arXiv subjects

Nils Thuerey

Publications and source records attributed to Nils Thuerey.

At least 91 records · Page 5Linked to original sources

arXiv2020

WeatherBench: A benchmark dataset for data-driven weather forecasting

Data-driven approaches, most prominently deep learning, have become powerful tools for prediction in many domains. A natural question to ask is whether data-driven methods could also be used to predict global weather patterns days in advance. First studies show promise but the lack of a common dataset and evaluation metrics make inter-comparison between studies difficult. Here we present a benchmark dataset for data-driven medium-range weather forecasting, a topic of high scientific interest for atmospheric and computer scientists alike. We provide data derived from the ERA5 archive that has been processed to facilitate the use in machine learning models. We propose simple and clear evaluation metrics which will enable a direct comparison between different methods. Further, we provide baseline scores from simple linear regression techniques, deep learning models, as well as purely physical forecasting models. The dataset is publicly available at https://github.com/pangeo-data/WeatherBench and the companion code is reproducible with tutorials for getting started. We hope that this dataset will accelerate research in data-driven weather forecasting.

physics.ao-ph↗

arXiv2020

Learning Temporal Coherence via Self-Supervision for GAN-based Video Generation

Our work explores temporal self-supervision for GAN-based video generation tasks. While adversarial training successfully yields generative models for a variety of areas, temporal relationships in the generated data are much less explored. Natural temporal changes are crucial for sequential generation tasks, e.g. video super-resolution and unpaired video translation. For the former, state-of-the-art methods often favor simpler norm losses such as $L^2$ over adversarial training. However, their averaging nature easily leads to temporally smooth results with an undesirable lack of spatial detail. For unpaired video translation, existing approaches modify the generator networks to form spatio-temporal cycle consistencies. In contrast, we focus on improving learning objectives and propose a temporally self-supervised algorithm. For both tasks, we show that temporal adversarial learning is key to achieving temporally coherent solutions without sacrificing spatial detail. We also propose a novel Ping-Pong loss to improve the long-term temporal consistency. It effectively prevents recurrent networks from accumulating artifacts temporally without depressing detailed features. Additionally, we propose a first set of metrics to quantitatively evaluate the accuracy as well as the perceptual quality of the temporal evolution. A series of user studies confirm the rankings computed with these metrics. Code, data, models, and results are provided at https://github.com/thunil/TecoGAN. The project page https://ge.in.tum.de/publications/2019-tecogan-chu/ contains supplemental materials.

cs.CV↗

arXiv2020

A Combined Data-driven and Physics-driven Method for Steady Heat Conduction Prediction using Deep Convolutional Neural Networks

With several advantages and as an alternative to predict physics field, machine learning methods can be classified into two distinct types: data-driven relying on training data and physics-driven using physics law. Choosing heat conduction problem as an example, we compared the data- and physics-driven learning process with deep Convolutional Neural Networks (CNN). It shows that the convergences of the error to ground truth solution and the residual of heat conduction equation exhibit remarkable differences. Based on this observation, we propose a combined-driven method for learning acceleration and more accurate solutions. With a weighted loss function, reference data and physical equation are able to simultaneously drive the learning. Several numerical experiments are conducted to investigate the effectiveness of the combined method. For the data-driven based method, the introduction of physical equation not only is able to speed up the convergence, but also produces physically more consistent solutions. For the physics-driven based method, it is observed that the combined method is able to speed up the convergence up to 49.0\% by using a not very restrictive coarse reference.

physics.comp-ph↗

arXiv2020

Latent Space Subdivision: Stable and Controllable Time Predictions for Fluid Flow

We propose an end-to-end trained neural networkarchitecture to robustly predict the complex dynamics of fluid flows with high temporal stability. We focus on single-phase smoke simulations in 2D and 3D based on the incompressible Navier-Stokes (NS) equations, which are relevant for a wide range of practical problems. To achieve stable predictions for long-term flow sequences, a convolutional neural network (CNN) is trained for spatial compression in combination with a temporal prediction network that consists of stacked Long Short-Term Memory (LSTM) layers. Our core contribution is a novel latent space subdivision (LSS) to separate the respective input quantities into individual parts of the encoded latent space domain. This allows to distinctively alter the encoded quantities without interfering with the remaining latent space values and hence maximizes external control. By selectively overwriting parts of the predicted latent space points, our proposed method is capable to robustly predict long-term sequences of complex physics problems. In addition, we highlight the benefits of a recurrent training on the latent space creation, which is performed by the spatial compression network.

cs.GR↗

arXiv2020

Tranquil Clouds: Neural Networks for Learning Temporally Coherent Features in Point Clouds

