Fraunhofer Institute for Industrial Mathematics

Despite its great success, machine learning can have its limits when dealing with insufficient training data. A potential solution is the additional integration of prior knowledge into the training process which leads to the notion of informed machine learning. In this paper, we present a structured overview of various approaches in this field. We provide a definition and propose a concept for informed machine learning which illustrates its building blocks and distinguishes it from conventional machine learning. We introduce a taxonomy that serves as a classification framework for informed machine learning approaches. It considers the source of knowledge, its representation, and its integration into the machine learning pipeline. Based on this taxonomy, we survey related research and describe how different knowledge representations such as algebraic equations, logic rules, or simulation results can be used in learning systems. This evaluation of numerous papers on the basis of our taxonomy uncovers key methods in the field of informed machine learning.

We present a general framework for several previously introduced boundary conditions for lattice Boltzmann models, such as the bounce-back rule and the linear and quadratic interpolations. The objectives are twofold: first to give theoretical tools to study the existing link-type boundary conditions and their corresponding accuracy; second to design boundary conditions for general flows which are third-order kinetic accurate. Using these new boundary conditions, Couette and Poiseuille flows are exact solutions of the lattice Boltzmann models for a Reynolds number Re=0 (Stokes limit) for arbitrary inclination with the lattice directions. Numerical comparisons are given for Stokes flows in periodic arrays of spheres and cylinders, linear periodic array of cylinders between moving plates, and for Navier-Stokes flows in periodic arrays of cylinders for Re<200. These results show a significant improvement of the overall accuracy when using the linear interpolations instead of the bounce-back reflection (up to an order of magnitude on the hydrodynamics fields). Further improvement is achieved with the new multireflection boundary conditions, reaching a level of accuracy close to the quasianalytical reference solutions, even for rather modest grid resolutions and few points in the narrowest channels. More important, the pressure and velocity fields in the vicinity of the obstacles are much smoother with multireflection than with the other boundary conditions. Finally the good stability of these schemes is highlighted by some simulations of moving obstacles: a cylinder between flat walls and a sphere in a cylinder.

Generative convolutional deep neural networks, e.g. popular GAN architectures, are relying on convolution based up-sampling methods to produce non-scalar outputs like images or video sequences. In this paper, we show that common up-sampling methods, i.e. known as up-convolution or transposed convolution, are causing the inability of such models to reproduce spectral distributions of natural training data correctly. This effect is independent of the underlying architecture and we show that it can be used to easily detect generated data like deepfakes with up to 100% accuracy on public benchmarks. To overcome this drawback of current generative models, we propose to add a novel spectral regularization term to the training optimization objective. We show that this approach not only allows to train spectral consistent GANs that are avoiding high frequency errors. Also, we show that a correct approximation of the frequency spectrum has positive effects on the training stability and output quality of generative networks.

A full morphology (FM) model has been developed for studying the two-phase characteristics of the gas diffusion medium in a polymer electrolyte fuel cell (PEFC). The three-dimensional (3D) fibrous microstructure for the nonwoven gas diffusion layer (GDL) microstructure has been reconstructed using a stochastic technique for Toray090 and SGL10BA carbon papers. The FM model directly solves for the capillary pressure-saturation relations on the detailed morphology of the reconstructed GDL from drainage simulations. The estimated capillary pressure-saturation curves can be used as valuable inputs to macroscopic two-phase models. Additionally, 3D visualization of the water distribution in the gas diffusion medium suggests that only a small number of pores are occupied by liquid water at breakthrough. Based on a reduced compression model, the two-phase behavior of the GDL under mechanical load is also investigated and the capillary pressure-saturation relations are evaluated for different compression levels.

Modeling financial time series by stochastic processes is a challenging task and a central area of research in financial mathematics. As an alternative, we introduce Quant GANs, a data-driven model which is inspired by the recent success of generative adversarial networks (GANs). Quant GANs consist of a generator and discriminator function, which utilize temporal convolutional networks (TCNs) and thereby achieve to capture long-range dependencies such as the presence of volatility clusters. The generator function is explicitly constructed such that the induced stochastic process allows a transition to its risk-neutral distribution. Our numerical results highlight that distributional properties for small and large lags are in an excellent agreement and dependence properties such as volatility clusters, leverage effects, and serial autocorrelations can be generated by the generator function of Quant GANs, demonstrably in high fidelity.

