Research Annie Cuyt

Abstract

To address environmental concerns, researchers focus on reducing the energy use of industrial machinery. Position-controlled systems allow for energy savings by optimizing the position function between fixed user-defined start and endpoints, requiring only adjusted drive settings for easy and cost-effective implementation. State-of-the-art optimizers rely on complex, machine-specific models, deterring machine builders. Furthermore, mismatches between model and reality, and changes in machine behavior over time can render optimized motion profiles suboptimal in practice. This project proposes a novel solution by optimizing the motion profile online during machine operation. Moreover, a key issue is that existing algorithms often achieve only local optimum motion profiles, potentially missing up to 11.3% of energy savings compared to the global optimum. This project proposes two steps to achieve global optimum motion profiles. First, the use of a global optimization algorithm. Secondly, the motion profile's mathematical formulation, typically constrained to specific bases (e.g., polynomial, splines), can limit revealing the global optimum. This project will employ Gaussian Processes to describe motion profiles, allowing unconstrained optimization potential by not limiting the profile to a specific form. Only an online motion profile without pre-defined profile bases can result in a machine operation with an absolute minimal energy need.

Researcher(s)

• Promoter: Derammelaere Stijn
• Co-promoter: Cuyt Annie
• Fellow: De Laet Robbe

Research team(s)

• Co-Design of Cyber-Physical Systems (Cosys-Lab)

Project type(s)

• Research Project

Abstract

The design and engineering of electrically driven machine mechanisms increasingly rely on optimisation. This allows the minimisation of objectives such as the initial component cost or electrical energy required to drive these machines, all without compromising the performance. Heuristic optimisers, popular in mechatronics, often result in local optima and so leave a significant untapped optimisation potential. Different domains such as trajectory, geometry, and controller should be optimised simultaneously in a co-design approach to find the global minimum. Therefore, an explicit model of the design variable's impact on the objective is required. However, the data collection necessary for such a high-dimensional model, simultaneously considering all the design parameters, results in an explosion of the needed number of motion simulations. So, the co-design objective is only attainable if the model can be built from a minimal number of simulations. Through recent developments in multi-dimensional data fitting techniques, a practically feasible method for co-design in a high-dimensional setting may now become available for the first time.

Researcher(s)

• Promoter: Derammelaere Stijn
• Co-promoter: Cuyt Annie

Research team(s)

• Co-Design of Cyber-Physical Systems (Cosys-Lab)

Project type(s)

• Research Project

Abstract

The EXPOWER project combines a broad spectrum of key research and training activities on Multi-Exponential Analysis with applications in industry, that are currently being undertaken in some premier research institutes. The network is interdisciplinary, intersectoral, unconventional and ambitious. It is unconventional in the sense that it connects stakeholders from seemingly separately developed fields: computational harmonic analysis, numerical linear algebra, computer algebra, nonlinear approximation theory, digital signal processing and their applications, in one and more variables. It is ambitious because the consortium stretches from mathematics to computational science and engineering and industry. Multi- exponential analysis might sound remote, but it touches our daily lives in many surprising ways, even if most people are unaware of how important it is. For example, a substantial amount of effort in signal processing and time series analysis is essentially dedicated to the analysis of multi-exponential functions. Multi-exponential analysis is also fundamental to several research fields and application domains that are the subject of the EXPOWER proposal: remote sensing, antenna design, digital imaging, testing and metrology, all impacting some major societal or industrial challenges such as energy, transportation, space research, health and telecommunications. The EXPOWER Beneficiaries and Third Country Partners, each bringing in their own complementary expertise, aim at solving some core challenges where the different domains involved with multi-exponential analysis meet. We target game-changing breakthroughs that will deliver a competitive advantage to industry. The EXPOWER project connects 9 countries, 8 universities, 3 international research institutes and 7 companies to explore this highly relevant thematic.

Researcher(s)

• Promoter: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

Researcher(s)

• Promoter: Cuyt Annie
• Promoter: In't Hout Karel
• Promoter: Vanroose Wim

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

This project represents a formal agreement between UAntwerpen and on the other hand the Flemish Public Service. UAntwerpen provides HPC infrastructure and support to researchers under the conditions as stipulated in this contract.

Researcher(s)

• Promoter: Cuyt Annie
• Promoter: Vanroose Wim

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

The National Competence Centres (NCCs) are the central points of contact for HPC and related technologies in their country. Their missions are to: - Develop and display a comprehensive and transparent map of HPC competences and institutions in their country - Act as a gateway for industry and academia to providers with suitable expertise or relevant projects, may that be national or international - Collect HPC training offers in their country and display them in a central place together with international training offers collected by other NCCs - Foster the industrial uptake of HPC

Researcher(s)

• Promoter: Cuyt Annie
• Promoter: Vanroose Wim

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

The National Competence Centres (NCCs) are the central points of contact for HPC and related technologies in their country. Their missions are to: - Develop and display a comprehensive and transparent map of HPC competences and institutions in their country - Act as a gateway for industry and academia to providers with suitable expertise or relevant projects, may that be national or international - Collect HPC training offers in their country and display them in a central place together with international training offers collected by other NCCs - Foster the industrial uptake of HPC

Researcher(s)

• Promoter: Cuyt Annie
• Promoter: Vanroose Wim

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

This project represents a formal agreement between UAntwerpen and on the other hand the Flemish Public Service. UAntwerpen provides HPC infrastructure and support to researchers under the conditions as stipulated in this contract.

Researcher(s)

• Promoter: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

There is a strong desire to maximize the efficiency or speed of industrial machinery. Designers of machines, performing repetitive motions, often only define the position start- and endpoint of a movement and not the exact position function. This flexibility opens the opportunity to optimize the trajectory of the mechanism. Moreover, for the machine design itself, machine builders often rely on standard components and dimensions. The effect of the geometric design on the optimal trajectory and energy need of the system is very often neglected. The literature mentions cases where ad-hoc optimizations reduce energy usage up to 39% thanks to trajectory and geometric optimization. This project will use available CAD models and sparse interpolation to extract a closed mathematical system property description. This will enable using an interval optimization technique which can guarantee to find the one true global optimal geometric design and trajectory. The knowledge of the system properties will be used to design a robust controller to ensure the machine follows the desired trajectory. Finally, any mismatch between the virtual and real model will be detected with online tracking techniques to assure the machine operation remains optimal. The potential impact for machine builders is high as this project enables them to construct machines with a reduced total cost of ownership or allow them to perform a task as fast as possible purely based on their readily available CAD models.

