Current Research Projects

Abstract

Non-smooth dynamical systems have, next to the evolution equation, a system of inequalities that limit the motion. Many systems in society and industry are modelled in this way, for example soft robotic systems. In this project we will develop novel mathematical methods for the automatic bifurcation analysis of these systems. We will develop novel subspace methods that take into account the inequalities in the system. The ultimate objective is to enable scalability to dynamical systems characterized by millions of unknowns, thereby facilitating comprehensive exploration and understanding of their complex behaviors

Researcher(s)

• Promoter: Vanroose Wim
• Fellow: Wagemakers Lara

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

Brailsports aims to revolutionise endurance training with AI-optimised sports-scientific models, including the Lactate Threshold and Personalized Fitness Fatigue models. The outputs of these models are currently implemented in an online dashboard, providing coaches tailored insights and customized analytics about their athletes' performance, recovery and training needs. This empowers coaches to make data-driven decisions, enhancing the training regimen's effectiveness and efficiency. This project's objective is to elevate our minimal viable product into a commercializable one, targeting the designated beachhead market of endurance coaches. Looking ahead, Brailsports envisions expanding from a coach-centric platform to developing athlete-focused solutions. We envision a sophisticated mobile application that serves as a personal coach in every athlete's pocket. This app will offer dynamic, AI-driven training plans that adjust in real time to reflect the athlete's current performance metrics, physiological responses and evolving objectives. By doing so, Brailsports aims to democratise access to elite-level training insights, making personalized, science-backed training regimens accessible to athletes at all levels. This expansion will empower athletes with the tools they need for optimal performance, fostering a more informed, connected, and personalized approach to endurance training. In addition to the commercialization of the dashboard, we aim to take the first steps in the development of this mobile application in this project.

Researcher(s)

• Promoter: Verdonck Tim
• Co-promoter: Latré Steven

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

This proposal bridges knowledge from robust statistics, machine learning and optimization and builds on my very recent work on robust covariance estimation to introduce general frameworks for unsupervised and supervised statistical learning under cellwise contamination. The project considers covariance estimation, principal component analysis, linear regression and logistic regression. It allows for extensions in the direction of regularized estimation and nonlinear modeling using kernels. In addition to the development of methodology, the project aims to assess the gravity of cellwise contamination in practical challenges by collaborating with experts on macro-economic time series modeling and drug development.

Researcher(s)

• Promoter: Raymaekers Jakob
• Fellow: Raymaekers Jakob

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

Financial transaction fraud remains an important societal challenge, despite decades of research on automatic fraud detection systems. In light of these struggles, I propose to tackle fraud from a different perspective: rather than reactively detecting fraud after it occurs, I aim to proactively prevent fraud before it even happens. The envisioned research project, FraudPANDA, aims to counter-act fraudsters by using Pro-Active (Network) Detection and Analysis. Firstly, I aim to proactively detect who is at risk of becoming targeted before the attack happens. I will develop methods to find the relevant customer characteristics. Secondly, I aim to analyse different preventive interventions and analyse their efficacy at decreasing a customer's fraud risk. This will be based on insights from causal inference. Thirdly, for both methods, I will also explore the possibility of using network information to improve prevention performance. This is motivated by recent success of network analysis in fraud detection. In the end, the ultimate goal of FraudPANDA is an innovative solution that operationalizes these insights by optimally allocating preventive interventions and minimizing fraudulent activities. A field test will be conducted at an industrial partner to evaluate FraudPANDA's ability to proactively prevent fraud in real-world scenarios.

