arXiv subjects

Nils Thuerey

Publications and source records attributed to Nils Thuerey.

At least 73 records · Page 4Linked to original sources

arXiv2022

Leveraging Stochastic Predictions of Bayesian Neural Networks for Fluid Simulations

We investigate uncertainty estimation and multimodality via the non-deterministic predictions of Bayesian neural networks (BNNs) in fluid simulations. To this end, we deploy BNNs in three challenging experimental test-cases of increasing complexity: We show that BNNs, when used as surrogate models for steady-state fluid flow predictions, provide accurate physical predictions together with sensible estimates of uncertainty. Further, we experiment with perturbed temporal sequences from Navier-Stokes simulations and evaluate the capabilities of BNNs to capture multimodal evolutions. While our findings indicate that this is problematic for large perturbations, our results show that the networks learn to correctly predict high uncertainties in such situations. Finally, we study BNNs in the context of solver interactions with turbulent plasma flows. We find that BNN-based corrector networks can stabilize coarse-grained simulations and successfully create multimodal trajectories.

physics.flu-dyn↗

arXiv2022

Modeling of the nonlinear flame response of a Bunsen-type flame via multi-layer perceptron

This paper demonstrates the ability of neural networks to reliably learn the nonlinear flame response of a laminar premixed flame, while carrying out only one unsteady CFD simulation. The system is excited with a broadband, low-pass filtered velocity signal that exhibits a uniform distribution of amplitudes within a predetermined range. The obtained time series of flow velocity upstream of the flame and heat release rate fluctuations are used to train the nonlinear model using a multi-layer perceptron. Several models with varying hyperparameters are trained and the dropout strategy is used as regularizer to avoid overfitting. The best performing model is subsequently used to compute the flame describing function (FDF) using mono-frequent excitations. In addition to accurately predicting the FDF, the trained neural network model also captures the presence of higher harmonics in the flame response. As a result, when coupled with an acoustic solver, the obtained neural network model is better suited than a classical FDF model to predict limit cycle oscillations characterized by more than one frequency. The latter is demonstrated in the final part of the present study. We show that the RMS value of the predicted acoustic oscillations together with the associated dominant frequencies are in excellent agreement with CFD reference data.

physics.flu-dyn↗

arXiv2022

TemporalUV: Capturing Loose Clothing with Temporally Coherent UV Coordinates

We propose a novel approach to generate temporally coherent UV coordinates for loose clothing. Our method is not constrained by human body outlines and can capture loose garments and hair. We implemented a differentiable pipeline to learn UV mapping between a sequence of RGB inputs and textures via UV coordinates. Instead of treating the UV coordinates of each frame separately, our data generation approach connects all UV coordinates via feature matching for temporal stability. Subsequently, a generative model is trained to balance the spatial quality and temporal stability. It is driven by supervised and unsupervised losses in both UV and image spaces. Our experiments show that the trained models output high-quality UV coordinates and generalize to new poses. Once a sequence of UV coordinates has been inferred by our model, it can be used to flexibly synthesize new looks and modified visual styles. Compared to existing methods, our approach reduces the computational workload to animate new outfits by several orders of magnitude.

cs.CV↗

arXiv2022

Realistic galaxy images and improved robustness in machine learning tasks from generative modelling

We examine the capability of generative models to produce realistic galaxy images. We show that mixing generated data with the original data improves the robustness in downstream machine learning tasks. We focus on three different data sets; analytical Sérsic profiles, real galaxies from the COSMOS survey, and galaxy images produced with the SKIRT code, from the IllustrisTNG simulation. We quantify the performance of each generative model using the Wasserstein distance between the distributions of morphological properties (e.g. the Gini-coefficient, the asymmetry, and ellipticity), the surface brightness distribution on various scales (as encoded by the power-spectrum), the bulge statistic and the colour for the generated and source data sets. With an average Wasserstein distance (Fréchet Inception Distance) of $7.19 \times 10^{-2}\, (0.55)$, $5.98 \times 10^{-2}\, (1.45)$ and $5.08 \times 10^{-2}\, (7.76)$ for the Sérsic, COSMOS and SKIRT data set, respectively, our best models convincingly reproduce even the most complicated galaxy properties and create images that are visually indistinguishable from the source data. We demonstrate that by supplementing the training data set with generated data, it is possible to significantly improve the robustness against domain-shifts and out-of-distribution data. In particular, we train a convolutional neural network to denoise a data set of mock observations. By mixing generated images into the original training data, we obtain an improvement of $11$ and $45$ per cent in the model performance regarding domain-shifts in the physical pixel size and background noise level, respectively.