Researcher(s)

• Promoter: Derammelaere Stijn
• Co-promoter: Cuyt Annie
• Fellow: Van Oosterwyck Nick

Research team(s)

• Co-Design of Cyber-Physical Systems (Cosys-Lab)

Project type(s)

• Research Project

Abstract

This project represents a formal agreement between UAntwerpen and 29 other parties on PRACE – Sixth Implementation Phase Project. UAntwerpen and its third parties are involved in several work packages as stipulated in this contract.

Researcher(s)

• Promoter: Cuyt Annie
• Co-promoter: Becuwe Stefan

Research team(s)

Project type(s)

• Research Project

Abstract

'Radar' is an acronym derived from the words Radio Detection and Ranging. It is used in maritime civil applications as a navigation aid to avoid collisions. The technique uses short bursts of an emitted electromagnetic wave at high frequency and precise direction. If an object is near the antenna transmitting these bursts, echos are sent back to the antenna. The time between the transmission and the reception of an echo is an indication of the distance between antenna and the object. The received echos (they are mainly changed in frequency and amplified) are processed and then represented on a screen. At the moment, the use of cathode ray tube screens (CRT) is less common than digital screens, so often a digitization is necessary. Therefore the analogue signal must be sampled. In order to correctly reconstruct the signal, at the receiving end the signal has to be sampled at a rate higher than the Nyquist frequency. This limit is generally accepted as a constraint for the cost and performance of radar systems in general. Making use of some recent results in exponential analysis developed at UAntwerpen, it is possible to break the Nyquist rate in signal processing. This project investigates the feasibility of these new techniques for analysing 3-dimensional echoes sampled at a sub-Nyquist rate. It is an interdisciplinary effort that joins HZS marine engineers, experienced in echo sounding, with researchers, specialised in computational mathematics, from UAntwerpen. The ambition is to achieve better performance in the use of electromagnetic pulses to detect objects at a low cost by using the most current algorithms, bypassing the investment in switching to more expensive hardware.

Researcher(s)

• Promoter: Cuyt Annie

Research team(s)

Project website

Project type(s)

• Research Project

Abstract

This project represents a formal agreement between UAntwerpen and on the other hand the Flemish Public Service. UAntwerpen provides HPC infrastructure and support to researchers under the conditions as stipulated in this contract.

Researcher(s)

• Promoter: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

This project represents a formal agreement between UAntwerpen and on the other hand the Flemish Public Service regarding the university's participation in the TIER 1 Supercomputing Platform under the conditions as stipulated in this contract.

Researcher(s)

• Promoter: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

As global energy demand will continue to rise and man's negative impact on global warming is known to be a fact, there is a strong desire to minimise the energy usage of industrial machinery. A significant opportunity lies in optimisations which do not require any adaptations or investments in installed hardware such as trajectory optimisation. Machine builders and users often only define the time to move from one point to another and the position of start- and endpoint. The exact position as a function of the time, or position function, in between these two points is very often not an issue for machine users. This flexibility opens the opportunity to optimise the position function. The literature mentions cases where ad-hoc optimisations reduce the energy usage of machinery used for repetitive tasks up to 50% by choosing optimised trajectories over the usual standard movement profiles. However, there is no scientific consensus on a computationally efficient technique which can guarantee to find the global optimum for systems with position varying mechanical load properties. Therefore, this project will assess the use and implementation of direct calculus optimisation. Applying this pure mathematical technique based on symbolic methods of trajectory optimisation would be a genuinely fundamental novelty, especially for machines with position varying dynamics. For one thing, this would eliminate the necessity of time-consuming iterative optimisations. On the contrary, direct calculus methods would lead to closed mathematical functions for the position function. To enable the use of this direct calculus methods, closed mathematical equations, describing the position-varying mechanical load properties, will be necessary. Obtaining such functions can be done theoretically based on Lagrange formulations. However, such an approach is not feasible in practice where the complexity of the machinery hampers analytical analysis. On the other hand, machine builders increasingly rely on CAD multibody software to design their machines. The promotor has expertise in extracting data by applying specific simulations on these virtual CAD models. The sampled data, obtained in this way, can be translated to explicit formulas, based on the expertise of the co-promotor. Developing such a technique to transform the sampled data to closed mathematical equations will be a core challenge of the project and the major enabler to apply direct calculus optimisation. Furthermore, to guarantee the machine still operates at its optimum if machine behaviour changes during operation, an online tracking method is necessary. For this purpose, the knowledge of the promotor on tracking the position dependency of machine parameters online in the frequency domain is essential. The data samples obtained in this way will again be translated to a mathematical description to allow a re-optimisation of the trajectory. For this purpose, the direct calculus optimisation method will be advantageous as it defines the optimised path as a function of position varying parameters. This definition enables direct re-optimisation. Moreover, where the current state of the art focusses on offline a priori or online optimisation, facilitating online re-optimisation based on a priori offline determined information will be another fundamental novelty of this project.

Researcher(s)

• Promoter: Derammelaere Stijn
• Co-promoter: Cuyt Annie
• Fellow: Van Oosterwyck Nick

Research team(s)

• Co-Design of Cyber-Physical Systems (Cosys-Lab)

Project type(s)

• Research Project

Abstract

This project represents a formal research agreement between UA and on the other hand the Flemish Public Service. UA provides the Flemish Public Service research results mentioned in the title of the project under the conditions as stipulated in this contract.

