arXiv subjects

Rüdiger Westermann

Publications and source records attributed to Rüdiger Westermann.

36 records · Page 2Linked to original sources

arXiv2022

Visual Analysis of Multiple Dynamic Sensitivities along Ascending Trajectories in the Atmosphere

Numerical weather prediction models rely on parameterizations for subgrid-scale processes, e.g., for cloud microphysics. These parameterizations are a well-known source of uncertainty in weather forecasts that can be quantified via algorithmic differentiation, which computes the sensitivities of prognostic variables to changes in model parameters. It is particularly interesting to use sensitivities to analyze the validity of physical assumptions on which microphysical parameterizations in the numerical model source code are based. In this article, we consider the use case of strongly ascending trajectories, so-called warm conveyor belt trajectories, known to have a significant impact on intense surface precipitation rates in extratropical cyclones. We present visual analytics solutions to analyze interactively the sensitivities of a selected prognostic variable, i.e. rain mass density, to multiple model parameters along such trajectories. We propose a visual interface that enables to a) compare the values of multiple sensitivities at a single time step on multiple trajectories, b) assess the spatio-temporal relationships between sensitivities and the shape and location of trajectories, and c) a comparative analysis of the temporal development of sensitivities along multiple trajectories. We demonstrate how our approach enables atmospheric scientists to interactively analyze the uncertainty in the microphysical parameterizations, and along the trajectories, with respect to a selected prognostic variable. We apply our approach to the analysis of convective trajectories within the extratropical cyclone "Vladiana", which occurred between 22-25 September 2016 over the North Atlantic.

physics.ao-ph↗

arXiv2022

A Streamline-guided De-Homogenization Approach for Structural Design

We present a novel de-homogenization approach for efficient design of high-resolution load-bearing structures. The proposed approach builds upon a streamline-based parametrization of the design domain, using a set of space-filling and evenly-spaced streamlines in the two mutually orthogonal direction fields that are obtained from homogenization-based topology optimization. Streamlines in these fields are converted into a graph, which is then used to construct a quad-dominant mesh whose edges follow the direction fields. In addition, the edge width is adjusted according to the density and anisotropy of the optimized orthotropic cells. In a number of numerical examples, we demonstrate the mechanical performance and regular appearance of the resulting structural designs, and compare them with those from classic and contemporary approaches.

cs.CE↗

arXiv2022

Fast Neural Representations for Direct Volume Rendering

Despite the potential of neural scene representations to effectively compress 3D scalar fields at high reconstruction quality, the computational complexity of the training and data reconstruction step using scene representation networks limits their use in practical applications. In this paper, we analyze whether scene representation networks can be modified to reduce these limitations and whether such architectures can also be used for temporal reconstruction tasks. We propose a novel design of scene representation networks using GPU tensor cores to integrate the reconstruction seamlessly into on-chip raytracing kernels, and compare the quality and performance of this network to alternative network- and non-network-based compression schemes. The results indicate competitive quality of our design at high compression rates, and significantly faster decoding times and lower memory consumption during data reconstruction. We investigate how density gradients can be computed using the network and show an extension where density, gradient and curvature are predicted jointly. As an alternative to spatial super-resolution approaches for time-varying fields, we propose a solution that builds upon latent-space interpolation to enable random access reconstruction at arbitrary granularity. We summarize our findings in the form of an assessment of the strengths and limitations of scene representation networks \changed{for compression domain volume rendering, and outline future research directions.

cs.GR↗

arXiv2022

3D-TSV: The 3D Trajectory-based Stress Visualizer

We present the 3D Trajectory-based Stress Visualizer (3D-TSV), a visual analysis tool for the exploration of the principal stress directions in 3D solids under load. 3D-TSV provides a modular and generic implementation of key algorithms required for a trajectory-based visual analysis of principal stress directions, including the automatic seeding of space-filling stress lines, their extraction using numerical schemes, their mapping to an effective renderable representation, and rendering options to convey structures with special mechanical properties. In the design of 3D-TSV, several perceptual challenges have been addressed when simultaneously visualizing three mutually orthogonal stress directions via lines. We present a novel algorithm for generating a space-filling and evenly spaced set of mutually orthogonal lines. The algorithm further considers the locations of lines to obtain a more regular appearance, and enables the extraction of a level-of-detail representation with adjustable sparseness of the trajectories along a certain stress direction. To convey ambiguities in the orientation of the principal stress directions, the user can select a combined visualization of two principal directions via oriented ribbons. Additional depth cues improve the perception of the spatial relationships between trajectories. 3D-TSV is accessible to end users via a C++- and OpenGL-based rendering frontend that is seamlessly connected to a MatLab-based extraction backend. The code (BSD license) of 3D-TSV as well as scripts to make ANSYS and ABAQUS simulation results accessible to the 3D-TSV backend are publicly available.

