Hanno Gottschalk

Bergische Universität Wuppertal | Uni-Wuppertal, BUW · Department of Mathematik und Informatik

In this work we present two video test data sets for the novel computer vision (CV) task of out of distribution tracking (OOD tracking). Here, OOD objects are understood as objects with a semantic class outside the semantic space of an underlying image segmentation algorithm, or an instance within the semantic space which however looks decisively d...

Shape optimization with constraints given by partial differential equations (PDE) is a highly developed field of optimization theory. The elegant adjoint formalism allows to compute shape gradients at the computational cost of a further PDE solve. Thus, gradient descent methods can be applied to shape optimization problems. However, gradient descen...

LU-Net is a simple and fast architecture for invertible neural networks (INN) that is based on the factorization of quadratic weight matrices $\mathsf{A=LU}$, where $\mathsf{L}$ is a lower triangular matrix with ones on the diagonal and $\mathsf{U}$ an upper triangular matrix. Instead of learning a fully occupied matrix $\mathsf{A}$, we learn $\mat...

Turbulent flow consists of structures with a wide range of spatial and temporal scales which are hard to resolve numerically. Classical numerical methods as the Large Eddy Simulation (LES) are able to capture fine details of turbulent structures but come at high computational cost. Applying generative adversarial networks (GAN) for the synthetic mo...

With climate change impacts like sea level rise and changing storms, proper prediction of significant wave height (SWH) becomes increasingly important for coastal protection and marine disaster prevention. In the coastal areas of the North Sea, the morphodynamically changing ebb-tidal delta (ETD) sandbanks cause non-linear wave propagation. Therefo...

This case-study aims at a comparison of the service quality of time-tabled buses as compared to on-demand ridepooling cabs in the late evening hours in the city of Wuppertal, Germany. To evaluate the efficiency of ridepooling as compared to bus services, and to simulate bus rides during the evening hours, transport requests are generated using a pr...

Convolutional neural networks revolutionized computer vision and natrual language processing. Their efficiency, as compared to fully connected neural networks, has its origin in the architecture, where convolutions reflect the translation invariance in space and time in pattern or speech recognition tasks. Recently, Cohen and Welling have put this...

Deep neural networks (DNN) have made impressive progress in the interpretation of image data so that it is conceivable and to some degree realistic to use them in safety critical applications like automated driving. From an ethical standpoint, the AI algorithm should take into account the vulnerability of objects or subjects on the street that rang...

Active learning as a paradigm in deep learning is especially important in applications involving intricate perception tasks such as object detection where labels are difficult and expensive to acquire. Development of active learning methods in such fields is highly computationally expensive and time consuming which obstructs the progression of rese...

To ensure safety in automated driving, the correct perception of the situation inside the car is as important as its environment. Thus, seat occupancy detection and classification of detected instances play an important role in interior sensing. By the knowledge of the seat occupancy status, it is possible to, e.g., automate the airbag deployment c...

In this work we present two video test data sets for the novel computer vision (CV) task of out of distribution tracking (OOD tracking). Here, OOD objects are understood as objects with a semantic class outside the semantic space of an underlying image segmentation algorithm, or an instance within the semantic space which however looks decisively d...

Domain adaptation is of huge interest as labeling is an expensive and error-prone task, especially when labels are needed on pixel-level like in semantic segmentation. Therefore, one would like to be able to train neural networks on synthetic domains, where data is abundant and labels are precise. However, these models often perform poorly on out-o...

The analysis of standardized low cycle fatigue (LCF) experiments shows that the failure times widely scatter. Furthermore, mechanical components often fail before the deterministic failure time is reached. A possibility to overcome these problems is to consider probabilistic failure times. Our approach for probabilistic life prediction is based on...

This book addresses readers from both academia and industry, since it is written by authors from both academia and industry. Accordingly, it takes on diverse viewing angles, but keeps a clear focus on machine-learned environment perception in autonomous vehicles. Special interest is on deep neural networks themselves, their robustness and uncertain...

Semantic segmentation is a crucial component for perception in automated driving. Deep neural networks (DNNs) are commonly used for this task, and they are usually trained on a closed set of object classes appearing in a closed operational domain. However, this is in contrast to the open world assumption in automated driving that DNNs are deployed...

This article presents numerical work on a special case of the cosmological semiclassical Einstein equation (SCE). The SCE describes the interaction of relativistic quantum matter by the expected value of the renormalized stress-energy tensor of a quantum field with classical gravity. Here we consider a free massless scalar field with general (not nec...