Researcher(s)

• Promoter: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

This project explores the application of a recently developed sub-Nyquist sampling technique to echosounding in underwater communication. Echosounding is a type of sonar widely used to navigate, detect, or communicate with objects under the surface of water. An echo-sounder contains a transducer device that sends acoustic pulses into the water. Another part of the echo-sounder, the hydrophone, receives an echo of these pulses after they are reflected by an obstacle in the water. In order to correctly reconstruct the signal, at the receiving end the signal has to be sampled at a rate higher than the Nyquist frequency. This limit has been accepted as a constraint for the cost and performance of echo sounding devices in general. Making use of some recent results in exponential analysis developed at UAtwerpen, one is able to break the Nyquist rate in signal processing. This project investigates the feasibility of these new techniques for analysing echoes sampled at a sub-Nyquist rate. It is an interdisciplinary effort that joins HZS marine engineers, experienced in echo sounding, with researchers, specialised in computational mathematics, from UAntwerpen. The ambition is to achieve better performance in underwater communication at a low cost by using the most current algorithms, bypassing the investment in switching to more expensive hardware.

Researcher(s)

• Promoter: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

We will develop a reliable validated computer arithmetic, in the form of a computational engine, to support reliable and validated evaluation of the large family of special functions available in the NIST DLMF website, yielding not only practically useful but also mathematically 100% correct results.

Researcher(s)

• Promoter: Cuyt Annie
• Fellow: Wu Min

Research team(s)

Project type(s)

• Research Project

Abstract

Interpolation algorithms are commonly used to compute analytical models that fit a given set of data samples (e.g. observations or measurements). In real-life applications, it is found that data is often contaminated by noise having various levels of uncertainty which complicates the modelling problem. A promising approach to deal with such inaccuracies is to model a set of uncertainty intervals rather than point-based data. Such a formulation has the benefit that it allows us to impose a predefined threshold on the approximation error. As technology advances, the complexity of real-world systems grows inevitably, which has the effect that the modelling task also becomes increasingly challenging and resource demanding. In order to deal with rapid variations in the data, rational functions are preferred over a polynomial fit as they have more expressive power and are often more closely related to the underlying physics of a system. In order to improve on the computational efficiency, it will be investigated if concepts from sparse modelling can be used to relieve the curse of dimensionality. In this project, three aspects will be investigated and exploited to improve the modelling procedure, namely the identification of 1) a sparse set of influential variables, 2) a sparse number of terms in the model representation, 3) a sparse set of key data samples that characterize the overall system behaviour. The efficacy of the resulting approach will be validated on several use-cases.

Researcher(s)

• Promoter: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

SPARSIT is a spin-off under construction for the valorization of a new unique technology that breaks the Nyquist sampling rate which underlies almost all signal acquisition in modern electronics. A patent application was filed in 2011. The inventors have explored a number of interesting applications. This project focuses on further business development in magnetic resonance spectroscopy.

Researcher(s)

• Promoter: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

Many real-time experiments involve the measurement of signals which fall exponentially with time. The task is then to determine, from such measurements, the number of terms n and the value of all the parameters in the exponentially damped model φ(t) = sum_{j=1}^n α_j exp(φ_j t), α_j =β_j +i γ_j, φ_j =ψ_j +i ω_j Here φ_j, ω_j, β_j and γ_j are respectively called the damping, frequency, amplitude and phase of each exponential term. Exponential models appear, for instance, in power system transient detection, motor fault diagnosis, electrophysiology, drug clearance monitoring and glucose tol- erance testing, magnetic resonance and infrared spectroscopy, vibration analysis, seismic data analysis, music signal processing, odour recognition and the electronic nose, typed keystroke recognition from a keyboard sound recording, nuclear science,...From this list, music is arguably the most highly structured signal. Decomposing a complex music signal into different components is an important and powerful preprocessing step for many applications. Much current research focuses on individual aspects of music (such as rhythm, or chords, or instruments) instead of the overall model, although these are anything but independent. Music is also one of the most popular types of online information and there are hundreds of music streaming and download services in operation. The general technique of multiexponential modelling is closely related to what is commonly known in the applied sciences as the Padé-Laplace method and the technique of sparse interpolation in the field of symbolic computation. We emphasize that it is generally believed that none of the listed limitations can be overcome! • The problem of multiexponential modelling is an inverse problem and may be ill-posed. Even the recent algorithms do not yield reliable output when applied to our problem statement. • The analysis of band-limited signals has given rise to a well-developed theory of resolution, associated with the names of Shannon and Nyquist. It states that, if Ω/2 is the highest frequency present in its spectrum, the frequency content of a signal is completely determined by its values at equidistantly spaced time points, 2π/Ω apart. A coarser time grid causes aliasing, identifying higher frequencies with lower frequencies without being able to distinguish between them. As a consequence, the exponential analysis as it is used today, suffers a similar frequency resolution limitation. • In addition, in the presence of noise, different exponential decays ψi cannot be resolved if the ratio of the damping factors is less than some threshold, in other words when the damping constants are too much alike. Our purpose is essentially to propose a regularization of the ill-posed problem above, by making use of the connections of the subject with sparse interpolation and Padé approximation. The trick is to exploit aliasing rather than avoid it! So the objective of the project can be summarized in the following keywords: • fast → because we make use of much smaller-sized structured numerical linear algebra problems than theoretically required in Padé-Laplace, • high-resolution → because we overcome the resolution limitations imposed by the Shannon-Nyquist bound on the one hand and the decay-grid on the other hand, • well-conditioned → because we use the aliasing effect as a way to control the condition number of all the involved structured matrices. Hence the regularization of a popular and widely present ill-posed multiexponential analysis problem!

Researcher(s)

• Promoter: Cuyt Annie
• Fellow: Briani Matteo

Research team(s)

Project type(s)

• Research Project

Abstract

This project represents a formal research agreement between UA and on the other hand the Flemish Public Service. UA provides the Flemish Public Service research results mentioned in the title of the project under the conditions as stipulated in this contract.