Abstract In this paper, a new framework for model order reduction of LTI parametric systems is introduced. After generating and reducing several local original models in the parameter space, a parametric reduced-order model is calculated by interpolating the system matrices of the local reduced models. The main task is to find compatible system representations with optimal interpolation properties. Two approaches for this purpose are presented together with several numerical simulations.

Summary In this article, we propose to discretize the problem of linear elastic homogenization by finite differences on a staggered grid and introduce fast and robust solvers. Our method shares some properties with the FFT‐based homogenization technique of Moulinec and Suquet, which has received widespread attention recently because of its robustness and computational speed. These similarities include the use of FFT and the resulting performing solvers. The staggered grid discretization, however, offers three crucial improvements. Firstly, solutions obtained by our method are completely devoid of the spurious oscillations characterizing solutions obtained by Moulinec–Suquet's discretization. Secondly, the iteration numbers of our solvers are bounded independently of the grid size and the contrast. In particular, our solvers converge for three‐dimensional porous structures, which cannot be handled by Moulinec–Suquet's method. Thirdly, the finite difference discretization allows for algorithmic variants with lower memory consumption. More precisely, it is possible to reduce the memory consumption of the Moulinec–Suquet algorithms by 50 % . We underline the effectiveness and the applicability of our methods by several numerical experiments of industrial scale. Copyright © 2015 John Wiley &amp; Sons, Ltd.

Inherently, IMRT treatment planning involves compromising between different planning goals. Multi-criteria IMRT planning directly addresses this compromising and thus makes it more systematic. Usually, several plans are computed from which the planner selects the most promising following a certain procedure. Applying Pareto navigation for this selection step simultaneously increases the variety of planning options and eases the identification of the most promising plan. Pareto navigation is an interactive multi-criteria optimization method that consists of the two navigation mechanisms 'selection' and 'restriction'. The former allows the formulation of wishes whereas the latter allows the exclusion of unwanted plans. They are realized as optimization problems on the so-called plan bundle -- a set constructed from pre-computed plans. They can be approximately reformulated so that their solution time is a small fraction of a second. Thus, the user can be provided with immediate feedback regarding his or her decisions. Pareto navigation was implemented in the MIRA navigator software and allows real-time manipulation of the current plan and the set of considered plans. The changes are triggered by simple mouse operations on the so-called navigation star and lead to real-time updates of the navigation star and the dose visualizations. Since any Pareto-optimal plan in the plan bundle can be found with just a few navigation operations the MIRA navigator allows a fast and directed plan determination. Besides, the concept allows for a refinement of the plan bundle, thus offering a middle course between single plan computation and multi-criteria optimization. Pareto navigation offers so far unmatched real-time interactions, ease of use and plan variety, setting it apart from the multi-criteria IMRT planning methods proposed so far.

Understanding the transport properties of porous materials plays an important role in the development and optimization of polymer electrolyte fuel cells (PEFCs). in this study numerical simulations of different transport properties are compared and validated with data obtained using recently developed experimental techniques. The study is based oil a Toray TGP-H-060 carbon paper, a common gas diffusion layer (GDL) material in PEFC. Diffusivity, permeability, and electric conductivity of the anisotropic, porous material are measured experimentally under various levels of compression. A sample of the GDL is imaged with synchrotron-based X-ray tomography under three different compression levels. Based oil these three-dimensional images, diffusivity, permeability, and conductivity are calculated numerically. Experimental and numerical results agree in general. Deviations are observed for the through-plane conductivity. An explanation for the discrepancy is presented and affirmed by numerical simulations on a virtually created structure model. This proves that numerical simulation based oil tomography data is a versatile tool for the investigation and development of porous structures used in PEFCs.

