2022 Springmeeting

Participants of the 2022 Spring meeting

Friday May 6, 2022, the Dutch-Flemish Scientific Computing Society organized its annual spring meeting. This year it took place at KU Leuven. A mix of young and senior researchers were invited to present their research.

Participation including lunch was free of charge. This year we had 47 registrations.

Location:
KU Leuven
Thermotechnisch Instituut
Kasteelpark Arenberg 41
3001   Leuven
Room 01.02 - at the aula of the Tweede Hoofdwet

Organization

The spring meeting is organized yearly by the Dutch-Flemish Scientific Computing Society (SCS), this year in cooperation with the Department of Computer Science from the KU Leuven.

Organizing comittee: Karl Meerbergen (KU Leuven), Barry Koren (TU Eindhoven) and Martine Anholt (CWI, Secretary SCS).

Support for this meeting has been obtained from Centrum Wiskunde & Informatica (CWI) and KU Leuven.

Program 2022

Speakers Spring meeting SCS 2022

	Olga Mula, Eindhoven University of Technology Olga Mula has recently joined TU Eindhoven in February 2022 as an Associate Professor in Data-Driven Computational Science. She obtained her PhD in Applied Mathematics in 2014 at Sorbonne University. After a one year postdoctoral stay at RWTH Aachen University, she was appointed Associate Professor at Paris Dauphine University and worked there for about six years until moving to TU/e.
	Emil Løvbak, KU Leuven Emil Løvbak obtained a BSc in Computer Science and Electrical engineering and an MSc in Mathematical Engineering from KU Leuven. He is now a PhD Fellow of the Research Foundation Flanders, hosted at KU Leuven under the supervision of professors Giovanni Samaey and Stefan Vandewalle. His research focuses on multilevel Monte Carlo simulation for simulation and stochastic optimization involving kinetic particle models.
	Hugo Verhelst, Delft University of Technology 2013-2016 Bachelor of Science in Maritime Engineering (cum laude)  – TU Delft 2016-2019 Master of Science in Maritime Engineering (cum laude)  – TU Delft 2016-2019 Master of Science in Applied Mathematics (cum laude) – TU Delft 2019-present PhD student in Computational Mechanics – TU Delft
	Sohely Sharmin, University of Hasselt received her B.Sc. degree in mathematics at the University of Dhaka, Bangladesh, in 2010. She then obtained her M.Sc. degree in mathematics at Heidelberg University, Germany, in 2015. Currently, she is pursuing her PhD degree in the Computational Mathematics research group at the Hasselt University in Belgium. Her topic focuses mainly on upscaling two-phase flow problems in porous media with moving interfaces at the pore scale.
	Wouter Edeling, CWI is a tenure tracker in the Scientific Computing group at CWI. He has a background in aerospace engineering, and obtained a joint-PhD from Delft University of Technology and Arts et Métiers ParisTech in 2015 on the topic of uncertainty quantification for Reynolds Averaged Navier-Stokes (RANS) turbulence closures. He is a recipient of the Center for Turbulence Research Postdoctoral fellowship at Stanford University, and has worked on physical model error representation in turbulence models, use of advanced Bayesian data analysis, and reduced order modelling for multiscale simulations. His current research interest lies at the intersection of machine learning, physical models and uncertainty quantification.
	Jacob Snoeijer, University of Antwerp In 2014 I received a double bachelor degree in both Computing Science and Mathematics at the University of Groningen. In 2016 I received a double MSc degree in Applied Mathematics at Delft University of Technology and in Computational Engineering at the Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany). Since 2016 I am working on a PhD in Applied Mathematics at the University of Antwerp. My research focuses mainly on efficient numerical approximation of solutions to high-dimensional partial differential equations with applications in both financial option valuation and scattering problems.
	Laura Scarabosio, Radboud University Nijmegen Laura Scarabosio is assistant professor at the Radboud University since 2020. She obtained the PhD in Mathematics from ETH Zürich in 2016 under the supervision of Ralf Hiptmair and co-supervision of Christoph Schwab. She spent four years as postdoctoral researcher at TU Münich, when she also conducted research visits at the Oden Institute at UT Austin. Her research interests cover shape uncertainty quantification, Bayesian inverse problems, uncertainty quantification for random multiscale materials and applications to biology and medicine.
	Magnus Botnan, Vrije Universiteit Amsterdam Is an assistant professor (tenure track) at the department of mathematics at the Vrije Universiteit (VU) in Amsterdam. Before coming to the Netherlands, I was a postdoc at TU Munich, and before that  I defended my PhD at the Norwegian University of Science and Technology in December 2015 under the supervision of Nils A. Baas. I work within the field of topological data analysis: a relatively recent branch of mathematics in which topological signatures are assigned to data. Enjoying being at both the pure and applied side of mathematics, my research includes pure elements such as representation theory of quivers, as well as more computational aspects, and applications towards the sciences.
	Nick Trefethen, University of Oxford and KU Leuven Nick Trefethen is Professor of Numerical Analysis and head of the Numerical Analysis Group at Oxford University.  He was educated at Harvard and Stanford and held positions at NYU, MIT, and Cornell before moving to Oxford in 1997.  He is a Fellow of the Royal Society and a member of the US National Academy of Engineering, and served during 2011-2012 as President of SIAM.  He has won many prizes including the Gold Medal of the Institute for Mathematics and its Applications, the Naylor Prize of the London Mathematical Society, and the Pólya and von Neumann Prizes from SIAM.  He holds honorary doctorates from the University of Fribourg and Stellenbosch University. As an author Trefethen is known for his books including Numerical Linear Algebra (1997), Spectral Methods in MATLAB (2000), Spectra and Pseudospectra (2005), Approximation Theory and Approximation Practice (2013/2019), and Exploring ODEs (2018). He organized the SIAM 100-Dollar, 100-Digit Challenge in 2002 and is the inventor of Chebfun.