Researcher(s)

• Promoter: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

In this project, novel computational methods are developed for optimal sampling of dMRI data that allows to either restrict the acquisition time and/or improve the accuracy of the measured diffusion profiles. Also, a general and efficient reconstruction scheme is developed to obtain high resolution dMRI images, which accounts for motion and distortion artefacts.

Researcher(s)

• Promoter: Sijbers Jan
• Co-promoter: Cuyt Annie

Research team(s)

• Vision lab

Project type(s)

• Research Project

Abstract

This project represents a formal research agreement between UA and on the other hand the Flemish Public Service. UA provides the Flemish Public Service research results mentioned in the title of the project under the conditions as stipulated in this contract.

Researcher(s)

• Promoter: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

An initiative that joins two research groups with complementary symbolic/algebraic and numeric/analytical expertise, through an interpretation of Padé approximants, to tackle the challenge of multivariate shape-frommoments problem that may allow certain operations and transformation in visualization and animation.

Researcher(s)

• Promoter: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

The goal of this project is: - to identify appropriate bases to represent each of the different biomedical signals sparsely and compute the coefficients in this representation, and - to estimate how the compact representations of the exact noise free signal perform in a noisy environment.

Researcher(s)

• Promoter: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

The VSC is a consortium of the five Flemish associations and aims to make more computational power and more storage capacity available to more researchers in all Flemish associations, independent research institutes and industry; to provide excellent user support for all aspects of HPC and technical leadership on HPC, a forum for cross-fertilization and a guiding framework to enable high(er)-level research and productivity. The VSC infrastructure will enable innovative research, stimulate the economic activity and Flanders and strengthen the international competitiveness of the Flemish industry.

Researcher(s)

• Promoter: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

This project represents a formal research agreement between UA and on the other hand the Flemish Public Service. UA provides the Flemish Public Service research results mentioned in the title of the project under the conditions as stipulated in this contract.

Researcher(s)

• Promoter: Cuyt Annie
• Co-promoter: Herrebout Wouter

Research team(s)

Project type(s)

• Research Project

Abstract

The main objective of this project is the development of robust and stable rational modelling algorithms to build parameterized reduced order models for complex physical systems. The order and complexity of the scalable rational models are specifically tailored towards the application at hand. The approximation and/or interpolation models are based on sparse scattered data, spread over the design space of interest, and the models are aimed to be sparse themselves in order to guarantee a minimal complexity.

Researcher(s)

• Promoter: Cuyt Annie
• Co-promoter: Van Deun Joris

Research team(s)

Project type(s)

• Research Project

Abstract

The VSC is a consortium of the five Flemish associations and aims to make more computational power and more storage capacity available to more researchers in all Flemish associations, independent research institutes and industry; to provide excellent user support for all aspects of HPC and technical leadership on HPC, a forum for cross-fertilization and a guiding framework to enable high(er)-level research and productivity. The VSC infrastructure will enable innovative research, stimulate the economic activity and Flanders and strengthen the international competitiveness of the Flemish industry.

Researcher(s)

• Promoter: Cuyt Annie
• Co-promoter: Herrebout Wouter

Research team(s)

Project website

Project type(s)

• Research Project

Abstract

In the past decennia the international financial markets are witnessing a huge increase in the trading of more and more complex products, such as exotic options and interest products, and this growth is only amplifying. For the exchanges and banks it is of crucial importance to be able to price these products accurately, and as fast as possible. The simulation of the current, sophisticated pricing models is, however, very time consuming with classical techniques such as Monte Carlo methods or binomial trees, and practical pricing formulas are often not at hand. This project is concerned with new models and techniques for robustly and efficiently pricing modern financial products. We investigate two complementary approaches: the first is based on partial differential equations and the second on quantum mechanical path integrals. In the first approach, we will consider operator splitting methods and meshfree methods for the effective numerical solution of these, often multi-dimensional, equations. In the second approach, path integral formulas for financial products will be studied by using the present theory concerning physical multi-particle systems and the comonotonicity coefficient. The obtained models and computational techniques will continually be mutually validated.

Researcher(s)

• Promoter: In't Hout Karel
• Co-promoter: Cuyt Annie
• Co-promoter: De Schepper Ann
• Co-promoter: Tempere Jacques

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

The aim of this project is to develop reliable and efficient software for a class of special functions, namely the multivariate hypergeometric functions. Those functions are generalizations into many dimensions of the classical Gauss hypergeometric function and the generalized hypergeometric function . In the bivariate case, we have the four Appell functions (part of the list of 34 Horn functions, bivariate hypergeometric series of order two) and the Kampé de Fériet functions (consisting of an arbitrary numbers of parameters). For an arbitrary number of variables, the Lauricella functions are the most well known.

Researcher(s)

• Promoter: Cuyt Annie
• Fellow: Van Deun Joris

Research team(s)

Project website

Project type(s)

• Research Project

Abstract

Since 2005, the University of Antwerp houses one of the most powerful academic Belgian computers: CalcUA. This investment should be protected at the level of support and maintenance. CalcUA supports 2 centres of excellence within the university: NANO and NEURO. Full-time support for CalcUA will be made possible thanks to this project: supporting both end users as well as contributing to formulating proposals for funding for computationally multidisciplinary research projects.