Point clouds, as a form of Lagrangian representation, allow for powerful and flexible applications in a large number of computational disciplines. We propose a novel deep-learning method to learn stable and temporally coherent feature spaces for points clouds that change over time. We identify a set of inherent problems with these approaches: without knowledge of the time dimension, the inferred solutions can exhibit strong flickering, and easy solutions to suppress this flickering can result in undesirable local minima that manifest themselves as halo structures. We propose a novel temporal loss function that takes into account higher time derivatives of the point positions, and encourages mingling, i.e., to prevent the aforementioned halos. We combine these techniques in a super-resolution method with a truncation approach to flexibly adapt the size of the generated positions. We show that our method works for large, deforming point sets from different sources to demonstrate the flexibility of our approach.

cs.CV↗

arXiv2020

Learning to Control PDEs with Differentiable Physics

Predicting outcomes and planning interactions with the physical world are long-standing goals for machine learning. A variety of such tasks involves continuous physical systems, which can be described by partial differential equations (PDEs) with many degrees of freedom. Existing methods that aim to control the dynamics of such systems are typically limited to relatively short time frames or a small number of interaction parameters. We present a novel hierarchical predictor-corrector scheme which enables neural networks to learn to understand and control complex nonlinear physical systems over long time frames. We propose to split the problem into two distinct tasks: planning and control. To this end, we introduce a predictor network that plans optimal trajectories and a control network that infers the corresponding control parameters. Both stages are trained end-to-end using a differentiable PDE solver. We demonstrate that our method successfully develops an understanding of complex physical systems and learns to control them for tasks involving PDEs such as the incompressible Navier-Stokes equations.

cs.LG↗

arXiv2019

Sparse Surface Constraints for Combining Physics-based Elasticity Simulation and Correspondence-Free Object Reconstruction

We address the problem to infer physical material parameters and boundary conditions from the observed motion of a homogeneous deformable object via the solution of an inverse problem. Parameters are estimated from potentially unreliable real-world data sources such as sparse observations without correspondences. We introduce a novel Lagrangian-Eulerian optimization formulation, including a cost function that penalizes differences to observations during an optimization run. This formulation matches correspondence-free, sparse observations from a single-view depth sequence with a finite element simulation of deformable bodies. In conjunction with an efficient hexahedral discretization and a stable, implicit formulation of collisions, our method can be used in demanding situation to recover a variety of material parameters, ranging from Young's modulus and Poisson ratio to gravity and stiffness damping, and even external boundaries. In a number of tests using synthetic datasets and real-world measurements, we analyse the robustness of our approach and the convergence behavior of the numerical optimization scheme.

cs.GR↗

arXiv2019

Spot the Difference: Accuracy of Numerical Simulations via the Human Visual System

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 crowd-sourced user studies in order to address the fundamental problems of widely used classical evaluation metrics. We demonstrate that such user studies, which inherently rely on the human visual system, 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 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.

physics.data-an↗

arXiv2019

Volumetric Isosurface Rendering with Deep Learning-Based Super-Resolution

Rendering an accurate image of an isosurface in a volumetric field typically requires large numbers of data samples. Reducing the number of required samples lies at the core of research in volume rendering. With the advent of deep learning networks, a number of architectures have been proposed recently to infer missing samples in multi-dimensional fields, for applications such as image super-resolution and scan completion. In this paper, we investigate the use of such architectures for learning the upscaling of a low-resolution sampling of an isosurface to a higher resolution, with high fidelity reconstruction of spatial detail and shading. We introduce a fully convolutional neural network, to learn a latent representation generating a smooth, edge-aware normal field and ambient occlusions from a low-resolution normal and depth field. By adding a frame-to-frame motion loss into the learning stage, the upscaling can consider temporal variations and achieves improved frame-to-frame coherence. We demonstrate the quality of the network for isosurfaces which were never seen during training, and discuss remote and in-situ visualization as well as focus+context visualization as potential applications

cs.GR↗

arXiv2019

A Multi-Pass GAN for Fluid Flow Super-Resolution

We propose a novel method to up-sample volumetric functions with generative neural networks using several orthogonal passes. Our method decomposes generative problems on Cartesian field functions into multiple smaller sub-problems that can be learned more efficiently. Specifically, we utilize two separate generative adversarial networks: the first one up-scales slices which are parallel to the XY-plane, whereas the second one refines the whole volume along the Z-axis working on slices in the YZ-plane. In this way, we obtain full coverage for the 3D target function and can leverage spatio-temporal supervision with a set of discriminators. Additionally, we demonstrate that our method can be combined with curriculum learning and progressive growing approaches. We arrive at a first method that can up-sample volumes by a factor of eight along each dimension, i.e., increasing the number of degrees of freedom by 512. Large volumetric up-scaling factors such as this one have previously not been attainable as the required number of weights in the neural networks renders adversarial training runs prohibitively difficult. We demonstrate the generality of our trained networks with a series of comparisons to previous work, a variety of complex 3D results, and an analysis of the resulting performance.

cs.GR↗

arXiv2019

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

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.