Researcher(s)

• Promoter: Verdonck Tim

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

Efficiently solving huge-scale optimization problems is undoubtedly very important in science and technology. Many optimization problems can be described using some underlying network structure. For example, the optimal assignment of a crew to a given flight schedule can be formulated as an optimization problem over a very large graph. Similarly, constraint based modelling of biochemical networks also leads to optimization problems with millions of unknowns. A network structure typically induces useful structure in the constraints, which then of course can be exploited by using suitably chosen linear algebra techniques. Current off-the-shelf software is not able to efficiently solve such problems when the number of variables is very large, especially when the objective function is nonconvex and possibly contains a nonsmooth term. Hence, there is a need to develop high-performance structure exploiting algorithms. In this project we aim to develop a wide range of efficient optimization algorithms for both convex and nonconvex problems, possibly containing a nonsmooth term in the objective function, by exploiting structure that arises from the networks. High-performance implementations of the resulting algorithms will be made available in an open- source software package such that non-expert practitioners can easily them.

Researcher(s)

• Promoter: Ahookhosh Masoud
• Co-promoter: Vanroose Wim
• Fellow: Rahimi Khorzoughi Morteza

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

We consider numerical methods for the efficient and stable solution of advanced, multidimensional partial integro-differential equations (PIDEs) and partial integro-differential complementarity problems (PIDCPs) arising in financial energy option valuation. Here the underlying uncertain factors, e.g. the electricity price, are modelled by exponential Lévy processes to account for the jumps that are often observed in the markets. These jumps give rise to the integral term in the PIDEs and PIDCPs and is nonlocal. For the effective numerical solution, we investigate in this project operator splitting methods. This broad class of methods has already been successfully applied and analysed in the special case of partial differential equations (PDEs). Many questions about their adaptation to PIDEs and PIDCPs are, however, still largely open. In this project we consider two main research topics: (1) infinite activity jumps and (2) swing options. The first topic concerns exponential Lévy processes with an infinite number of jumps in every time interval. The second topic deals with a popular type of exotic energy option that has multiple exercise times. We develop novel, second-order operator splitting methods of the implicit-explicit (IMEX) and alternating direction implicit (ADI) kind. We analyse their fundamental properties of stability, consistency, monotonicity and convergence. The acquired theoretical results are validated by ample numerical experiments.

Researcher(s)

• Promoter: In't Hout Karel

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: Vanroose Wim

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

Due to technological advances, the available amount of data has increased exponentially over the last decade. The field of data science (DS) has followed this growth as it provides an indispensable tool for translating data into insight and knowledge. Where DS was traditionally concerned with learning associations in data, it has become clear in recent times that causal relations often provide a deeper understanding of the data and a stronger tool in many practical applications. One of the established approaches to causal modeling is to use a directed acyclical graph (DAG) to represent the causal relations. These DAGs have to be learned based on observed data. Many of the SOTA techniques for DAG learning are very sensitive to anomalies, and yield unreliable results in their presence. We aim to develop methods for DAG learning that remain efficient and reliable under contamination of the data. The project starts by building a solid foundation for the concepts of robustness in DAG learning. Building upon these foundations, we will then proceed to build a general robust DAG learning methodology. The project envisions three different but complementary approaches to the development of robust DAG learning methods. The developed methodology will be evaluated theoretically and empirically, and tested in a variety of real world cases.

Researcher(s)

• Promoter: Verdonck Tim
• Co-promoter: Latré Steven
• Co-promoter: Raymaekers Jakob
• Fellow: Leyder Sarah

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

In the last two decades, the emergence of big data mathematical modeling leads to the appearance of large- to huge-scale optimization problems with special structures. Moreover, a wide range of such practical problems does not have Lipschitz (Holder) continuous derivatives. Due to this and the existence of a huge number of data, the classical optimization methods cannot be applied to these types of problems, which increase the demand for new algorithmic developments that are convergent and also computationally reasonable for solving these structured optimization problems. As such, designing, analyzing, and implementing efficient optimization algorithms for nonsmooth and nonconvex problems is the subject of investigation in this proposal. In the other words, we assume that some parts of the objective functions are (high-order) relatively smooth and develop first-, second-, and high-order non-Euclidean methods using generalized Bregman distances to find approximate (high-order) critical points of the objective functions. In addition, we analyze the evaluation complexity of these non-Euclidean methods, which is used as a measure of efficiency. We finally apply our developed algorithms to many applications from signal and image processing, machine learning, data science, and systems biology.