Researcher(s)

• Promoter: Cuyt Annie

Research team(s)

Project website

Project type(s)

• Research Project

Abstract

Virtually all present-day computer systems, from personal computers to the largest supercomputers, implement the IEEE 54-bit floating-point arithmetic standard, which provides 53 binary or approximately 15 decimal digits accuracy. For most scientific applications, this is more than sufficient. However, for a rapidly expanding body of applications, 54-bit IEEE arithmetic is no longer sufficient. These range from some interesting new mathematical investigations to large-scale physical simulations performed on highly parallel supercomputers. Moreover in these applications, portions of the code typically involve numerically sensitive calculations, which produce results of questionable accuracy using conventional arithmetic [3]. These inaccurate results may in turn induce other errors, such as taking the wrong path in a conditional branch. Such blocks of code benefit enormously from a combination of reliable numeric techniques and the use of high-precision arithmetic. Indeed, the aim of reliable numeric techniques is to deliver, together with the computed result, a guaranteed upper bound on the total error or, equivalently, to compute an enclosure for the exact result. It is perhaps not a coincidence that interest in high-precision computations has arisen in the same period that many scientific computations are implemented on highly parallel and distributed, often heterogeneous, computer systems. Such systems have made possible much larger-scale runs than before, greatly magnifying numerical difficulties. Switching from hardware to high-precision arithmetic to tackle these difficulties, has benefits in its own right. Since high-precision arithmetic is implemented in software, the result is independent of the specific hardware in the heterogeneous system on which it is computed. In [3] the successful solution of several problems in scientific computing using high-precision arithmetic is described. It is worth noting that all of these successful applications of high-precision arithmetic have arisen in the past ten years. This may be indicative of the birth of a new era of scientific computing, in which the numerical precision required for a computation is as important to the program design as are the algorithms and data structures. Aim of the project It is the aim of the project team to contribute to the solution of a number of open problems in computational physics, in particular nanotechnology, which require the use of high-precision and reliable computations. The nanoscopic domain is a scale of length situated between the microscopic (atom and molecular scale) and the macroscopic scale. Characteristic for nanotechnology research is that a finite number (on the order of 10 to 10000) of particles (e.g. atoms, molecules, electrons) are involved, and hence that surface effects are of crucial importance. The large number of particles implies that it is practically impossible to obtain analytic results and that one needs to focus on computational methods. As will become clear from the project description, the key to the solution of the open problems in nanotechnology is the high-precision, reliable evaluation of certain special functions. Up to this date, even environments such as Maple, Mathematica, MATLAB and libraries such as IMSL, CERN and NAG offer no routines for the reliable evaluation of special functions.

Researcher(s)

• Promoter: Partoens Bart
• Promoter: Verdonk Brigitte
• Co-promoter: Cuyt Annie
• Co-promoter: Partoens Bart
• Co-promoter: Peeters Francois

Research team(s)

Project type(s)

• Research Project

Abstract

Simulation and modelling are ubiquitous in computational science. Typical application domains are queueing problems, computer and telecommunication networks, weather prediction, electromagnetics, surface and shape re-engineering or reconstruction, population dynamics, supply chain management, inventory control, econometrics and so on. During the design and analysis of a complex system, computer-based experiments or simulations are ofren used to limit the number of expensive prototypes or real-life measurements. However, despite the steady growth of computing power and speed, the computational cost of complex high-accuracy simulations can still be high - especially during optimization and sensitivity analysis -since a single si mulation of a design may take several hours to complete. Then the use of a simplified modelof the complex phenomenon is crucial. Since real-life experimems are often too costly and too time-consuming, virtual design environments in which a model is computed and irs parameters are optimized, are essential nowadays. Irrespective of the fact whether deterministic or random simulation is used, we focus on methods for expensil'e simulations, meaning simulations that require much computer time per run. A run takes the simulation model from its initial state to its final state. The initial state depends on the specific combination of all the inputs also called variables, parameters, factors) of the simulation model. Over the years, several approaches and modeling techniques for the design and analysis of computer experimems. have been developed independently of each other in different disciplines. The general idea is to perform the following three essential steps : I) In a first step, the (possibly large) amount of variables, having an impact on the complex system, is screened and the di mension of the parameter space is reduced. Only the important variables are retained. II) Then a global model is constructed, covering the full design space if possible. In this project, t"o main approaches -namely Kriging and rational metamodeling -are studied, compared and combined, to ootain the best of both worlds, because the demands imposed on models are becoming stricter all the time. III) Last, hut not least, the optimal values for the parameters of the model are determined by means of an optimization procedure.

Researcher(s)

• Promoter: Cuyt Annie
• Co-promoter: Dhaene Tom
• Co-promoter: Verdonk Brigitte

Research team(s)

Project type(s)

• Research Project

Abstract

Zowel bij geometrisch ontwerp, computergestuurde productie als zogenaamde reverse engineering, spelen vloeiende lijnen in kurven, oppervlakken en vormen een centrale rol. Men wenst in de geometrische komponenten geen ongedefinieerde regio's of onverantwoorde stijle pieken. In de onthalende onderzoeksgroep is sinds een aantal jaar een techniek, die bekend is om singulariteiten in functies van één enkele veranderlijke op te sporen, veralgemeend naar functies van meerdere veranderlijken. De techniek is dus nu bruikbaar voor oppervlakken en vormen in de ruimte. Een aantal open problemen moet echter nog opgelost worden om de techniek in de praktijk bruikbaar te maken.

Researcher(s)

• Promoter: Cuyt Annie
• Fellow: Lee Wen-Shin

Research team(s)

Project type(s)

• Research Project

Abstract

The problem the teams plan to tackle in this project is this: how can a rational modelling problem be formulated such that it is optimally conditioned, especially in a multidimensional context? Given the very large range of applications, the answer to this problem is important. The following example is prototypical for the problem formulated. The identification problem in the frequency domain is a rational approximation problem on the imaginary axis or the complex unit circle. The spectral transfer function is measured in a number of discrete points together with stochastic information of the measurement noise. The representation of the model as a couple of polynomials represented by monomials leads to unacceptable conditioning problems. In, the conditioning problem was largely solved by a quasi-optimal choice of the representation of the model in terms of orthogonal vector valued polynomials .The project promotors want to continue along this road, as explained in the project objectives. The team is especially interested in problems involving the modelling of multivariate data and/or matrix-valued data.

Researcher(s)

• Promoter: Cuyt Annie
• Promoter: Verdonk Brigitte
• Co-promoter: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

Guaranteed passive broadband circuit models that capture the complex input-output behavior of general multiport passive linear structures are the holy grail in microwave and RF modeling. The macromodels must be compact, fast, numerically stable, physics-based (i.e. causal and passive), and applicable in time domain as well as in frequency domain simulations. The goal of this research project is to build physics-based, guaranteed passive rational (pole/zero) broadband circuit models, starting from existing approximated models, whose passivity is not guaranteed.