cs.LG↗

arXiv2019

Generating Liquid Simulations with Deformation-aware Neural Networks

We propose a novel approach for deformation-aware neural networks that learn the weighting and synthesis of dense volumetric deformation fields. Our method specifically targets the space-time representation of physical surfaces from liquid simulations. Liquids exhibit highly complex, non-linear behavior under changing simulation conditions such as different initial conditions. Our algorithm captures these complex phenomena in two stages: a first neural network computes a weighting function for a set of pre-computed deformations, while a second network directly generates a deformation field for refining the surface. Key for successful training runs in this setting is a suitable loss function that encodes the effect of the deformations, and a robust calculation of the corresponding gradients. To demonstrate the effectiveness of our approach, we showcase our method with several complex examples of flowing liquids with topology changes. Our representation makes it possible to rapidly generate the desired implicit surfaces. We have implemented a mobile application to demonstrate that real-time interactions with complex liquid effects are possible with our approach.

cs.GR↗

arXiv2019

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.

cs.LG↗

arXiv2018

Liquid Splash Modeling with Neural Networks

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.

cs.GR↗

arXiv2018

Coupled Fluid Density and Motion from Single Views

We present a novel method to reconstruct a fluid's 3D density and motion based on just a single sequence of images. This is rendered possible by using powerful physical priors for this strongly under-determined problem. More specifically, we propose a novel strategy to infer density updates strongly coupled to previous and current estimates of the flow motion. Additionally, we employ an accurate discretization and depth-based regularizers to compute stable solutions. Using only one view for the reconstruction reduces the complexity of the capturing setup drastically and could even allow for online video databases or smart-phone videos as inputs. The reconstructed 3D velocity can then be flexibly utilized, e.g., for re-simulation, domain modification or guiding purposes. We will demonstrate the capacity of our method with a series of synthetic test cases and the reconstruction of real smoke plumes captured with a Raspberry Pi camera.

cs.GR↗

arXiv2017

Data-Driven Synthesis of Smoke Flows with CNN-based Feature Descriptors

We present a novel data-driven algorithm to synthesize high-resolution flow simulations with reusable repositories of space-time flow data. In our work, we employ a descriptor learning approach to encode the similarity between fluid regions with differences in resolution and numerical viscosity. We use convolutional neural networks to generate the descriptors from fluid data such as smoke density and flow velocity. At the same time, we present a deformation limiting patch advection method which allows us to robustly track deformable fluid regions. With the help of this patch advection, we generate stable space-time data sets from detailed fluids for our repositories. We can then use our learned descriptors to quickly localize a suitable data set when running a new simulation. This makes our approach very efficient, and resolution independent. We will demonstrate with several examples that our method yields volumes with very high effective resolutions, and non-dissipative small scale details that naturally integrate into the motions of the underlying flow.

cs.GR↗

arXiv2017

SMASH: Physics-guided Reconstruction of Collisions from Videos

Collision sequences are commonly used in games and entertainment to add drama and excitement. Authoring even two body collisions in the real world can be difficult, as one has to get timing and the object trajectories to be correctly synchronized. After tedious trial-and-error iterations, when objects can actually be made to collide, then they are difficult to capture in 3D. In contrast, synthetically generating plausible collisions is difficult as it requires adjusting different collision parameters (e.g., object mass ratio, coefficient of restitution, etc.) and appropriate initial parameters. We present SMASH to directly read off appropriate collision parameters directly from raw input video recordings. Technically we enable this by utilizing laws of rigid body collision to regularize the problem of lifting 2D trajectories to a physically valid 3D reconstruction of the collision. The reconstructed sequences can then be modified and combined to easily author novel and plausible collisions. We evaluate our system on a range of synthetic scenes and demonstrate the effectiveness of our method by accurately reconstructing several complex real world collision events.

cs.GR↗

arXiv2017

Primal-Dual Optimization for Fluids

We apply a novel optimization scheme from the image processing and machine learning areas, a fast Primal-Dual method, to achieve controllable and realistic fluid simulations. While our method is generally applicable to many problems in fluid simulations, we focus on the two topics of fluid guiding and separating solid-wall boundary conditions. Each problem is posed as an optimization problem and solved using our method, which contains acceleration schemes tailored to each problem. In fluid guiding, we are interested in partially guiding fluid motion to exert control while preserving fluid characteristics. With our method, we achieve explicit control over both large-scale motions and small-scale details which is valuable for many applications, such as level-of-detail adjustment (after running the coarse simulation), spatially varying guiding strength, domain modification, and resimulation with different fluid parameters. For the separating solid-wall boundary conditions problem, our method effectively eliminates unrealistic artifacts of fluid crawling up solid walls and sticking to ceilings, requiring few changes to existing implementations. We demonstrate the fast convergence of our Primal-Dual method with a variety of test cases for both model problems.

cs.GR↗