There are numerous physical situations in which a hole or leak is introduced in an otherwise closed chaotic system. The leak can have a natural origin, it can mimic measurement devices, and it can also be used to reveal dynamical properties of the closed system. A unified treatment of leaking systems is provided and applications to different physical problems, in both the classical and quantum pictures, are reviewed. The treatment is based on the transient chaos theory of open systems, which is essential because real leaks have finite size and therefore estimations based on the closed system differ essentially from observations. The field of applications reviewed is very broad, ranging from planetary astronomy and hydrodynamical flows to plasma physics and quantum fidelity. The theory is expanded and adapted to the case of partial leaks (partial absorption and/or transmission) with applications to room acoustics and optical microcavities in mind. Simulations in the lima\ifmmode \mbox{\c{c}}\else \c{c}\fi{}on family of billiards illustrate the main text. Regarding billiard dynamics, it is emphasized that a correct discrete-time representation can be given only in terms of the so-called true-time maps, while traditional Poincar\'e maps lead to erroneous results. Perron-Frobenius-type operators are generalized so that they describe true-time maps with partial leaks.

Abstract Nondestructive quality inspection with terahertz waves has become an emerging technology, especially in the automotive and aviation industries. Depending on the specific application, different terahertz systems—either fully electronic or based on optical laser pulses—cover the terahertz frequency region from 0.1 THz up to nearly 10 THz and provide high-speed volume inspections on the one hand and high-resolution thickness determination on the other hand. In this paper, we present different industrial applications, which we have addressed with our terahertz systems within the last couple of years. First, we show three-dimensional imaging of glass fiber–reinforced composites and foam structures, and demonstrate thickness determination of multilayer plastic tube walls. Then, we present the characterization of known and unknown multilayer systems down to some microns and the possibility of measuring the thickness of wet paints. The challenges of system reliability in industrial environments, e.g., under the impact of vibrations, and effective solutions are discussed. This paper gives an overview of state-of-the-art terahertz technology for industrial quality inspection. The presented principles are not limited to the automotive and aviation industries but can also be adapted to many other industrial fields.

Offering a unique balance between applications and calculations, Monte Carlo Methods and Models in Finance and Insurance incorporates the application background of finance and insurance with the theory and applications of Monte Carlo methods. It presents recent methods and algorithms, including the multilevel Monte Carlo method, the statistical Rom

In the present paper multilane models for vehicular traffic are considered. A microscopic multilane model based on reaction thresholds is developed. Based on this model an Enskog- like kinetic model is developed. In particular, care is taken to incorporate the correlations between the vehicles. From the kinetic model a fluid dynamic model is derived. The macroscopic coefficients are deduced from the underlying kinetic model. Numerical simulations are presented for all three levels of description in [A. Klar and R. Wegener, SIAM J. Appl. Math., 59 (1999), pp. 1002--1011]. Moreover, a comparison of the results is given there.

A fully parameterized microscale model for lithium ion cells is presented in which the solid and pores (filled by electrolyte) are spatially resolved, and the mass and charge transport equations describing diffusion and migration in each phase are solved separately. Such a model allows: (1) the correlation of structure-scale, non-homogeneous material properties with macroscopic battery performance, and (2) the correlation of geometrical electrode morphology with macroscopic battery performance (electrode design). The micro-model approach discussed here allows for a simpler parameterization as fewer constitutive relations are needed in contrast to the macro-homogenous physical-based approaches. Input parameters were measured experimentally on lithium manganese oxide electrodes and LiPF 6 in 3:7 EC:DMC. Verification and validation for the model is also reported.

Quantum sensing is highly attractive for accessing spectral regions in which the detection of photons is technically challenging: Sample information is gained in the spectral region of interest and transferred via biphoton correlations into another spectral range, for which highly sensitive detectors are available. This is especially beneficial for terahertz radiation, where no semiconductor detectors are available and coherent detection schemes or cryogenically cooled bolometers have to be used. Here, we report on the first demonstration of quantum sensing in the terahertz frequency range in which the terahertz photons interact with a sample in free space and information about the sample thickness is obtained by the detection of visible photons. As a first demonstration, we show layer thickness measurements with terahertz photons based on biphoton interference. As nondestructive layer thickness measurements are of high industrial relevance, our experiments might be seen as a first step toward industrial quantum sensing applications.

The usability of pulsed broadband terahertz radiation for the inspection of composite materials from the aeronautics industry is investigated, with the goal of developing a mobile time-domain spectroscopy system that operates in reflection geometry. A wide range of samples based on glass and carbon fiber reinforced plastics with various types of defects is examined using an imaging system; the results are evaluated both in time and frequency domain. The conductivity of carbon fibers prevents penetration of the respective samples but also allows analysis of coatings from the reflected THz pulses. Glass fiber composites are, in principle, transparent for THz radiation, but commonly with significant absorption for wavelengths >1 THz. Depending on depth, matrix material, and size, defects like foreign material inserts, delaminations, or moisture contamination can be visualized. If a defect is not too deep in the sample, its location can be correctly identified from the delay between partial reflections at the surface and the defect itself.