Researcher(s)

• Promoter: Dhaene Tom
• Co-promoter: Broeckhove Jan
• Co-promoter: Cuyt Annie
• Co-promoter: Verdonk Brigitte

Research team(s)

• Internet Data Lab (IDLab)

Project type(s)

• Research Project

Abstract

In this project we want to deliver a performant and validated multiprecision implementation of several classes of special functions (hypergeometric functions, error function, exponetial integral, ...). We will focus on continued fraction approximations. Choosing the appropriate representation, identification of the domain, refining the upper bounds for the truncation error and refining existing techniques to estimate the rounding error are just some of the topics we will consider.

Researcher(s)

• Promoter: Cuyt Annie
• Fellow: Becuwe Stefan

Research team(s)

Project type(s)

• Research Project

Abstract

The problems of reconstruction and characterization of the shape of an object or region are ubiquitous in computational science, engineering and computer vision. Important tools in solving these problems are moments and Fourier descriptors. Both have proved to be very useful in respectively shape reconstruction and characterization. From the literature on the shape-from-moments reconstruction problem, one can see that until recently the shape inverting problem was tackled using univariate techniques in one complex variable. This approach imposes restrictions on the shape of the object under reconstruction as well as on the dimensionality of the problem. Our aim is on one hand to further explore the three-dimensional problem, using true multidimensional techniques instead of reducing the problem to one-dimensional subproblems, and on the other hand to eliminate the current restrictions on the shape of the object under study. With respect to Fourier descriptors (FDs) used for shape characterization, interesting problems remain to be solved as well. Two-dimensional (2D) FDs have been exploited from the early 70's for the characterization of the contours of 2D objects. From the 90's on, methods for the computation of 3D Fourier descriptors were developed for the characterization of the surface of binary objects. Existing methods, however, still suffer from complexity problems, especially when the number of vertices is large (>5000). In general, 3D FDs are computed by mapping the object's polyhedron onto the surface of a unit sphere, after which it is expanded in spherical harmonics. This mapping from the object space (surface) to the parameter space (sphere) is non-trivial and current techniques suffer from computational problems. Our goal is to develop a robust method which implements this mapping in an efficient way, in other words, such that the computational time grows linearly with the number of vertices.

Researcher(s)

• Promoter: Verdonk Brigitte
• Co-promoter: Cuyt Annie
• Co-promoter: Sijbers Jan
• Co-promoter: Van Dyck Dirk

Research team(s)

Project type(s)

• Research Project

Abstract

Researcher(s)

• Promoter: Cuyt Annie
• Co-promoter: Verdonk Brigitte

Research team(s)

Project type(s)

• Research Project

Abstract

Researcher(s)

• Promoter: Cuyt Annie
• Co-promoter: Daelemans Walter
• Co-promoter: De Schutter Erik
• Co-promoter: Peeters Francois
• Co-promoter: Van Alsenoy Kris
• Co-promoter: Van Broeckhoven Christine

Research team(s)

Project type(s)

• Research Project

Abstract

During the last 4 decades, the `Bateman Project' (50's) and the `Handbook of Mathematical Functions' (1964) where THE references when describing Bessel functions, hypergeometric functions, orthogonal polynomials,... These `special' functions appear in a very wide range of physical and engineering problems.The technological situation nowadays makes an `update' of these projects necessary, and the proposed project is located in this context. It wants to contribute to the development of a software library which evaluates special functions on a reliable manner, on an as big as possible domain of parameters and arguments. It's essential for this project that every number that's produced, is a correct number.The construction of such a library is a very huge project, and our contribution will mainly concentrate on the approximation of special functions using continued fractions. Instead of approximating special functions using power series, one can use continued fraction approximations, which in many cases converge faster or on a larger domain. These cases in particular will be the focus of our project.

Researcher(s)

• Promoter: Verdonk Brigitte
• Co-promoter: Cuyt Annie
• Fellow: Vervloet Johan

Research team(s)

Project type(s)

• Research Project

Abstract

The goal is to develop efficient univariate and multivariate sampling algorithms, based on rational and polynomial interpolation, which establish accurate surrogate models for linear dynamic systems, such as passive microwave and RF systems. This reflective exploration technique must sample the (one- or multidimensional) parameter space in an optimal way in order to minimize the number of samples, without assuming any a priori knowledge of the system.

Researcher(s)

• Promoter: Dhaene Tom
• Co-promoter: Cuyt Annie
• Co-promoter: Verdonk Brigitte

Research team(s)

• Internet Data Lab (IDLab)

Project type(s)

• Research Project

Abstract

During the last 4 decades, the `Bateman Project' (50's) and the `Handbook of Mathematical Functions' (1964) where THE references when describing Bessel functions, hypergeometric functions, orthogonal polynomials,... These `special' functions appear in a very wide range of physical and engineering problems. The technological situation nowadays makes an `update' of these projects necessary, and the proposed project is located in this context. It wants to contribute to the development of a software library which evaluates special functions on a reliable manner, on an as big as possible domain of parameters and arguments. It's essential for this project that every number that's produced, is a correct number. The construction of such a library is a very huge project, and our contribution will mainly concentrate on the approximation of special functions using continued fractions. Instead of approximating special functions using power series, one can use continued fraction approximations, which in many cases converge faster or on a larger domain. These cases in particular will be the focus of our project.

Researcher(s)

• Promoter: Cuyt Annie
• Co-promoter: Verdonk Brigitte
• Fellow: Vervloet Johan

Research team(s)

Project type(s)

• Research Project

Abstract

This project will analyze the performance of advanced technological systems such as communication networks (including the Internet), computer systems, and distributed multiprocessor systems, with the aim of optimizing their design and dimensions. This analysis will use probabilistic models, the parameters of which will be obtained by statistical estimates based on measurements of actual traffic. The computation of the performance functions and the design of optimal networks both lead to complex computational problems, which will be approached by si mulation and by novel numerical analysis techniques such as multivariate rational approximations. The many interactions between all these aspects require an intensive collaboration between the three research groups.

