# Invited and accepted minisymposia abstracts and speakers

**New Trends in Model Order Reduction and Learning**

##### Organizers: Silke Glas (University of Twente), Mario Ohlberger (University of Münster) and Tizian Wenzel (Universität Hamburg)

Model order reduction for parameterized systems has seen a tremendous development in recent years.

Particular challenges for MOR procedures include their usage in PDE constrained optimization and data assimilation, for complex multiscale and/or nonlinear problems as well as for convection dominated reactive flow problems. Moreover, structure preserving methods got increasing attention as well as combined machine learning and model order reduction sapproaches. In this session new ideas to tackle such challenges will be addressed.

**Numerical methods for nonlinear hyperbolic problems**

##### Organizers: Stephane Clain (Universidade de Coimbra), Peter Frolkovič (Slovak University of Technology), Raphael Loubere (University of Bordeaux) and Gabriella Puppo (Università di Roma La Sapienza)

Nonlinear partial differential equations of hyperbolic type find many applications in industry and research. Their approximate solutions require very often advanced numerical techniques and algorithms. Some recent advances in this topic will be presented at this minisymposium.

**Model and data-driven algorithms in imaging**

##### Organizers: Martin Huska (University of Bologna), Alessandro Lanza (University of Bologna) and Serena Morigi (University of Bologna)

The allure of image processing has led to an explosion in its applications in science and industry, from medicine and biology to satellite imagery and automation.

While each imaging application may have its own unique data type, mathematically, the observed input image can be modeled as the product of a forward operator, which captures the specific distortions that occur during the acquisition process. A widely used approach to recovering the original image is to solve the inverse problem of the forward process, which is typically ill-posed.

The choice of a prior is crucial for accurate reconstructions. Classical priors exploit global properties, such as sparsity or regularity. However, recent advances in storage capability have made it possible to collect large datasets of training examples, which can be used to design more sophisticated data-driven priors that can model complex structures in images.

This session will focus on new results and applications of data-driven approaches to inverse problems in imaging science, with a particular emphasis on the variability and challenges posed by the input data. We will explore the synergies between model-based and data-driven approaches, and analyze novel strategies for extracting meaningful information from the available data.

**Structure-preserving finite element methods for computational fluid dynamics**

##### Organizers: Dmitri Kuzmin (University of Technology, Dortmund) and Andreas Rupp (Lappeenranta-Lahti University of Technology)

Recent years have seen significant interest of the finite element community in high-order methods that preserve certain properties of exact solutions. The design criteria for the development of such methods may include, e.g., local discrete maximum principles for scalar quantities of interest, global positivity preservation, kinetic energy preservation, and/or entropy conditions. In the presence of source terms, it may be essential to ensure well balancing, i.e., preservation of important steady-state equilibria (such as “lake at rest” in shallow water models). Additionally, the impact of unstructured grids, non-conforming approximations, super-parametric elements, boundary conditions, numerical quadrature rules and time discretization procedures needs to be taken into account. Algorithmic tools for enforcing the desired properties include artificial diffusion operators, flux/slope limiters, convex blending, and the summation-by-parts formalism. As a rule, only nonlinear numerical approximations can meet the conflicting demands for high accuracy and validity of all relevant constraints. The need to deal with challenging nonlinear problems requires new approaches to the analysis and design of property-preserving finite element methods. Exploration of such approaches is currently under way, and the state of the art is rapidly evolving. This minisymposium will enable developers of continuous and discontinuous Galerkin methods to synchronize their efforts and further advance both approaches. The applications to be discussed range from scalar conservation laws to the equations of compressible gas dynamics and geophysical fluid dynamics.