Researcher(s)

• Promoter: Ahookhosh Masoud
• Fellow: Kabgani Alireza

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

CalcUA stimulates the use of scientific and technical computing by providing access to state-of-the art computer hardware infrastructure. It shares knowledge, expertise, and training on the efficient use of this hardware in combination with the best available algorithms. It makes it possible to solve largescale scientific problems in a distributed way. In this way users will take advantage of the latest possibilities of scientific and technical computing in their research and R&D. It creates an environment for the exchange of ideas and expertise on large-scale simulation and the processing of large sets of data and related scientific problems. It is part of the Flemish Supercomputer Centre, which provides part of the funding for the personnel and hardware. Funding as a core facility will create a multiplier effect at UAntwerpen by investing in training, community building and the creation of new applications and externally funded joint projects between research groups, CalcUA, and local industry at the national and international level.

Researcher(s)

• Promoter: Vanroose Wim
• Co-promoter: Becuwe Stefan
• Co-promoter: De Winter Hans
• Co-promoter: Herrebout Wouter
• Co-promoter: Latré Steven

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

Recent advances have made possible the acquisition, storing, and processing of very large amounts of data, strongly impacting many branches of science and engineering. A way to interpret these data and explore their features is to use techniques that represent them as certain low-dimensional objects that allow for an intuitive interpretation by domain-specific experts. Such techniques typically factorize the data as two or more structured objects—e.g., orthogonal matrices, sparse tensors—with a lower rank than the original data. The factorizations can usually be formulated as solutions to large-scale nonconvex optimization problems; it is of interest to develop fast algorithms to solve them and, in particular, algorithms for which one can prove that they always converge to useful solutions. One cannot enforce this guarantee in many methods; however, we argue that recent developments made by the applicants on Bregman proximal envelopes and on block and multi-block relative smooth functions are excellent tools to develop such algorithms. In short, this project aims (i) to introduce and study a very general formulation for nonsmooth, structured low-rank optimization, (ii) to establish conditions under which this formulation is tractable (even if nonconvex), (iii) to design provably convergent algorithms to address it, and (iv) to apply and test the new model and algorithms in problems from two domains: image processing and genomic analysis.

Researcher(s)

• Promoter: Ahookhosh Masoud

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

Process optimization is of crucial importance to businesses. Because of the involved complexity, businesses typically rely on domain experts for operating business processes. In this proposal, the aim is to develop a data-driven approach by leveraging recent advances in causal machine learning (CML) to support decision-making. To this end, Process Optimization with Sequential Individual Treatment Effects (POSITE) is introduced. POSITE is a powerful, reliable and flexible methodology that is capable of learning models to accurately predict causal effects in complex, sequential decision-making processes using causal machine learning. The resulting causal models are interpretable and robust, as such ensuring reliability and usability. The methodology is embedded within a cost-sensitive, constrained and stochastic decision-making framework to guide process operators in optimization process outcomes. The envisioned solution is an actionable and innovative approach toward process optimization that opens various directions for future fundamental and applied research.

Researcher(s)

• Promoter: Verdonck Tim

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

The European High-Performance Computing Joint Undertaking (EuroHPC JU) is pooling European resources to develop top-of-the-range exascale supercomputers for processing big data, based on competitive European technology. One of the pan-European pre-exascale supercomputers, LUMI, is located in CSC's data center in Kajaani, Finland. The supercomputer is hosted by the LUMI consortium. The LUMI (Large Unified Modern Infrastructure) consortium countries are Finland, Belgium, the Czech Republic, Denmark, Estonia, Iceland, the Netherlands, Norway, Poland, Sweden, and Switzerland.