Researcher(s)

• Promoter: Cuyt Annie
• Co-promoter: Blondia Chris
• Co-promoter: Rousseeuw Peter

Research team(s)

Project type(s)

• Research Project

Abstract

Starting from observed data (like traffic on the Internet), robust statistical methods (i.e., techniques that give reliable results even when deviations occur in the input data) will be applied to construct a model for the observed system. From the specific architecture and structure of the system one can often derive interesting properties of the performance measure in advance, such as its monotonicity relative to a given system parameter, or its asymptotic behavior. These properties are helpful when constructing the performance measure, but by themselves they are not sufficient. Robust, efficient and accurate approximations of the exact solution are indispensable. A possible approach is based on power series, but since many performance functions have singularities a better approach is to use Pade approximations.

Researcher(s)

• Promoter: Blondia Chris
• Co-promoter: Cuyt Annie
• Co-promoter: Rousseeuw Peter

Research team(s)

• Internet Data Lab (IDLab)

Project type(s)

• Research Project

Abstract

The goal of this project is the realisation of ARITHMOS, a scientific computing environment which is offered in a higher, object-oriented programming language and allows one to solve numerical problems using different number representations in a flexible, efficient and reliable way, without losing sight of compatibility across platforms and performance requirements of numerical software.

Researcher(s)

• Promoter: Cuyt Annie
• Co-promoter: Verdonk Brigitte

Research team(s)

Project type(s)

• Research Project

Abstract

The aim is to develop a system of reliable algorithms to tackle the problems of multivariate Pad approximation (normal and non-normal tables) and multivariate rational Hermite interpolation (grids of data and scattered data).

Researcher(s)

• Promoter: Cuyt Annie
• Fellow: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

In the first part of this project, the aim is to write a research monograph, in which the expertise and the results of 20 years of research in the area of rational approximation theory, and more specifically multivariate Padé approximation, are compiled. The course Computer Arithmetic and Numerical Techniques, which has been taught for several years already at the University of Antwerp, received a UGCSA award (Undergraduate Computational Science Award) from the US-based Kell Institute for its innovative contribution to the field. Starting from the course text, we aim to write out a full-fledged textbook on Computer Arithmetic and Numerical Techniques in the second part of this project.

Researcher(s)

• Promoter: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

The analysis and performance evaluation of advanced technical systems, such as computer systems, telecommunication systems and distributed multiprocessor systems often involve solving a complex computational problem. This is due to the fact that the complexity increases with the size of the system under study or with the dimensions of the system model. This implies that it is preferable to use rational functions rather than polynomials.

Researcher(s)

• Promoter: Blondia Chris
• Co-promoter: Cuyt Annie
• Co-promoter: Rousseeuw Peter

Research team(s)

Project type(s)

• Research Project

Abstract

Researcher(s)

• Promoter: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

Similar to hybrid systems, in which both analogue and digital elements coexist and interact, hybrid computational techniques combine both continuous and discrete representations of numerical objects such as (multiprecision) floating-point, (multiprecision) interval, rational, rational interval, symbolic representations and so on. The aim of this project is to develop on one hand reliable, hybrid algorithms for the approximation of functions, and on the other hand application-independent arithmetic tools for reliable hybrid computation. The results obtained can be applied to solve problems in domains such as robotics where there is a close link between numeric computations and Boolean decisions, or in applications such as computational biochemistry, where existing, exact algorithms can not be applied, for instance due to the limited accuracy of the data.

Researcher(s)

• Promoter: Cuyt Annie
• Fellow: Verdonk Brigitte

Research team(s)

Project type(s)

• Research Project

Abstract

The goal of this project is to deliver an integrated environment which continues to support the present IEEE floating-point hardware, but also features multiple-precision floating-point, interval, and rational arithmetic, by means of a platform-independent library, directly available in C++ .

Researcher(s)

• Promoter: Cuyt Annie
• Fellow: Verschaeren Dennis

Research team(s)

Project type(s)

• Research Project

Abstract

Researcher(s)

• Promoter: Cuyt Annie
• Fellow: Rubben Sven

Research team(s)

Project type(s)

• Research Project

Abstract

Orthogonal functions and especially orthogonal polynomials have a lot of applications in numeric analysis. It has been proven that fast algorithms for the computation of rational approximants, compute at the same time orthogonal polynomials, since they appear in the determinators of the rational approximants. If the rational approximation problem is linearized, we are dealing with particularly structured coefficient matrices. In this research project we want to study the links between the different research topics mentioned above, with possible generalizations of the theory to multivariate functions, matrix- and vectorfunctions etc.

Researcher(s)

• Promoter: Cuyt Annie
• Co-promoter: Verdonk Brigitte

Research team(s)

Project type(s)

• Research Project

Abstract

Researcher(s)

• Promoter: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

The aim is to develop a system of reliable algorithms to tackle the problems of multivariate Pad approximation (normal and non-normal tables) and multivariate rational Hermite interpolation (grids of data and scattered data).

Researcher(s)

• Promoter: Cuyt Annie
• Fellow: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

For univariate functions there is a story link between their Pade approximants and the theory of orthogonal polynomials. In the past decennia several multivariate generalizations of the theory of orthogonal polynomials have been generalized, but until now none related to the well-developed theory of multivariate Pade approximants. It is our aim to try to fill this gap in this research project.

Researcher(s)

• Promoter: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

The aim of the scientific research network (14 partners) is : to develop advanced numerical methods, with focus on time-integration of differential equations and numerical linear algebra; to study the interaction of these methods in applications (fluid dynamics, image reconstruction, control problems, ...).