Exponentially expanding space-times play a central role in contemporary cosmology, most importantly in the theory of inflation and in the Dark Energy driven expansion in the late universe. In this work, we give a complete list of de Sitter solutions of the semiclassical Einstein equation (SCE), where classical gravity is coupled to the expected val...

Deep neural networks (DNN) have made impressive progress in the interpretation of image data, so that it is conceivable and to some degree realistic to use them in safety critical applications like automated driving. From an ethical standpoint, the AI algorithm should take into account the vulnerability of objects or subjects on the street that ran...

While automated driving is often advertised with better-than-human driving performance, this chapter reviews that it is nearly impossible to provide direct statistical evidence on the system level that this is actually the case. The amount of labeled data needed would exceed dimensions of present-day technical and economical capabilities. A commonl...

Bringing deep neural networks (DNNs) into safety critical applications such as automated driving, medical imaging and finance, requires a thorough treatment of the model's uncertainties. Training deep neural networks is already resource demanding and so is also their uncertainty quantification. In this overview article, we survey methods that we de...

We present a mathematically well-founded approach for the synthetic modeling of turbulent flows using generative adversarial networks (GAN). Based on the analysis of chaotic, deterministic systems in terms of ergodicity, we outline a mathematical proof that GAN can actually learn to sample state snapshots from the invariant measure of the chaotic s...

The overall goal of this work is to enrich training data for automated driving with so called corner cases. In road traffic, corner cases are critical, rare and unusual situations that challenge the perception by AI algorithms. For this purpose, we present the design of a test rig to generate synthetic corner cases using a human-in-the-loop approac...

Semantic segmentation is a crucial component for perception in automated driving. Deep neural networks (DNNs) are commonly used for this task and they are usually trained on a closed set of object classes appearing in a closed operational domain. However, this is in contrast to the open world assumption in automated driving that DNNs are deployed t...

VRUs in a reachable area depending on the ego-car's velocity. Moreover, filtering via the degree of detection, allows for further contextualization in two regards. We measure a segmentation CNN's detection ability of well as visualization tools for the usecase of semantic segmentation in autonomous driving. Our approach present and implement method...

For the semantic segmentation of images, state-of-the-art deep neural networks (DNNs) achieve high segmenta-tion accuracy if that task is restricted to a closed set of classes. However, as of now DNNs have limited ability to operate in an open world, where they are tasked to identify pixels belonging to unknown objects and eventually to learn novel...

This article presents numerical work on a special case of the cosmological semiclassical Einstein equation (SCE). The SCE describes the interaction of relativistic quantum matter by the expected value of the renormalized stress-energy tensor of a quantum field with classical gravity. Here we consider a free massless scalar field with general (not n...

While automated driving is often advertised with better-than-human driving performance, this work reviews that it is nearly impossible to provide direct statistical evidence on the system level that this is actually the case. The amount of labeled data needed would exceed dimensions of present day technical and economical capabilities. A commonly u...

We present a mathematically well founded approach for the synthetic modeling of turbulent flows using generative adversarial networks (GAN). Based on the analysis of chaotic, deterministic systems in terms of ergodicity, we outline a mathematical proof that GAN can actually learn to sample state snapshots form the invariant measure of the chaotic s...

We present a novel post-processing tool for semantic segmentation of LiDAR point cloud data, called LidarMetaSeg, which estimates the prediction quality segmentwise. For this purpose we compute dispersion measures based on network probability outputs as well as feature measures based on point cloud input features and aggregate them on segment level...

To ensure safety in automated driving, the correct perception of the situation inside the car is as important as its environment. Thus, seat occupancy detection and classification of detected instances play an important role in interior sensing. By the knowledge of the seat occupancy status, it is possible to, e.g., automate the airbag deployment c...

Reliable epistemic uncertainty estimation is an essential component for backend applications of deep object detectors in safety-critical environments. Modern network architectures tend to give poorly calibrated confidences with limited predictive power. Here, we introduce novel gradient-based uncertainty metrics and investigate them for different o...

We develop a comprehensive framework in which the existence of solutions to the semiclassical Einstein equation (SCE) in cosmological spacetimes is shown. Different from previous work on this subject, we do not restrict to the conformally coupled scalar field and we admit the full renormalization freedom. Based on a regularization procedure, which...

A simple multi-physical system for the potential flow of a fluid through a shroud, in which a mechanical component, like a turbine vane, is placed, is modeled mathematically. We then consider a multi-criteria shape optimization problem, where the shape of the component is allowed to vary under a certain set of second-order Hölder continuous differe...