Many emerging applications in the terahertz (THz) frequency range demand highly sensitive, broadband detectors for room-temperature operation. Field-effect transistors with integrated antennas for THz detection (TeraFETs) have proven to meet these requirements, at the same time offering great potential for scalability, high-speed operation, and functional integrability.

Summary The FFT‐based homogenization method of Moulinec–Suquet has recently emerged as a powerful tool for computing the macroscopic response of complex microstructures for elastic and inelastic problems. In this work, we generalize the method to problems discretized by trilinear hexahedral elements on Cartesian grids and physically nonlinear elasticity problems. We present an implementation of the basic scheme that reduces the memory requirements by a factor of four and of the conjugate gradient scheme that reduces the storage necessary by a factor of nine compared with a naive implementation. For benchmark problems in linear elasticity, the solver exhibits mesh‐ and contrast‐independent convergence behavior and enables the computational homogenization of complex structures, for instance, arising from computed tomography computed tomography (CT) imaging techniques. There exist 3D microstructures involving pores and defects, for which the original FFT‐based homogenization scheme does not converge. In contrast, for the proposed scheme, convergence is ensured. Also, the solution fields are devoid of the spurious oscillations and checkerboarding artifacts associated to conventional schemes. We demonstrate the power of the approach by computing the elasto‐plastic response of a long‐fiber reinforced thermoplastic material with 172 × 10 6 (displacement) degrees of freedom. Copyright © 2016 John Wiley &amp; Sons, Ltd.

Intrahospital transports are often required for diagnostic or therapeutic reasons. Depending on the hospital layout, transportation between nursing wards and service units is either provided by ambulances or by trained personnel who accompany patients on foot. In many large German hospitals, the patient transport service is poorly managed and lacks work-flow coordination. This contributes to higher hospital costs (e.g., because a patient is not delivered to the operating room on time) and to patient inconvenience (e.g., because of long waiting times). We designed a computer-based planning system, Opti-TRANS © , that supports all phases of the transportation flow, including travel booking, dispatching transport requests, and monitoring and reporting trips in real time. The methodology, which we developed to solve the underlying optimization problem—a dynamic dial-a-ride problem with hospital-specific constraints, draws on fast heuristic methods to ensure the efficient and timely provision of transports. We illustrate the strong impact of Opti-TRANS on the daily performance of the patient transportation service of a large German hospital. The major benefits of Opti-TRANS include streamlined transportation processes and work flow, significant savings, and improved patient satisfaction. Moreover, it has contributed to increased awareness among hospital staff of the importance of implementing efficient logistics practices.

The thermal behavior of lithium ion batteries has a huge impact on their lifetime and the initiation of degradation processes. The development of hot spots or large local overpotentials leading, e.g., to lithium metal deposition depends on material properties as well as on the nano- und microstructure of the electrodes. In recent years a theoretical structure emerges, which opens the possibility to establish a systematic modeling strategy from atomistic to continuum scale to capture and couple the relevant phenomena on each scale. We outline the building blocks for such a systematic approach and discuss in detail a rigorous approach for the continuum scale based on rational thermodynamics and homogenization theories. Our focus is on the development of a systematic thermodynamically consistent theory for thermal phenomena in batteries at the microstructure scale and at the cell scale. We discuss the importance of carefully defining the continuum fields for being able to compare seemingly different phenomenological theories and for obtaining rules to determine unknown parameters of the theory by experiments or lower-scale theories. The resulting continuum models for the microscopic and the cell scale are numerically solved in full 3D resolution. The complex very localized distributions of heat sources in a microstructure of a battery and the problems of mapping these localized sources on an averaged porous electrode model are discussed by comparing the detailed 3D microstructure-resolved simulations of the heat distribution with the result of the upscaled porous electrode model. It is shown, that not all heat sources that exist on the microstructure scale are represented in the averaged theory due to subtle cancellation effects of interface and bulk heat sources. Nevertheless, we find that in special cases the averaged thermal behavior can be captured very well by porous electrode theory.