Researcher(s)

• Promoter: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

The main aim of the project is the integration of operational issues into the design process of object oriented systems. To master the growing complexity of current computer, communication and information systems, one divides these systems into small functional entities which are more or less independent of each other. The object-oriented paradigm supports this modular view. A first objective of the project is to develop a formalism that is sufficiently universal to bridge the structural differences between the various modules and subsystems. A second objective is to improve the interoperatability of object oriented information systems, by investigating properties and structure of the interfaces between system components. A further objective is the analysis of configurations of complex systems. One way to tackle this problem is to reduce it to that of finding an eigenvector of a large matrix.

Researcher(s)

• Promoter: Janssens Dirk
• Co-promoter: Blondia Chris
• Co-promoter: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

For the numerical solution of a problem, the accuracy and reliability of the computations are as important as the correct choice of the algorithm. For the former SC-programming languages were developed. For the latter expert systems are useful. We want to combine both technologies into a prototype scientific expert system for the problem domain of multivariate rational interpolation.

Researcher(s)

• Promoter: Cuyt Annie
• Fellow: Verdonk Brigitte

Research team(s)

Project type(s)

• Research Project

Abstract

The goal of this project is to deliver an integrated environment which continues to support the present IEEE floating-point hardware, but also features multiple-precision floating-point, interval, and rational arithmetic, by means of a platform-independent library, directly available in C++ .

Researcher(s)

• Promoter: Cuyt Annie
• Fellow: Verschaeren Dennis

Research team(s)

Project type(s)

• Research Project

Abstract

Reliable algorithms for the computation of multivariate Pade approximants are needed : they are used in CAD-CAM, signal filtering and systems theory. We consider recursive algorithms and continued fractions. We will study the structure of the multivariate table of rational functions in detail and solve questions concerning singularities in the denominator. We believe these problems may be tackled by block bordering methods. Afterwards, we can develop general recursive computation algorithms. The use of continued fractions implices working with a qd-like algorithm. We will try to understand all possible information contained in the qd-table. As a result, an algorithm will be developed which deduces from a series expansion, information about the function itself.

Researcher(s)

• Promoter: Cuyt Annie
• Fellow: Becuwe Stefan

Research team(s)

Project type(s)

• Research Project

Abstract

In this project tools are developed to build intelli gent scientific programming environments. Such envi ronments will integrate problem solvers and arithme tic implementations in such a way that scientific computations yield maximally accurate and validated results. To achieve these goals, integration of symbolic and numeric algorithms at all levels (data and code) is essential. The term "numeric" also covers all recent, intelligent implementations of computer arithmetic, not just the traditional floa ting-point arithmetic.

Researcher(s)

• Promoter: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

While the complexity of numerical problems increases, so does the number of algorithms to solve these problems. The amount of expertise available to select the most appropriate algorithm greatly influences the quality of the numeric output. On the other hand, one can only make sure that variation in the numeric results is mainly due to the quality of the approxi mation rather than to the accumulation of rounding errors, if the algorithms generate guaranteed re sults. It is the aim of this project to make availa ble, for a particular case study, the necessary expertise and to implement the algorithms in such a way that they deliver maximally accurate, guaranteed results.

Researcher(s)

• Promoter: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

The investigation of multivariate approximation techniques has become very important in the past few years, especially with the growing computer resources. For multivariate Pade-approximants only a limited number of convergence results is known and it is our aim to fill this gap.

Researcher(s)

• Promoter: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

In the present research project we aim at studying the process of language acquisition adapting a data-driven approach and to conduct experiments with artificial learning algorithms in which cue-based competitive learning can readily be implemented.

Researcher(s)

• Promoter: De Schutter Georges
• Co-promoter: Cuyt Annie
• Co-promoter: Daelemans Walter
• Co-promoter: Gillis Steven

Research team(s)

Project type(s)

• Research Project

Abstract

Query languages and update languages are designed for object oriented database systems. Their user interfaces are studied. The relationship with logic is als discussed. The theory is applied to numerical mathematics.

Researcher(s)

• Promoter: Paredaens Jan
• Co-promoter: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

In two articles in Journ. Comp. Appl. Math. important and very desired convergence results for multivariate Padé approximants were obtained. This project will investigate similar questions for multivariate Newton-Padé approximants.

Researcher(s)

• Promoter: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

Researcher(s)

• Promoter: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

For the numerical solution of a problem, the accuracy and reliability of the computations are as important as the correct choice of the algorithm. For the former SC-programming languages were developed. For the latter expert systems are useful. We want to combine both technologies into a prototype scientific expert system for the problem domain of multivariate rational interpolation.

Researcher(s)

• Promoter: Cuyt Annie
• Fellow: Verdonk Brigitte

Research team(s)

Project type(s)

• Research Project

Abstract

The aim is to develop a system of reliable algorithms to tackle the problems of multivariate Pad approximation (normal and non-normal tables) and multivariate rational Hermite interpolation (grids of data and scattered data).

Researcher(s)

• Promoter: Cuyt Annie
• Fellow: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

Globally speaking we want to concentrate on the development of some scientific object-oriented technology with higher computer arithmetic for use in several scientific applications. In this project we want to couple the object-oriented facilities of a language like CH to the guaranteed accuracy of a scientific programming language.

Researcher(s)

• Promoter: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

We consider the insurance market as a special case of an "incomplete market" and our aim is to develop some new results concerning the existence and the number of equilibria, and the stability of these equilibria in functions of the parameters involved

Researcher(s)

• Promoter: Cuyt Annie
• Fellow: De Waegenaere Anja

Research team(s)

Project type(s)

• Research Project

Abstract

Researcher(s)

• Promoter: Cuyt Annie

Research team(s)

Project type(s)

• Research Project

Abstract

Researcher(s)

• Promoter: Cuyt Annie
• Co-promoter: Rousseeuw Peter

Research team(s)

Project type(s)

• Research Project

Abstract

The aim is to develop a system of reliable algorithms to tackle the problems of multivariate Pad approximation (normal and non-normal tables) and multivariate rational Hermite interpolation (grids of data and scattered data).

Researcher(s)

• Promoter: Wuytack Luc
• Fellow: Cuyt Annie

Research team(s)

Project type(s)

• Research Project