Confirmed Speakers | Title of the contribution |
---|---|

Dmitri Kuzmin (TU Dortmund University) | Dissipation-based WENO stabilization for high-order finite element discretizations of hyperbolic problems |

Andreas Rupp (Lappeenranta-Lahti University of Technology) | Limiter-based entropy stabilization of semi-discrete and fully discrete schemes for nonlinear hyperbolic problems |

Andres Rueda-Ramirez (University of Cologne) | Monolithic Convex Limiting for Legendre–Gauss–Lobatto Discontinuous Galerkin Spectral Element Methods |

Jesse Chan (Rice University) | Enforcing cell entropy inequalities using subcell limiting |

Sara Faghih-Naini (University of Bayreuth) | A quadrature-free p-adaptive discontinuous Galerkin discretization for the shallow water equations |

Joshua Vedral (TU Dortmund University) | Strongly consistent low-dissipation WENO schemes for finite elements |

## Modelling and simulation of flow, reactive transport and deformation in porous media

##### Organizers: Iuliu Sorin Pop (University of Hasselt)

Porous media processes like flow, reactive transport and deformation appear in numerous applications of societal and technological relevance. For a thorough understanding of such processes, mathematical modelling and numerical simulation are key technologies. Typically, the mathematical models are expressed in terms of coupled systems of nonlinear, possibly degenerate equations, and involve multiple scales, which makes the development of efficient numerical algorithms a challenging task.

This minisymposium will address issues related to the mathematical modelling of various processes taking place in a porous medium, and the development of efficient numerical algorithms for such models. Next to modelling details, the presentations will present convergence results for the numerical schemes, like a priori error estimates, a posteriori error control, the convergence of iterative schemes for solving nonlinear equations and coupling different model components.

Confirmed Speakers | Title of the contribution |
---|---|

John Stockie (Simon Fraser University) | A multi-scale model for freeze/thaw-induced pressure generation in maple trees |

Dumitru Trucu (University of Dundee) | Computational Multiscale Modelling of Glioblastoma Growth and Spread within Fibrous Brain Environment |

Carmen Rodrigo Cardiel (University of Zaragoza) | Oscillation-free numerical scheme for the Biot’s model |

Marco Berardi (CNR-IRSA) | Modeling root water uptake activity in the unsaturated water flow framework |

Johannes Kraus (University of Duisburg-Essen) | Fixed-stress method for a class of nonlinear poroelasticity problems |

Koondanibha Mitra (Eindhoven University of Technology/Hasselt University) | Robust time-discretization, linearization and adaptive algorithms for coupled problems in porous media |

Muhammad Awais Khan (Monash University) | An iterative scheme for the stochastic Stefan problem |

Sorin Pop (Hasselt University) | Linear iterative schemes for degenerate parabolic problems |

## Numerical, analytical, experimental, and image processing approaches to combustion, flame propagation, and evolution of interfaces

##### Organizers: **Shigetoshi Yazaki** (Meiji University)

Since the dawn of history, fire has provided humankind with many benefits and caused many fires. Fire is a double-edged sword of convenience and threat, and especially fire is a threat because it is difficult to control and cope with.

This minisymposia explores combustion and related phenomena from multiple perspectives, including numerical, analytical, experimental, and image processing approaches, to quantitatively and qualitatively elucidate its mechanisms.

## Interface motion in complex systems

##### Organizers: Michal Beneš (Czech Technical University, Prague) and Koya Sakakibara (Kanazawa University)

This mini-symposium is focused on computational aspects of moving-boundary problems arising in physics, biology, environment protection or image processing. The computational methods include direct parametric approach, level-set, phase-field and immersed-boundary methods. The contributions involve and are not restricted to applications in real problems in the climate change, physics of multi-phase flow, crystal growth, motion of biological structures or processing of biomedical data. The mini-symposium is devoted to get together senior and young researchers worldwide to allow an intense exchange of results and experience.

## Computational methods and algorithms for biomedical applications

##### Organizers: Elfriede Friedmann (University of Kassel) and Jurjen Duintjer Tebbens (Charles University, Hradec Kralove)

The aim of this minisymposium is to present recent algorithmic developments used in mathematical biology. The focus is on the computational techniques and on applications with a medical component. Examples are numerical methods for computational fluid dynamics and fluid solid interactions to describe body fluids and circulation or computations of periodic and oscillatory concentration behavior that arises with repeated drug dosing or in biological clocks.