This paper describes the project GivEn that develops a novel multiobjective optimization process for gas turbine blades and vanes using modern “adjoint” shape optimization algorithms. Given the many start and shut-down processes of gas power plants in volatile energy grids, besides optimizing gas turbine geometries for efficiency, the durability un...

Gas turbines are used in aviation and energy production. As efficiency of gas turbines increases with firing temperatures, the hot gas components of a gas turbine are subject to extreme termo-mechanical load.

Instance segmentation with neural networks is an essential task in environment perception. However, the networks can predict false positive instances with high confidence values and true positives with low ones. Hence, it is important to accurately model the uncertainties of neural networks to prevent safety issues and foster interpretability. In a...

Deep neural networks (DNNs) for the semantic segmen-tation of images are usually trained to operate on a pre-defined closed set of object classes. This is in contrast to the "open world" setting where DNNs are envisioned to be deployed to. From a functional safety point of view, the ability to detect so-called "out-of-distribution" (OoD) samples, i...

We consider the simultaneous optimization of the reliability and the cost of a ceramic component in a biobjective PDE constrained shape optimization problem. A probabilistic Weibull-type model is used to assess the probability of failure of the component under tensile load, while the cost is assumed to be proportional to the volume of the component...

In recent years, generative adversarial networks (GANs) have demonstrated impressive experimental results while there are only a few works that foster statistical learning theory for GANs. In this work, we propose an infinite dimensional theoretical framework for generative adversarial learning. Assuming the class of uniformly bounded $k$-times $\a...

We investigate the stationary diffusion equation with a coefficient given by a (transformed) L\'evy random field. L\'evy random fields are constructed by smoothing L\'evy noise fields with kernels from the Mat\'ern class. We show that L\'evy noise naturally extends Gaussian white noise within Minlos' theory of generalized random fields. Results on...

In this work, we present an uncertainty-based method for sensor fusion with camera and radar data. The outputs of two neural networks, one processing camera and the other one radar data, are combined in an uncertainty aware manner. To this end, we gather the outputs and corresponding meta information for both networks. For each predicted object, th...

We present a novel region based active learning method for semantic image segmentation, called MetaBox+. For acquisition, we train a meta regression model to estimate the segment-wise Intersection over Union (IoU) of each predicted segment of unlabeled images. This can be understood as an estimation of segment-wise prediction quality. Queried regio...

Convolutional neural networks (CNNs) have seen spectacular advances over the past century, particularly improving the state-of-the-art in computer vision tasks. Semantic segmentation, an image classification at pixel-level, is an essential step in understanding a vehicle's surroundings via camera images for autonomous driving. While CNNs keep becom...

Deep neural networks (DNNs) have proven to be powerful tools for processing unstructured data. However for high-dimensional data, like images, they are inherently vulnerable to adversarial attacks. Small almost invisible perturbations added to the input can be used to fool DNNs. Various attacks, hardening methods and detection methods have been int...

This paper shows how to use discrete CFD and FEM adjoint surface sensitivities to derive objective-based tolerances for turbine blades, instead of relying on geometric tolerances. For this purpose a multidisciplinary adjoint evaluation tool chain is introduced to quantify the effect of real manufacturing imperfections on aerodynamic efficiency and...

Multigrid methods have proven to be an invaluable tool to efficiently solve large sparse linear systems arising in the discretization of partial differential equations (PDEs). Algebraic multigrid methods and in particular adaptive algebraic multigrid approaches have shown that multigrid efficiency can be obtained without having to resort to propert...

We suggest a novel approach for the efficient and reliable approximation of the Pareto front of sufficiently smooth unconstrained bi-criteria optimization problems. Optimality conditions formulated for weighted sum scalarizations of the problem yield a description of (parts of) the Pareto front as a parametric curve, parameterized by the scalarizat...

bstract. A simple multi-physical system for the potential flow of a fluid through a shroud in which a mechanical component, like a turbine vane, is placed, is modeled mathematically. We then consider a multi criteria shape optimization problem, when the shape of the component is allowed to vary under a certain set of 2nd order Hölder continuous dif...

This paper shows how to use discrete CFD and FEM ad-joint surface sensitivities to derive objective-based tolerances for turbine blades, instead of relying on geometric tolerances. For this purpose a multidisciplinary adjoint evaluation tool chain is introduced to quantify the effect of real manufacturing imperfections on aerodynamic efficiency and...