Researcher(s)

• Promoter: Vanroose Wim

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

This FWO scientific research network will focus on interdisciplinary research (mathematics – physics) in the area of stochastic modelling based on the interaction between theory, numerical computations and applications in financial markets. Hereto the network will make use of the complementary expertise present in the participating research groups.

Researcher(s)

• Promoter: In't Hout Karel

Research team(s)

• Applied mathematics

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

In this IOF POC, we aim to bring together the expertise in sports science and machine learning to develop intelligent tools for coaching endurance sports. These tools will assist the coach in tracking the fitness level of the athletes and provide early warning of any potential issues within the physiological data. By leveraging the power of machine learning, we hope to create a more efficient and effective coaching process that can help athletes reach their full potential. Additionally, by integrating sports science knowledge, we aim to ensure that the tools we develop are grounded in the latest research and understanding of how the body responds to endurance training.

Researcher(s)

• Promoter: Verdonck Tim
• Co-promoter: Latré Steven

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

In this project we will develop interior point methods with mixed precision. Novel hardware can do floating point arithmetic with lower precision. We will analyse how the interior point method can be accelerated with the help of low precision preconditions

Researcher(s)

• Promoter: Vanroose Wim
• Fellow: Cornelis Jeffrey

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

Just like many industries today, the accountancy sector is also confronted with disruptive digitalization. This digitization means that accountants are expected to provide more and more proactive services, where the focus used to be on executive and compliance-related work. With our project we want to help accountants to fulfill these new expectations. By applying advanced statistical methods and machine learning techniques, we want to focus strongly on following two research topics. First of all, we want to test and develop different methods to discover anomalies ​​in accounting data. This helps the accountant to automate standard checks, but also to discover potential opportunities. Secondly, we want to test and develop robust and interpretable cash flow forecasting models. In both areas we are convinced that there is still enormous potential to create added value for the accountant. The collaboration with Boltzmann provides the ideal context for this project due to the presence of a rich, ever-expanding dataset, combined with professional expertise in various areas within the framework project team.

Researcher(s)

• Promoter: Verdonck Tim

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

The Generalized Linear Model (GLM) is a very popular and flexible class of regression models that generalizes ordinary linear regression by allowing for example non-normal response variables. Logistic regression, which is widely used for binary classification, and Poisson regression, often used to model count data, both belong to this class. The parameters are typically estimated using maximum likelihood, but this very often leads to various problems when analyzing real data from practice. Firstly, outliers in the data may heavily influence classical methods, yielding unreliable results. Secondly, estimation and interpretability becomes very difficult or impossible when the number of variables becomes very high. Thirdly, real data often display a more complex dispersion behavior than expected under the GLM model. To solve these issues, sparse and robust estimation methods that model simultaneously the mean and the dispersion behavior in the context of GLMs will be developed. Their mathematical properties will be thoroughly investigated. The newly proposed methods should also be computationally efficient such that modern large datasets can be analyzed easily. Open-access user-friendly software will be provided.

Researcher(s)

• Promoter: Verdonck Tim
• Fellow: Tubex Lise

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

In recent years a major trend towards solving scientific problems of ever larger scales that include larger and larger data sets can be observed in practically all academic and industrial applications. These include the simulation of vast ocean circulation models, global climate prediction models, extremely fine-scale combustion models, etc. The representation of these models on a computer requires the solution of a large-scale system of equations that typically consists of millions of unknowns. Due to the huge size of these model calculations, computations are often spread across parallel computer platforms to reduce the time-to-solution. Krylov methods have been established as the benchmark iterative solvers for the sparse linear algebra problems that appear in these applications. However, Krylov methods are not adapted to scale to future parallel hardware due to the long communication latencies. Hence, new numerical methods have to be designed and analyzed mathematically. The aim of this project is to develop and analyze new scalable iterative methods based on asynchronous communication that hide the communication latency by overlapping compute and communication tasks. Furthermore we will develop blocked versions of these algorithms for problems where the same matrix equation needs to be solved for multiple right hand sides. Demonstrators will be built that show the performance improvements for a wide range of applications in data science and scientific computing.