Abstracts Spring meeting SCS 2022

Olga Mula, Technical University of Eindhoven
Inverse State and Parameter Estimation: Optimal Algorithms and Applications
In this talk, I will present an overview of recent works aiming at solving inverse problems (state and parameter estimation) by combining measurement observations and physical PDE models. After defining a notion of optimal performance in terms of the smallest possible reconstruction error that any reconstruction algorithm can achieve, I will present practical numerical algorithms based on nonlinear reduced models for which we can prove that they can deliver a performance close to optimal. The performance of the approach will be illustrated on simple benchmark examples and also on non trivial applications such as urban pollution, and some biomedical problems. Finally, I will outline certain intrinsic limitations arising in inverse problems for transport dominated PDEs, and discuss some possible remedies.

Emil Løvbak, KU Leuven
Stochastic optimization for divertor design in tokamak fusion reactors
Nuclear fusion is an exciting potential source of clean, reliable energy for the future. However, significant challenges still remain in developing a reactor capable of supplying the power grid. One such challenge is designing the divertor, a component that removes waste particles from the reactor. The divertor comes into contact with a dense plasma, modeled as a fluid, as well as lower density neutral particles, modeled as a kinetic process.
The B2-EIRENE research code simulates the coupled plasma-neutral model through a combination of finite volume and Monte Carlo particle methods. The design is iteratively refined in an adjoint based optimization routine, i.e., gradients are computed by simulating the adjoint model with a similar discretization. The current Monte Carlo simulations are unfortunately too expensive for feasible in silico divertor design.
At KU Leuven we have developed a variety of techniques for accelerating these codes. We have developed a new class of asymptotic-preserving Multilevel Monte Carlo schemes for accelerating both the forward and adjoint simulations. We have also developed a discrete adjoint approach in which we use the same stochastic paths for the forward and adjoint Monte Carlo simulation, with the goal of reducing the number of iterations required in the optimization routine. In this talk, I will introduce these techniques, as well as our current work on challenges remaining on the path towards valorization in the B2-EIRENE code.

Hugo Verhelst, Delft University of Technology
On the modeling of wrinkling instabilities using isogeometric shell analysis
Wrinkling is a phenomenon that is omnipresent in nature: wrinkles occur on our skin, in dough or on edges of leafs. In engineering sciences, wrinkling is typically present when dealing with very thin membranes, where the bending stiffness (typically governed by the thickness) is very low compared to the in-plane stiffness. Examples of wrinkles in engineering applications include thin membranes for solar sails and the novel idea of thin membranes for offshore photo voltaics (PV).
A recent advancement in computational mechanics is isogeometric analysis (IGA). By employing spline constructions from computer-aided design (CAD) in finite element analysis (FEA) models, IGA aims to unify design and analysis. Because of the geometric exactness of IGA, advantages of the method are found in shape and topology optimization, as well as multi-physics applications with domain interfaces. Because of the global smoothness of spline basis functions, IGA is known to provide high accuracy per-degree of freedom.
In this talk, an overview of the work of modeling wrinkling instabilities using isogeometric shell analysis is given. In the first part of the talk, the basics of isogeometric analysis and its application to shell elements are given. Thereafter, an overview of solution methods for wrinkling analysis is given. The talk concludes with some results as well as future direction for isogeometric shell analysis for wrinkling analysis and other industrial applications.