astro-ph.GA↗

arXiv2022

Half-Inverse Gradients for Physical Deep Learning

Recent works in deep learning have shown that integrating differentiable physics simulators into the training process can greatly improve the quality of results. Although this combination represents a more complex optimization task than supervised neural network training, the same gradient-based optimizers are typically employed to minimize the loss function. However, the integrated physics solvers have a profound effect on the gradient flow as manipulating scales in magnitude and direction is an inherent property of many physical processes. Consequently, the gradient flow is often highly unbalanced and creates an environment in which existing gradient-based optimizers perform poorly. In this work, we analyze the characteristics of both physical and neural network optimizations to derive a new method that does not suffer from this phenomenon. Our method is based on a half-inversion of the Jacobian and combines principles of both classical network and physics optimizers to solve the combined optimization task. Compared to state-of-the-art neural network optimizers, our method converges more quickly and yields better solutions, which we demonstrate on three complex learning problems involving nonlinear oscillators, the Schroedinger equation and the Poisson problem.

cs.LG↗

arXiv2022

Simulating Liquids with Graph Networks

Simulating complex dynamics like fluids with traditional simulators is computationally challenging. Deep learning models have been proposed as an efficient alternative, extending or replacing parts of traditional simulators. We investigate graph neural networks (GNNs) for learning fluid dynamics and find that their generalization capability is more limited than previous works would suggest. We also challenge the current practice of adding random noise to the network inputs in order to improve its generalization capability and simulation stability. We find that inserting the real data distribution, e.g. by unrolling multiple simulation steps, improves accuracy and that hiding all domain-specific features from the learning model improves generalization. Our results indicate that learning models, such as GNNs, fail to learn the exact underlying dynamics unless the training set is devoid of any other problem-specific correlations that could be used as shortcuts.

cs.LG↗

arXiv2021

Physics-driven Learning of the Steady Navier-Stokes Equations using Deep Convolutional Neural Networks

Recently, physics-driven deep learning methods have shown particular promise for the prediction of physical fields, especially to reduce the dependency on large amounts of pre-computed training data. In this work, we target the physics-driven learning of complex flow fields with high resolutions. We propose the use of \emph{Convolutional neural networks} (CNN) based U-net architectures to efficiently represent and reconstruct the input and output fields, respectively. By introducing Navier-Stokes equations and boundary conditions into loss functions, the physics-driven CNN is designed to predict corresponding steady flow fields directly. In particular, this prevents many of the difficulties associated with approaches employing fully connected neural networks. Several numerical experiments are conducted to investigate the behavior of the CNN approach, and the results indicate that a first-order accuracy has been achieved. Specifically for the case of a flow around a cylinder, different flow regimes can be learned and the adhered "twin-vortices" are predicted correctly. The numerical results also show that the training for multiple cases is accelerated significantly, especially for the difficult cases at low Reynolds numbers, and when limited reference solutions are used as supplementary learning targets.

physics.flu-dyn↗

arXiv2021

Self-Supervised Collision Handling via Generative 3D Garment Models for Virtual Try-On

We propose a new generative model for 3D garment deformations that enables us to learn, for the first time, a data-driven method for virtual try-on that effectively addresses garment-body collisions. In contrast to existing methods that require an undesirable postprocessing step to fix garment-body interpenetrations at test time, our approach directly outputs 3D garment configurations that do not collide with the underlying body. Key to our success is a new canonical space for garments that removes pose-and-shape deformations already captured by a new diffused human body model, which extrapolates body surface properties such as skinning weights and blendshapes to any 3D point. We leverage this representation to train a generative model with a novel self-supervised collision term that learns to reliably solve garment-body interpenetrations. We extensively evaluate and compare our results with recently proposed data-driven methods, and show that our method is the first to successfully address garment-body contact in unseen body shapes and motions, without compromising realism and detail.

cs.CV↗

arXiv2021

Numerical investigation of minimum drag profiles in laminar flow using deep learning surrogates