Researcher(s)

• Promoter: Vanroose Wim
• Co-promoter: Cools Siegfried
• Fellow: Cornelis Jeffrey

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

Current and future physical equipment collects more and more data from multiple scattered fields simultaneously, for example in the imaging of molecules, which adds to the complexity of the reconstruction through numerical simulation. This dramatic increase in data requires new scalable mathematical techniques to reconstruct the high-dimensional object of interest. This project aspires to develop efficient ways to solve the high-dimensional Helmholtz and Schrödinger problem for this purpose. A successful and already awarded initial approach, based on the novel idea of reformulating the PDEs involved on a complex-valued manifold, was recently developed by the applicant. The proposed technique makes the potentially high-dimensional problem more tractable and amenable to large-scale iterative solvers. The main aim of this project is the development and rigorous analysis of scalable HPC iterative solution methods for wave scattering problems.

Researcher(s)

• Promoter: Cools Siegfried

Research team(s)

• Applied mathematics

Project website

Project type(s)

• Research Project

Abstract

Phase Contrast X‐ray Computed Tomography (CT) measures besides the intensity also changes in the phase of a transmitted X‐rays. These changes give exquisite and complementary information about the object, in particular about soft tissues. More and more CT systems are able to measure these phases. However, the development of efficient mathematical reconstruction algorithms that reconstruct the 3D object from the measured data is only in its early stages. This project will make progress in the modelling of the data acquisition process and the reconstruction algorithms. It is a collaboration between the group A pplied Mathematics and the V ision Lab . Valorisation will be realized by the distribution of the new algorithms through the ASTRA toolbox and the initiation of research collaborations, licensing deals and contract research with industry.

Researcher(s)

• Promoter: Vanroose Wim
• Co-promoter: Sijbers Jan

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

In recent years, a major trend towards solving scientific problems of ever larger scales can be observed in practically all academic and industrial applications. These include the simulation of vast ocean circulation models, global climate prediction models, seismic oil reservoir models spanning hundreds of kilometers, extremely fine-scale combustion models, etc. The representation of these models on a computer requires the solution of a large-scale system of equations that typically consists of millions of unknowns. Due to the huge size of these model calculations, computations are often spread across parallel computer platforms to reduce computational time. Furthermore, only the numerical methods with optimal compute and communication complexity are able to efficiently solve these large scale problems. Krylov methods have been established as the benchmark iterative solvers for sparse linear algebra problems due to their robustness and good performance in function of the number of unknowns. However, present-day Krylov methods are not adapted to scale to future parallel hardware. Hence, new numerical methods have to be designed and analyzed mathematically, taking into account numerical rounding error propagation, which possibly has a detrimental effect on convergence. The aim of this project is to develop and analyze new scalable iterative methods that are numerically stable and resilient to the errors that typically arise in these large-scale computations.

Researcher(s)

• Promoter: Vanroose Wim
• Fellow: Cools Siegfried

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

In this research project our aim is to investigate the convergence of ADI schemes in the numerical solution of multi-dimensional time-dependent PDEs arising in financial mathematics. As mentioned above, these PDEs possess essentially different features from those in other application areas. In particular, mixed spatial derivative terms are pervasive in finance and ADI schemes were not originally developed for PDEs with such terms. Recently, however, various natural adaptations, of increasing sophistication, have been defined: the Douglas (Do) scheme, the Craig-Sneyd (CS) scheme, the Modified Craig-Sneyd (MCS) scheme and the Hundsdorfer-Verwer (HV) scheme, see [3,11,12,16]. ADI schemes now constitute a main class of numerical methods in academic and industrial finance, and their range of financial applications continues to extend.

Researcher(s)

• Promoter: In't Hout Karel
• Fellow: Wyns Maarten

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

The aim of the project is to extend the applicability of prediction of compound activity and the extension of the number of data sources that can be combined. We alos aim to apply the the methods to currently running drug development. Due to the scale and the size of the data sets high performance computing is required.