cs.GR↗

arXiv2021

Stress Topology Analysis for Porous Infill Optimization

The optimization of porous infill structures via local volume constraints has become a popular approach in topology optimization. In some design settings, however, the iterative optimization process converges only slowly, or not at all even after several hundreds or thousands of iterations. This leads to regions in which a distinct binary design is difficult to achieve. Interpreting intermediate density values by applying a threshold results in large solid or void regions, leading to sub-optimal structures. We find that this convergence issue relates to the topology of the stress tensor field that is simulated when applying the same external forces on the solid design domain. In particular, low convergence is observed in regions around so-called trisector degenerate points. Based on this observation, we propose an automatic initialization process that prescribes the topological skeleton of the stress field into the material field as solid simulation elements. These elements guide the material deposition around the degenerate points, but can also be remodelled or removed during the optimization. We demonstrate significantly improved convergence rates in a number of use cases with complex stress topologies. The improved convergence is demonstrated for infill optimization under homogeneous as well as spatially varying local volume constraints.

cs.CE↗

arXiv2021

Differentiable Direct Volume Rendering

We present a differentiable volume rendering solution that provides differentiability of all continuous parameters of the volume rendering process. This differentiable renderer is used to steer the parameters towards a setting with an optimal solution of a problem-specific objective function. We have tailored the approach to volume rendering by enforcing a constant memory footprint via analytic inversion of the blending functions. This makes it independent of the number of sampling steps through the volume and facilitates the consideration of small-scale changes. The approach forms the basis for automatic optimizations regarding external parameters of the rendering process and the volumetric density field itself. We demonstrate its use for automatic viewpoint selection using differentiable entropy as objective, and for optimizing a transfer function from rendered images of a given volume. Optimization of per-voxel densities is addressed in two different ways: First, we mimic inverse tomography and optimize a 3D density field from images using an absorption model. This simplification enables comparisons with algebraic reconstruction techniques and state-of-the-art differentiable path tracers. Second, we introduce a novel approach for tomographic reconstruction from images using an emission-absorption model with post-shading via an arbitrary transfer function.

cs.GR↗

arXiv2021

Efficient wide-field radio interferometry response

Radio interferometers do not measure the sky brightness distribution directly but rather a modified Fourier transform of it. Imaging algorithms, thus, need a computational representation of the linear measurement operator and its adjoint, irrespective of the specific chosen imaging algorithm. In this paper, we present a C++ implementation of the radio interferometric measurement operator for wide-field measurements which is based on "improved $w$-stacking". It can provide high accuracy (down to $\approx 10^{-12}$), is based on a new gridding kernel which allows smaller kernel support for given accuracy, dynamically chooses kernel, kernel support and oversampling factor for maximum performance, uses piece-wise polynomial approximation for cheap evaluations of the gridding kernel, treats the visibilities in cache-friendly order, uses explicit vectorisation if available and comes with a parallelisation scheme which scales well also in the adjoint direction (which is a problem for many previous implementations). The implementation has a small memory footprint in the sense that temporary internal data structures are much smaller than the respective input and output data, allowing in-memory processing of data sets which needed to be read from disk or distributed across several compute nodes before.

astro-ph.IM↗

arXiv2021

Comparison of classical and Bayesian imaging in radio interferometry

CLEAN, the commonly employed imaging algorithm in radio interferometry, suffers from a number of shortcomings: in its basic version it does not have the concept of diffuse flux, and the common practice of convolving the CLEAN components with the CLEAN beam erases the potential for super-resolution; it does not output uncertainty information; it produces images with unphysical negative flux regions; and its results are highly dependent on the so-called weighting scheme as well as on any human choice of CLEAN masks to guiding the imaging. Here, we present the Bayesian imaging algorithm resolve which solves the above problems and naturally leads to super-resolution. We take a VLA observation of Cygnus~A at four different frequencies and image it with single-scale CLEAN, multi-scale CLEAN and resolve. Alongside the sky brightness distribution resolve estimates a baseline-dependent correction function for the noise budget, the Bayesian equivalent of weighting schemes. We report noise correction factors between 0.4 and 429. The enhancements achieved by resolve come at the cost of higher computational effort.

