Deep Fluids: A Generative Network for Parameterized Fluid Simulations

By Byungsoo Kim, Vinicius C. Azevedo, Nils Thürey, Theodore Kim, Markus H. Gross, Barbara Solenthaler. 2018

436 citations recorded by the source corpus.

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×.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Statistical and Nonlinear Physics

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Citations in the corpus

PhyGeoNet: Physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain (2020, methodology): “[57] presented a generative CNN model to synthesize fluid simulations with the strictly imposed divergence-free condition using stream functions, and a similar idea was investigated by Mohan et al.”
Learning data-driven discretizations for partial differential equations (2018, methodology): “, the solution of Poisson’s equation in incompressible fluid simulations (9), subgrid cloud models in climate simulations (10), or building reduced-order models that approximate dynamics in a lowerdimensional space (8, 13, 14).”
Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems (2020, neutral): “8) [72] [49] [37] [316] [151] [292] [308] [59] [296] [248]”
Integrating Physics-Based Modeling with Machine Learning: A Survey (2020, neutral): “Data Generation [187] [78] [62] [40] [28] [133] [268] [288] [298] [49] [274] [231]”
PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network (2018, background): “An interesting fact is that some popular networks in computer vision, such as ResNet[15, 16], have close relationship with ODEs/PDEs and can be naturally merged with traditional computational mathematics in various tasks [17, 18, 19, 20, 21, 22, 23, 24, 25, 26].”
Deep Generative Models in Engineering Design: A Review (2021, methodology): “Shu et al. [70] take an iterative retraining approach by retraining a GAN on high performance models evaluated using Computational Fluid Dynamics (CFD) evaluation.”
Lagrangian Fluid Simulation with Continuous Convolutions (2020, background): “…to accelerate the expensive pressure correction step of grid-based solvers, while other works have focused on super-resolution (Xie et al., 2018), learning time evolution via the Koopman operator (Morton et al., 2018), and learning reduced representations (Wiewel et al., 2019; Kim et al., 2019).”
Digital Twin: Values, Challenges and Enablers From a Modeling Perspective (2019, neutral): “[334] B.”
Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers (2020, background): “Additionally, convolutional neural networks (CNNs) were studied for stochastic sub-grid modeling [60], airfoil flow problems [56, 67], and as part of generative networks to leverage the fast inference of pre-trained models [10, 66, 29].”
Factorized Fourier Neural Operators (2021, background): “However, machine learning methods need not incorporate such constraints – for example, Kim et al. (2019) use a generative CNN model to represent velocity ﬁelds in a low-dimensional latent space and a feedforward neural network to advance the latent space to the next time point.”