Researcher(s)

• Promoter: Vanroose Wim

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

The increased trading in multi-name financial products has required state-of-the-art multivariate models that are, at the same time, computationally tractable and flexible enough to explain the stylized facts of asset returns and of their dependence structure. The project is aimed at developing and calibrating multivariate models that can replicate financial market data whatever the level of investor's fear in the market. To this end, we will use advanced stochastic processes, such as Lévy processes, Sato processes and continuous time Markov chains. We will also develop fast and accurate calibration algorithms based on series expansions and on the matching of market implied moments and co-moments extracted from current market quotes. Particular attention will be given to the models' ability to explain the asset dependence structure, which plays a crucial role in the assessment of correlation risk. A correct management of this new kind of financial risk, which is inherent to any multi-name financial product, has indeed appeared to be vital during recent systemic crashes, such as the global financial crisis of 2007-2008.

Researcher(s)

• Promoter: Guillaume Florence
• Promoter: In't Hout Karel
• Fellow: Boen Lynn

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

The project is aimed at comparing the liquidity in different markets and during periods characterized by different market turmoil levels, using the recently developed conic finance theory. We will apply state-of-the art statistical techniques to highlight the trend of liquidity times series. As numerical study, we investigate the impact of two market distress periods, namely the dot-com bubble and the 2007-2008 global financial crisis.

Researcher(s)

• Promoter: Guillaume Florence

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

In this research project our aim is to investigate the convergence of ADI schemes in the numerical solution of multi-dimensional time-dependent PDEs arising in financial mathematics. As mentioned above, these PDEs possess essentially different features from those in other application areas. In particular, mixed spatial derivative terms are pervasive in finance and ADI schemes were not originally developed for PDEs with such terms. Recently, however, various natural adaptations, of increasing sophistication, have been defined: the Douglas (Do) scheme, the Craig-Sneyd (CS) scheme, the Modified Craig-Sneyd (MCS) scheme and the Hundsdorfer-Verwer (HV) scheme, see [3,11,12,16]. ADI schemes now constitute a main class of numerical methods in academic and industrial finance, and their range of financial applications continues to extend.

Researcher(s)

• Promoter: In't Hout Karel
• Fellow: Wyns Maarten

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

In this research project our aim is to investigate the convergence of ADI schemes in the numerical solution of multi-dimensional time-dependent PDEs arising in financial mathematics. As mentioned above, these PDEs possess essentially different features from those in other application areas. In particular, mixed spatial derivative terms are pervasive in finance and ADI schemes were not originally developed for PDEs with such terms. Recently, however, various natural adaptations, of increasing sophistication, have been defined: the Douglas (Do) scheme, the Craig-Sneyd (CS) scheme, the Modified Craig-Sneyd (MCS) scheme and the Hundsdorfer-Verwer (HV) scheme, see [3,11,12,16]. ADI schemes now constitute a main class of numerical methods in academic and industrial finance, and their range of financial applications continues to extend.

Researcher(s)

• Promoter: In't Hout Karel
• Fellow: Wyns Maarten

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

The EXA2CT project brings together experts at the cutting edge of the development of solvers, related algorithmic techniques, and HPC software architects for programming models and communication. It will take a revolutionary approach to exascale solvers and programming models, rather thean the incremental approach of other projects.

Researcher(s)

• Promoter: Vanroose Wim

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

In recent years the computational complexity of mathematical models employed in financial mathematics has witnessed a tremendous growth. Advanced numerical techniques are imperative for the most present-day applications in financial industry. The motivation for this training network is the need for a network of highly educated European scientists in the field of financial mathematics and computational science, so as to ex-change and discuss current insights and ideas, and to lay groundwork for future collaborations.

