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

Wiewel, Steffen; Becher, Moritz; Thuerey, Nils

doi:10.48550/arxiv.1802.10123

Cited by 13 publications

(18 citation statements)

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“…Our inspiration comes from the latest development of deep learning techniques in computer vision. 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]. However, existing deep networks designed in deep learning mostly emphasis on expressive power and prediction accuracy.…”

Section: Existing Work and Motivationsmentioning

confidence: 99%

PDE-Net 2.0: Learning PDEs from data with a numeric-symbolic hybrid deep network

Long

Dong

2019

Journal of Computational Physics

466

293

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Partial differential equations (PDEs) are commonly derived based on empirical observations. However, recent advances of technology enable us to collect and store massive amount of data, which offers new opportunities for data-driven discovery of PDEs. In this paper, we propose a new deep neural network, called PDE-Net 2.0, to discover (time-dependent) PDEs from observed dynamic data with minor prior knowledge on the underlying mechanism that drives the dynamics. The design of PDE-Net 2.0 is based on our earlier work [1] where the original version of PDE-Net was proposed. PDE-Net 2.0 is a combination of numerical approximation of differential operators by convolutions and a symbolic multi-layer neural network for model recovery. Comparing with existing approaches, PDE-Net 2.0 has the most flexibility and expressive power by learning both differential operators and the nonlinear response function of the underlying PDE model. Numerical experiments show that the PDE-Net 2.0 has the potential to uncover the hidden PDE of the observed dynamics, and predict the dynamical behavior for a relatively long time, even in a noisy environment.

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Section: Existing Work and Motivationsmentioning

confidence: 99%

PDE-Net 2.0: Learning PDEs from data with a numeric-symbolic hybrid deep network

Long

Dong

2019

Journal of Computational Physics

466

293

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“…CNN-based architectures were employed in Eulerian contexts to substitute the pressure projection step [Tompson et al 2016;] and to synthesize flow simulations from a set of reduced parameters . A LSTM-based [Wiewel et al 2018] approach predicted changes on pressure fields for multiple subsequent time-steps. Closer to our work, Chu and Thuerey [2017] enhance simulations with patch correspondences between low and high resolution simulations.…”

Section: Related Workmentioning

confidence: 99%

Transport-based neural style transfer for smoke simulations

et al. 2019

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Artistically controlling fluids has always been a challenging task. Optimization techniques rely on approximating simulation states towards target velocity or density field configurations, which are often handcrafted by artists to indirectly control smoke dynamics. Patch synthesis techniques transfer image textures or simulation features to a target flow field. However, these are either limited to adding structural patterns or augmenting coarse flows with turbulent structures, and hence cannot capture the full spectrum of different styles and semantically complex structures. In this paper, we propose the first Transport-based Neural Style Transfer (TNST) algorithm for volumetric smoke data. Our method is able to transfer features from natural images to smoke simulations, enabling general content-aware manipulations ranging from simple patterns to intricate motifs. The proposed algorithm is physically inspired, since it computes the density transport from a source input smoke to a desired target configuration. Our transport-based approach allows direct control over the divergence of the stylization velocity field by optimizing incompressible and irrotational potentials that transport smoke towards stylization. Temporal consistency is ensured by transporting and aligning subsequent stylized velocities, and 3D reconstructions are computed by seamlessly merging stylizations from different camera viewpoints.

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“…Due to the heavy computational overhead of physical models, there is an increasing trend to apply data-driven deep-learning (DL) / machine-learning (ML) methods to model physical phenomena [13,14]. Application of ML-based approaches has been categorised into three areas [15]: 1.…”

Section: Related Workmentioning

confidence: 99%

Statistical and machine learning ensemble modelling to forecast sea surface temperature

Wolff,

O'Donncha,

Chen

2019

Preprint

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In situ and remotely sensed observations have huge potential to develop data-driven predictive models for oceanography. A suite of machine learning models, including regression, decision tree and deep learning approaches were developed to estimate sea surface temperatures (SST). Training data consisted of satellite-derived SST and atmospheric data from The Weather Company. Models were evaluated in terms of accuracy and computational complexity. Predictive skills were assessed against observations and a state-of-the-art, physics-based model from the European Centre for Medium Weather Forecasting. Results demonstrated that by combining automated feature engineering with machine-learning approaches, accuracy comparable to existing state-of-the-art can be achieved. Models captured seasonal trends in the data together with short-term variations driven by atmospheric forcing. Further, it demonstrated that machinelearning-based approaches can be used as transportable prediction tools for ocean variables -a challenge for existing physics-based approaches that rely heavily on user parametrisation to specific geography and topography. The low computational cost of inference makes the approach particularly attractive for edge-based computing where predictive models could be deployed on low-power devices in the marine environment.

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

Cited by 13 publications

References 0 publications

PDE-Net 2.0: Learning PDEs from data with a numeric-symbolic hybrid deep network

PDE-Net 2.0: Learning PDEs from data with a numeric-symbolic hybrid deep network

Transport-based neural style transfer for smoke simulations

Statistical and machine learning ensemble modelling to forecast sea surface temperature

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