Efficiently predicting the flowfield and load in aerodynamic shape optimisation remains a highly challenging and relevant task. Deep learning methods have been of particular interest for such problems, due to their success for solving inverse problems in other fields. In the present study, U-net based deep neural network (DNN) models are trained with high-fidelity datasets to infer flow fields, and then employed as surrogate models to carry out the shape optimisation problem, i.e. to find a drag minimal profile with a fixed cross-section area subjected to a two-dimensional steady laminar flow. A level-set method as well as Bezier-curve method are used to parameterise the shape, while trained neural networks in conjunction with automatic differentiation are utilized to calculate the gradient flow in the optimisation framework. The optimised shapes and drag force values calculated from the flowfields predicted by DNN models agree well with reference data obtained via a Navier-Stokes solver and from the literature, which demonstrates that the DNN models are capable of predicting not only flowfield but also yield satisfactory aerodynamic forces. This is particularly promising as the DNNs were not specifically trained to infer aerodynamic forces. In conjunction with the fast runtime, the DNN-based optimisation framework shows promise for general aerodynamic design problems.

physics.flu-dyn↗

arXiv2021

Global Transport for Fluid Reconstruction with Learned Self-Supervision

We propose a novel method to reconstruct volumetric flows from sparse views via a global transport formulation. Instead of obtaining the space-time function of the observations, we reconstruct its motion based on a single initial state. In addition we introduce a learned self-supervision that constrains observations from unseen angles. These visual constraints are coupled via the transport constraints and a differentiable rendering step to arrive at a robust end-to-end reconstruction algorithm. This makes the reconstruction of highly realistic flow motions possible, even from only a single input view. We show with a variety of synthetic and real flows that the proposed global reconstruction of the transport process yields an improved reconstruction of the fluid motion.

cs.CV↗

arXiv2021

Neural Scene Graphs for Dynamic Scenes

Recent implicit neural rendering methods have demonstrated that it is possible to learn accurate view synthesis for complex scenes by predicting their volumetric density and color supervised solely by a set of RGB images. However, existing methods are restricted to learning efficient representations of static scenes that encode all scene objects into a single neural network, and lack the ability to represent dynamic scenes and decompositions into individual scene objects. In this work, we present the first neural rendering method that decomposes dynamic scenes into scene graphs. We propose a learned scene graph representation, which encodes object transformation and radiance, to efficiently render novel arrangements and views of the scene. To this end, we learn implicitly encoded scenes, combined with a jointly learned latent representation to describe objects with a single implicit function. We assess the proposed method on synthetic and real automotive data, validating that our approach learns dynamic scenes -- only by observing a video of this scene -- and allows for rendering novel photo-realistic views of novel scene compositions with unseen sets of objects at unseen poses.

cs.CV↗

arXiv2021

Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers

Finding accurate solutions to partial differential equations (PDEs) is a crucial task in all scientific and engineering disciplines. It has recently been shown that machine learning methods can improve the solution accuracy by correcting for effects not captured by the discretized PDE. We target the problem of reducing numerical errors of iterative PDE solvers and compare different learning approaches for finding complex correction functions. We find that previously used learning approaches are significantly outperformed by methods that integrate the solver into the training loop and thereby allow the model to interact with the PDE during training. This provides the model with realistic input distributions that take previous corrections into account, yielding improvements in accuracy with stable rollouts of several hundred recurrent evaluation steps and surpassing even tailored supervised variants. We highlight the performance of the differentiable physics networks for a wide variety of PDEs, from non-linear advection-diffusion systems to three-dimensional Navier-Stokes flows.

physics.comp-ph↗

arXiv2020

Perceptual Evaluation of Liquid Simulation Methods

This paper proposes a novel framework to evaluate fluid simulation methods based on crowd-sourced user studies in order to robustly gather large numbers of opinions. The key idea for a robust and reliable evaluation is to use a reference video from a carefully selected real-world setup in the user study. By conducting a series of controlled user studies and comparing their evaluation results, we observe various factors that affect the perceptual evaluation. Our data show that the availability of a reference video makes the evaluation consistent. We introduce this approach for computing scores of simulation methods as visual accuracy metric. As an application of the proposed framework, a variety of popular simulation methods are evaluated.

cs.GR↗

arXiv2020

ScalarFlow: A Large-Scale Volumetric Data Set of Real-world Scalar Transport Flows for Computer Animation and Machine Learning