Researcher(s)

• Promoter: In't Hout Karel

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

In this project we propose alternatives for the existing SIS method that can be used for massive data with some extra complications such as outliers, for estimating quantiles of the response (in order to get an overview of the whole distribution of the response) and for incorporating grouping effects of some predictors. The proposed methods have the idea of SIS in common, namely they are based on marginal regressions, however, by changing the loss or objective function they allow for more complex data.

Researcher(s)

• Promoter: Verhasselt Anneleen

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

We consider models with varying coefficients, i.e. linear models in which the response and/or explanatory variables vary with another variable, for example time. These types of models can for example be used in HIV research, where the number of T-cells decreases over time and in addition depends on the number of T-cells at the time of infection. Moreover we study ordinary differential equations with varying coefficients that allow describing the dynamics of continuously changing processes. We estimate the varying coefficients by P-splines. This widely used sparse flexible smoothing technique has as an important advantage (over other smoothing techniques such as B-splines or smoothing splines) that the unknown functions can be modeled in a rich basis, while introducing sparsity by adding a penalty. The main aim of this project is to develop statistical methods that focus on qualitative features of the varying coefficients functions, e.g. whether a coefficient is really varying (in contrast to being constant) or whether it is a monotonic increasing function. Moreover we want to test general hypotheses concerning the coefficient functions, by exploiting the nice properties of P-splines such as its linearity in the basis functions.

Researcher(s)

• Promoter: Vanroose Wim
• Promoter: Verhasselt Anneleen
• Fellow: Ahkim Mohamed

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

This is a fundamental research project financed by the Research Foundation - Flanders (FWO). The project was subsidized after selection by the FWO-expert panel.

Researcher(s)

• Promoter: Verhasselt Anneleen

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

The aim of the project is to develop efficient numerical methods for solving PDEs using stencil computations and sparse linear solvers on modern multi- and many-core hardware. Resulting methods will have to exploit the memory layout to achieve good per core performance and good scaling over multiple cores. We will also focus on scalability of Krylov solvers (CG and GMRES) for sparse linear systems on very large distributed memory clusters.

Researcher(s)

• Promoter: Ghysels Pieter

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

In this research project we derive theoretical stability results for finite difference methods on general non-uniform grids. We consider several applications from financial mathematics. First of all we start with the well-known 1-dimensional Black-Scholes equation. After that we move on to higher dimensional partial differential equations, for example the Heston-Hull-White model. Our theoretical results are supported by numerical experiments.

Researcher(s)

• Promoter: In't Hout Karel
• Fellow: Volders Kim

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

Grating based differential phase contrast tomography is a new experimental technique to offers very exquisite images of soft tissues. However, the artifacts in the current images prohibit the accurate reconstruction of the inside of an object. The project aims to develop the algorithms that allow a quantitative reconstruction of this technique

Researcher(s)

• Promoter: Vanroose Wim
• Co-promoter: Sijbers Jan

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

This FWO scientific research network will focus on interdisciplinary research (mathematics – physics) in the area of stochastic modelling based on the interaction between theory, numerical computations and applications in financial markets. Hereto the network will make use of the complementary expertise present in the participating research groups.

Researcher(s)

• Promoter: In't Hout Karel

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

In this work, we focus on the numerical treatment of vortex patterns in realistic systems modeled by the Ginzburg-Landau equations, i.e., phase field equations that are frequently used to model physical systems exhibiting patterns. They are used, amongst others, to model superconductors, Bose-Einstein condensates, nonlinear waves, and objects of string field theory.

Researcher(s)

• Promoter: Vanroose Wim
• Fellow: Schlömer Nico

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

This project represents a research agreement between the UA and on the onther hand IWT. UA provides IWT research results mentioned in the title of the project under the conditions as stipulated in this contract.

Researcher(s)

• Promoter: Vanroose Wim
• Co-promoter: Broeckhove Jan

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

This is a fundamental research project financed by the Research Foundation - Flanders (FWO). The project was subsidized after selection by the FWO-expert panel.