Sohely Sharmin, University of Hasselt
Upscaling of two-phase porous-media flows with solute-dependent surface tension effects
Two-phase flow in porous media appears in a wide range of applications such as biological processes, geological carbon sequestration and nuclear waste disposal. Moreover, in microfluidics, thin-film flows or enhanced oil recovery soluble surfactants present in the fluids play an important role by altering the surface tension at the interface separating the two fluids.
We study two-phase flow in porous media by starting from a model valid at the pore scale. Next to this, we study the case when a solute is transported in one of the fluids and we account for the effect of variable surface tension. At the pore scale, the flow is modelled by the Navies-Stokes equation, and the convection-diffusion equation describes the solute transport. The major challenge is due to the moving interface separating the two immiscible fluids as the fluids flow through the pores of the porous medium. At the pore scale, this translates into free boundary problems. To model this for a given simple geometry, we use a sharp-interface formulation, but for a more general domain, a phase-field approach is used, where the Cahn-Hilliard equations model the phase separation. We formulate a dimensionless pore-scale model by rescaling the model parameters and variables. Under various assumptions on the characteristic non-dimensional numbers, we derive effective/averaged models valid at the larger (Darcy) scale by applying formal upscaling techniques. In particular, transversal averaging is applied to the simple geometry, whereas homogenization is used for the more complex domain. The upscaled models describe the averaged behaviour of the system and include pore-scale information through effective parameters. Finally, by solving the upscaled models numerically, we can show the effect of variable surface tension.

Wouter Edeling, CWI
High-dimensional parametric uncertainty quantification
The deep active subspace method is a neural-network based tool for the propagation of uncertainty through computational models with high-dimensional input spaces. Unlike the original active subspace method, it does not require access to the gradient of the model.  It relies on an orthogonal projection matrix constructed with Gram-Schmidt orthogonalization, which is used to linearly project the (high-dimensional) input space to a low-dimensional active subspace. This matrix is incorporated into a neural network as the weight matrix of the first hidden layer, and optimized using back propagation to identify the active subspace of the input.  We propose several theoretical extensions, starting with a new analytic relation for the derivatives of Gram-Schmidt vectors, which are required for back propagation. We also strengthen the connection between deep active subspaces and the original active subspace method, and study the use of vector-valued model outputs, which is difficult in the case of the original active subspace method. Additionally, we extract more traditional global sensitivity indices from the neural network to identify important inputs, and compare the resulting reduction of the input space to the dimension of the identified active subspace. Finally, we will assess the performance of the deep active subspace method on (epidemiological) problems with high dimensional input spaces, including an HIV model with 27 inputs and a COVID19 model with a 51-dimensional input space.

Jacob Snoeijer, University of Antwerp
Solving for the low-rank tensor components of the wave function in scattering problems with multiple ionization
Information about small, microscopic systems, such as molecules, comes from experiments where light or electrons scatter from the object.  The measured cross section can be predicted from first principles, starting from a multi-particle Schrödinger equation. This is equivalent to a high-dimensional driven Helmholtz equation with the scattering wave as unknown and a righthand side that describes the initial object.
We propose to use a low-rank representation of the scattering solution and solve for its factors. This reduces the linear system to a series of small low-dimensional scattering problems that are solved in a sequence. These linear systems can be related to solve the coupled channel equation.
In this presentation, we discuss a proof of principle for a two-dimensional problem and the extension to higher dimensions using tensors. We solve the Helmholtz equation with a space dependent wave number and calculate the cross section. The low-rank approximation to the solution of the Helmholtz equation is sufficient to get a good approximation to the differential cross section.
Finally, we also demonstrate the application to high-dimensional problems. Instead of matrix equations, as in the two-dimensional problems, we now obtain tensor equations. The solution to the high-dimensional Helmholtz equation is represented as a Tucker tensor. Using this representation similar algorithms and update equations for the factor matrices in the Tucker tensor representation are derived.

Laura Scarabosio, Radboud University Nijmegen
Shape uncertainty quantification for the strongly damped wave equation
The strongly damped wave equation is found in many applications for the modeling of viscoelastic materials. In this talk, we consider the effect of uncertainty in the shape of a scatterer on the solution to such an equation. To handle the shape variations, we consider a mapping approach to a reference configuration with fixed shape. We show that, in the presence of the strong damping, the map from the high-dimensional parameter describing the shape uncertainties to the solution on the reference configuration is holomorphic. This allows to apply high order quadrature methods for the computation of moments of the solution, which are robust with respect to the dimension of the parameter characterizing the shape variations. The performance of one of these algorithms, namely dimension adaptive sparse grids, will be shown in numerical experiments.

Magnus Botnan, VU  Amsterdam
An introduction to topological data analysis
Topological data analysis (TDA) is a branch of data science which applies topology to study the shape of data, i.e., the coarse-scale, global, non-linear geometric features of data. Examples of such features include clusters, loops, and tendrils in point cloud data, as well as modes and ridges in functional data. While the history of TDA dates back to the 1990’s, in recent years the field has advanced rapidly, leading to a rich theoretical foundation, highly efficient algorithms and software, and many applications. In this talk I will give a brief introduction to persistent homology, arguably the most important tool in TDA. 

Nick Trefethen, University of Oxford and KU Leuven
Numerical computation with rational functions
I have been involved in a number of recent and ongoing developments with rational functions, notably:

• AAA, AAA-Lawson, and AAA-LS algorithms (with Nakatsukasa, Sète, and Costa)
• Lightning and log-lightning approximations (with Gopal, Brubeck, Nakatsukasa, Weideman, and Baddoo).

The talk will give a tour of these ideas. On sabbatical here in Leuven, I am just beginning a new book to be called -Rational Functions-.