In this paper, we present ScalarFlow, a first large-scale data set of reconstructions of real-world smoke plumes. We additionally propose a framework for accurate physics-based reconstructions from a small number of video streams. Central components of our algorithm are a novel estimation of unseen inflow regions and an efficient regularization scheme. Our data set includes a large number of complex and natural buoyancy-driven flows. The flows transition to turbulent flows and contain observable scalar transport processes. As such, the ScalarFlow data set is tailored towards computer graphics, vision, and learning applications. The published data set will contain volumetric reconstructions of velocity and density, input image sequences, together with calibration data, code, and instructions how to recreate the commodity hardware capture setup. We further demonstrate one of the many potential application areas: a first perceptual evaluation study, which reveals that the complexity of the captured flows requires a huge simulation resolution for regular solvers in order to recreate at least parts of the natural complexity contained in the captured data.

cs.GR↗

arXiv2020

Data-driven medium-range weather prediction with a Resnet pretrained on climate simulations: A new model for WeatherBench

Numerical weather prediction has traditionally been based on physical models of the atmosphere. Recently, however, the rise of deep learning has created increased interest in purely data-driven medium-range weather forecasting with first studies exploring the feasibility of such an approach. To accelerate progress in this area, the WeatherBench benchmark challenge was defined. Here, we train a deep residual convolutional neural network (Resnet) to predict geopotential, temperature and precipitation at 5.625 degree resolution up to 5 days ahead. To avoid overfitting and improve forecast skill, we pretrain the model using historical climate model output before fine-tuning on reanalysis data. The resulting forecasts outperform previous submissions to WeatherBench and are comparable in skill to a physical baseline at similar resolution. We also analyze how the neural network creates its predictions and find that, with some exceptions, it is compatible with physical reasoning. Finally, we perform scaling experiments to estimate the potential skill of data-driven approaches at higher resolutions.

physics.ao-ph↗

arXiv2020

Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows

With this study we investigate the accuracy of deep learning models for the inference of Reynolds-Averaged Navier-Stokes solutions. We focus on a modernized U-net architecture, and evaluate a large number of trained neural networks with respect to their accuracy for the calculation of pressure and velocity distributions. In particular, we illustrate how training data size and the number of weights influence the accuracy of the solutions. With our best models we arrive at a mean relative pressure and velocity error of less than 3% across a range of previously unseen airfoil shapes. In addition all source code is publicly available in order to ensure reproducibility and to provide a starting point for researchers interested in deep learning methods for physics problems. While this work focuses on RANS solutions, the neural network architecture and learning setup are very generic, and applicable to a wide range of PDE boundary value problems on Cartesian grids.

cs.LG↗

arXiv2020

Data-driven Regularization via Racecar Training for Generalizing Neural Networks

We propose a novel training approach for improving the generalization in neural networks. We show that in contrast to regular constraints for orthogonality, our approach represents a {\em data-dependent} orthogonality constraint, and is closely related to singular value decompositions of the weight matrices. We also show how our formulation is easy to realize in practical network architectures via a reverse pass, which aims for reconstructing the full sequence of internal states of the network. Despite being a surprisingly simple change, we demonstrate that this forward-backward training approach, which we refer to as {\em racecar} training, leads to significantly more generic features being extracted from a given data set. Networks trained with our approach show more balanced mutual information between input and output throughout all layers, yield improved explainability and, exhibit improved performance for a variety of tasks and task transfers.

cs.CV↗

arXiv2020

Learning Similarity Metrics for Numerical Simulations

We propose a neural network-based approach that computes a stable and generalizing metric (LSiM) to compare data from a variety of numerical simulation sources. We focus on scalar time-dependent 2D data that commonly arises from motion and transport-based partial differential equations (PDEs). Our method employs a Siamese network architecture that is motivated by the mathematical properties of a metric. We leverage a controllable data generation setup with PDE solvers to create increasingly different outputs from a reference simulation in a controlled environment. A central component of our learned metric is a specialized loss function that introduces knowledge about the correlation between single data samples into the training process. To demonstrate that the proposed approach outperforms existing metrics for vector spaces and other learned, image-based metrics, we evaluate the different methods on a large range of test data. Additionally, we analyze generalization benefits of an adjustable training data difficulty and demonstrate the robustness of LSiM via an evaluation on three real-world data sets.

cs.LG↗