Confirmed Speakers | Title of the contribution |
---|---|

Jurjen Duintjer Tebbens (Charles University Prague) | Oscillations in diffusion-driven gene regulatory networks for nuclear receptors |

Mads Kyed (Flensburg University of Applied Sciences) | Unconstrained steady motion of a droplet in a two-phase flow |

Tomáš Bodnár (Czech Technical University Prague) | On the estimation of blood hemolysis index from viscoelastic stretch model |

Elfriede Friedmann (University of Kassel) | Pharmacological models and numerical algorithms for the refinement of therapeutic approaches for retinal diseases |

Marília Pires (Évora University) | Localized numerical stabilization based on conformation tensor spectrum for viscoelastic fluids flows simulations |

Marcin Zagórski (Jagiellonian University) | Formation of gene expression patterns in developing spinal cord |

## ECMI SIG: Computational Methods for Finance and Energy Markets

##### Organizers: Matthias Ehrhardt (Bergische Universität Wuppertal) and Daniel Ševčovič (Comenius University in Bratislava)

This minisymposium is an activity of the ECMI Special Interest Group (SIG) on Computational Finance. The SIG was launched at ECMI-2014 in Taormina and (together with the ITN-STRIKE network (2013-2016)) organized several sessions of a minisym-posium in Computational Finance.

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 aim of this minisymposium is to present most recent developments of effective and robust numerical schemes for solving linear and nonlinear problems arising from the mathematical theory of pricing financial derivatives and related financial products.

## Numerical linear algebra in PDEs

##### Organizers: Michal Outrata (Virginia Tech), Conor McCoid (University Laval) and Martin Gander (University of Geneva)

Many real-world applications in science and engineering lead to problems posed as partial differential equations (PDEs). To solve these, one uses some form of discretization and linearization, and then applies various techniques from numerical linear algebra. This minisymposium puts emphasis on considering all of these steps in relation to each other, as well as to the original PDE. The speakers will introduce new methods as well as analyze existing ones, and look at applying these to various PDEs in the field. We hope to bring together professionals with PDEs to solve and researchers with linear algebra expertise so that new collaborations can ensue.

Confirmed Speakers | Title of the contribution |
---|---|

Conor McCoid (University Laval) | Adaptively optimised transmission conditions in Schwarz methods |

Michal Outrata (Virginia Tech) | HAM: Hierarchical approximate maps for updating preconditioners |

Jan Papez (Czech Academy of Science) | Algebraic error in Adaptive Finite Element Method |

Eric de Sturler (Virginia Tech) | Sketching and Recycling GMRES for a Sequence of PDE Solves |

Niall Bootland (STFC Rutherford Appleton Laboratory) | Multipreconditioning with Domain Decomposition for High-Frequency Helmholtz Problems |

Kshitij Patil (Simon Fraiser University) | Steklov properties of the Helmholtz operator in the plane |

Miranda Boutilier (Université Côte d’Azur) | Robust Methods for Multiscale Coarse Approximations in Perforated Domains |

Liudi Lu (University of Geneva) | Time domain decomposition methods for parabolic optimal control problems |

Hayden Ringer (Virginia Tech) | Shape From Sound: The Inverse Laplacian Eigenvalue Problem |

## Scientific Machine Learning: Algorithms and Applications

##### Organizers: Alena Kopanicakova (Brown University), Hardik Kothari (Università della Svizzera italiana), Rolf Krause (Università della Svizzera italiana and FernUni) and Simone Pezzuto (University of Trento)

Physics-based mathematical modeling is ubiquitous in science. Still, there is an apparent and ever-growing success of purely data-driven machine learning applications. Recently, there has been a surge in interest in blending mathematical modeling with machine-learning methodologies. These novel Scientific Machine Learning (SciML) approaches bear tremendous potential for scenarios where data is scarce for a purely data-driven approach and physics is known only to some extent. SciML also extends to parametric PDEs, inverse problems, model order reduction, and the solution of high-dimensional problems. However, SciML encounters challenges, including computationally intensive training and the lack of explicit error control and robustness, which limit their reliability in real-world applications.