astro-ph.IM↗

arXiv2020

A comparative study of convolutional neural network models for wind field downscaling

We analyze the applicability of convolutional neural network (CNN) architectures for downscaling of short-range forecasts of near-surface winds on extended spatial domains. Short-range wind field forecasts (at the 100 m level) from ECMWF ERA5 reanalysis initial conditions at 31 km horizontal resolution are downscaled to mimic HRES (deterministic) short-range forecasts at 9 km resolution. We evaluate the downscaling quality of four exemplary model architectures and compare these against a multi-linear regression model. We conduct a qualitative and quantitative comparison of model predictions and examine whether the predictive skill of CNNs can be enhanced by incorporating additional atmospheric variables, such as geopotential height and forecast surface roughness, or static high-resolution fields, like land-sea mask and topography. We further propose DeepRU, a novel U-Net-based CNN architecture, which is able to infer situation-dependent wind structures that cannot be reconstructed by other models. Inferring a target 9 km resolution wind field from the low-resolution input fields over the Alpine area takes less than 10 milliseconds on our GPU target architecture, which compares favorably to an overhead in simulation time of minutes or hours between low- and high-resolution forecast simulations.

physics.ao-ph↗

arXiv2020

Interactive Focus+Context Rendering for Hexahedral Mesh Inspection

The visual inspection of a hexahedral mesh with respect to element quality is difficult due to clutter and occlusions that are produced when rendering all element faces or their edges simultaneously. Current approaches overcome this problem by using focus on specific elements that are then rendered opaque, and carving away all elements occluding their view. In this work, we make use of advanced GPU shader functionality to generate a focus+context rendering that highlights the elements in a selected region and simultaneously conveys the global mesh structure in the surrounding. To achieve this, we propose a gradual transition from edge-based focus rendering to volumetric context rendering, by combining fragment shader-based edge and face rendering with per-pixel fragment lists. A fragment shader smoothly transitions between wireframe and face-based rendering, including focus-dependent rendering style and depth-dependent edge thickness and halos, and per-pixel fragment lists are used to blend fragments in correct visibility order. To maintain the global mesh structure in the context regions, we propose a new method to construct a sheet-based level-of-detail hierarchy and smoothly blend it with volumetric information. The user guides the exploration process by moving a lens-like hotspot. Since all operations are performed on the GPU, interactive frame rates are achieved even for large meshes.

cs.GR↗

arXiv2020

A Comparison of Rendering Techniques for Large 3D Line Sets with Transparency

This paper presents a comprehensive study of interactive rendering techniques for large 3D line sets with transparency. The rendering of transparent lines is widely used for visualizing trajectories of tracer particles in flow fields. Transparency is then used to fade out lines deemed unimportant, based on, for instance, geometric properties or attributes defined along them. Since accurate blending of transparent lines requires rendering the lines in back-to-front or front-to-back order, enforcing this order for 3D line sets with tens or even hundreds of thousands of elements becomes challenging. In this paper, we study CPU and GPU rendering techniques for large transparent 3D line sets. We compare accurate and approximate techniques using optimized implementations and a number of benchmark data sets. We discuss the effects of data size and transparency on quality, performance and memory consumption. Based on our study, we propose two improvements to per-pixel fragment lists and multi-layer alpha blending. The first improves the rendering speed via an improved GPU sorting operation, and the second improves rendering quality via a transparency-based bucketing.

