT always converges to user-set tolerances, generally well-exceeding and always close to the best wall-clock times across all previous nonlinear time step solvers, irrespective of the deformation applied.

Decomposed Optimization Time Integrator for Large-Step Elastodynamics