Researcher(s)

• Promoter: Vanroose Wim

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

In this research project we derive theoretical stability results for finite difference methods on general non-uniform grids. We consider several applications from financial mathematics. First of all we start with the well-known 1-dimensional Black-Scholes equation. After that we move on to higher dimensional partial differential equations, for example the Heston-Hull-White model. Our theoretical results are supported by numerical experiments.

Researcher(s)

• Promoter: In't Hout Karel
• Fellow: Volders Kim

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

An accurate simulation of laser ablation requires a good description of the solid state, melt, Knudsen layer, plasma and interaction with the laser beam. We propose a hybrid model for these simulations that combines particle-based simulations with partial differential equations. The project will develop and analyze the numerical methods and apply them to realistic systems. The new approach may have a large impact on the field.

Researcher(s)

• Promoter: Vanroose Wim
• Co-promoter: Bogaerts Annemie

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

Researcher(s)

• Promoter: Vanroose Wim
• Fellow: Schlömer Nico

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

The aim of the project is to develop efficient computational methods, based on Krylov space methods, to solve the linear and non-linear Schrödinger equations. This will enable the theoretical methods to move from the approximate 2D models to the more realistic 3D description. The methods will be applied to practical physical problems: to solve the non-linear time-dependent and time-independent Ginzburg-Landau equations for the study of the vortex structure and dynamics in mesoscopic superconductors and to solve the linear Schrödinger equation for realistic self-assembled quantum dots.

Researcher(s)

• Promoter: Vanroose Wim
• Co-promoter: Milosevic Milorad
• Co-promoter: Partoens Bart

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

The aim of the project is to develop hybrid methods that divide the spatial domain into subdomains where an appropriate microscopic or macroscopic model is used. The domains are connected in a physical and mathematically correct way. This makes it possible to limit the use of the expensive particle based methods to the regions of space where they are strictly necessary. We will apply this method to decribe the transport of particles in laser ablation from the surface. More specifically, the Knudsen layer, which is formed between the surface and the bulk, will be described at the particle level.

Researcher(s)

• Promoter: Vanroose Wim
• Co-promoter: Bogaerts Annemie

Research team(s)

• Applied mathematics

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 goal of this project is to analyze the stability of numerical processes for time-dependent partial differential equations. We investigate important open stability questions concerning both space- and time-discretization methods. In answering these questions, we employ among others the recent numerical stability theory based on resolvent conditions.

Researcher(s)

• Promoter: In't Hout Karel

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

This research project concerns the design and analysis of numerical methods for multi-dimensional, time-dependent convection-diffusion-reaction equations with applications to financial mathematics. We study operator splitting methods, in particular ADI schemes, which are highly promising for the numerical solution of these, large-scale problems. Our analysis deals with fundamental properties such as stability and convergence.

Researcher(s)

• Promoter: In't Hout Karel

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

This project proposes to develop numerical and mathematical methods for wave and scattering problems that are scalable to a large number of unknowns. The aim is to be able to simulate realistic problems in their full dimension and complexity. The focus is to extend multigrid methods to the Helmholtz probem

Researcher(s)

• Promoter: Vanroose Wim

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

Many systems in science and technology are well understood at the level of the individuals e.g.: the atoms, molecules, or bacteria. In this project we will develop numerical and mathematical techniques to predict the macroscopic and collective behavior of a system with a large number of individuals. We use the micro/macro techniques to translate the behavior of individuals to the macroscopic evolution.

Researcher(s)

• Promoter: Vanroose Wim

Research team(s)

• Applied mathematics

Project type(s)

• Research Project

Abstract

This project represents a research contract awarded by the University of Antwerp. The supervisor provides the Antwerp University research mentioned in the title of the project under the conditions stipulated by the university.

Researcher(s)

• Promoter: Vanroose Wim
• Fellow: Vanroose Wim

Research team(s)

• Applied mathematics

Project type(s)

• Research Project