cs.GR↗

arXiv2020

Visual Analysis of Multi-Parameter Distributions across Ensembles

For an ensemble of data points in a multi-parameter space, we present a visual analytics technique to select a representative distribution of parameter values, and analyse how representative this distribution is in all ensemble members. A multi-parameter cluster in a representative ensemble member is visualized via a parallel coordinates plot, to provide initial distributions and let domain experts interactively select relevant parameters and value ranges. Since unions of value ranges select hyper-cubes in parameter space, data points in these unions are not necessarily contained in the cluster. By using a multi-parameter kD-tree to further refine the selected parameter ranges, in combination with a covariance analysis of refined sets of data points, a tight partition in multi-parameter space with reduced number of falsely selected points is obtained. To assess the representativeness of the selected multi-parameter distribution across the ensemble, a linked side-by-side view of per-member violin plots is provided. We propose modifications of violin plots to show multi-parameter distributions simultaneously, and investigate the visual design that effectively conveys (dis-)similarities in multi-parameter distributions. In a linked spatial view, users can analyse and compare the spatial distribution of selected points in different ensemble members via interval-based isosurface raycasting. In two real-world application cases we show how our approach is used to analyse the multi-parameter distributions across an ensemble of 3D fields.

cs.HC↗

arXiv2020

Inverting the Feature Visualization Process for Feedforward Neural Networks

This work sheds light on the invertibility of feature visualization in neural networks. Since the input that is generated by feature visualization using activation maximization does, in general, not yield the feature objective it was optimized for, we investigate optimizing for the feature objective that yields this input. Given the objective function used in activation maximization that measures how closely a given input resembles the feature objective, we exploit that the gradient of this function w.r.t. inputs is---up to a scaling factor---linear in the objective. This observation is used to find the optimal feature objective via computing a closed form solution that minimizes the gradient. By means of Inverse Feature Visualization, we intend to provide an alternative view on a networks sensitivity to certain inputs that considers feature objectives rather than activations.

cs.LG↗

arXiv2020

Learning Adaptive Sampling and Reconstruction for Volume Visualization

A central challenge in data visualization is to understand which data samples are required to generate an image of a data set in which the relevant information is encoded. In this work, we make a first step towards answering the question of whether an artificial neural network can predict where to sample the data with higher or lower density, by learning of correspondences between the data, the sampling patterns and the generated images. We introduce a novel neural rendering pipeline, which is trained end-to-end to generate a sparse adaptive sampling structure from a given low-resolution input image, and reconstructs a high-resolution image from the sparse set of samples. For the first time, to the best of our knowledge, we demonstrate that the selection of structures that are relevant for the final visual representation can be jointly learned together with the reconstruction of this representation from these structures. Therefore, we introduce differentiable sampling and reconstruction stages, which can leverage back-propagation based on supervised losses solely on the final image. We shed light on the adaptive sampling patterns generated by the network pipeline and analyze its use for volume visualization including isosurface and direct volume rendering.

cs.GR↗

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

Unified Radio Interferometric Calibration and Imaging with Joint Uncertainty Quantification

The data reduction procedure for radio interferometers can be viewed as a combined calibration and imaging problem. We present an algorithm that unifies cross-calibration, self-calibration, and imaging. Being a Bayesian method, that algorithm does not only calculate an estimate of the sky brightness distribution, but also provides an estimate of the joint uncertainty which entails both the uncertainty of the calibration and the one of the actual observation. The algorithm is formulated in the language of information field theory and uses Metric Gaussian Variational Inference (MGVI) as the underlying statistical method. So far only direction-independent antenna-based calibration is considered. This restriction may be released in future work. An implementation of the algorithm is contributed as well.

astro-ph.IM↗

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↗

arXiv2018

A Voxel-based Rendering Pipeline for Large 3D Line Sets

We present a voxel-based rendering pipeline for large 3D line sets that employs GPU ray-casting to achieve scalable rendering including transparency and global illumination effects that cannot be achieved with GPU rasterization. Even for opaque lines we demonstrate superior rendering performance compared to GPU rasterization of lines, and when transparency is used we can interactively render large amounts of lines that are infeasible to be rendered via rasterization. To achieve this, we propose a direction-preserving encoding of lines into a regular voxel grid, along with the quantization of directions using face-to-face connectivity in this grid. On the regular grid structure, parallel GPU ray-casting is used to determine visible fragments in correct visibility order. To enable interactive rendering of global illumination effects like low-frequency shadows and ambient occlusions, illumination simulation is performed during ray-casting on a level-of-detail (LoD) line representation that considers the number of lines and their lengths per voxel. In this way we can render effects which are very difficult to render via GPU rasterization. A detailed performance and quality evaluation compares our approach to rasterization-based rendering of lines.

cs.GR↗