In this mini-symposium, we will discuss recent developments on the enhancement of SciML via numerical methods, and vice versa, in order to enhance their applicability to real-world problems. We invite submissions on various topics concerning the integration of deep learning and classical numerical methods, encompassing, but not limited to:

- The development of novel types of SciML surrogates, including approaches that incorporate physical and geometric constraints into the architectural design of neural networks.
- The integration of state-of-the-art numerical methods with SciML techniques to enhance the training process.
- Techniques that combine SciML surrogates with state-of-the-art numerical solution methods for increased efficiency and efficacy.
- Hybridization of standard numerical methods (Finite Element, Iso-geometric analysis, etc.) with deep learning algorithms.

## Numerical methods for convection-dominated problems

##### Organizers: Volker John (WIAS Berlin) and Petr Knobloch (Charles University, Prague)

In many mathematical models of physical, technical or biological processes, convection effects represent the dominating mechanism which determines the distribution of the modelled quantities. Numerical solution of this type problems is very challenging since standard methods often provide approximate solutions polluted by spurious oscillations. Since these oscillations are not acceptable in many applications, various special numerical techniques have been developed during the past decades. However, despite these efforts, methods being accurate and efficient at the same time are still rather rare. The aim of the minisymposium is to present the recent progress in this field.

Confirmed Speakers | Title of the contribution |
---|---|

Marius Paul Bruchhäuser (Helmut-Schmidt-Universität Hamburg) | Investigation of the Dual Weighted Residual method for convection-dominated problems |

Volker John (WIAS Berlin) | On Using Machine Learning Techniques for the Numerical Solution of Convection-Diffusion Problems |

Petr Knobloch (Charles University) | Algebraic stabilizations of convection-diffusion problems and their convergence on general meshes |

Julia Novo (Universidad Autónoma de Madrid) | Second order bounds in time for POD-ROM methods for the Navier-Stokes equations |

Hendrik Ranocha (Universität Hamburg) | Energy-preserving numerical methods for some dispersive shallow water models |

Martin Vohralík (INRIA Paris) | Guaranteed and robust L2-norm a posteriori error estimates for 1D linear advection(-reaction) problems |

## Parallel in time methods for High-Performance Computing

##### Organizers: Christian Engwer (University of Muenster) and Martin Gander (University of Geneva)

Methods of time-parallel time integration have gained increasing interest in the last decade due to the advent of massively parallel computers.

Applications are constantly growing in complexity and at the same time modern hardware architectures continue evolving rapidely. Constantly increasing parallelism and vectorisation pose particular challenges. This has led to the emergence of new numerical paradigms to overcome the limitations of modern hardware and benefit from the developments. One particular approach is time-parallel (PinT) methods for solving instationary partial differential equations (PDEs), where the time direction yields additional structure and increases the computational load to take advantage of the available hardware.

The time direction however is special, and for evolution problems there is a causality principle: the solution at a later time is determined by the solution earlier in time, but not vice versa. Algorithms trying to use the time direction for parallelization must therefore be special, and take this very different property of the time dimension into account.

In this minisymposium we try to bring together experts from the fields of PinT and High performance computing to discuss recent advances.

## Advanced numerical methods for dissipative systems

##### Organizers: Simon Lemaire (Inria, University of Lille) and Maxime Herda (Inria, University of Lille)

Motivated by the simulation of complex systems arising from physics and biology, there is a constant demand concerning the design and analysis of reliable and efficient numerical methods. In this regard, we are interested in novel approaches for the approximation of nonlinear dissipative PDEs of parabolic and elliptic type, using low- and high-order numerical methods, on possibly general meshes. On the one hand, we are interested in the preservation at the discrete level of fundamental physical properties from the model at hand, such as bounds, asymptotics, symmetries, energy or entropy structures. On the other hand, we also have in mind the discrete preservation of algebraic properties such as underlying Hilbertian complex and cohomology structures, which are known to be a keystone to ensure the well-posedness and robustness of numerical methods.

Keywords: numerical analysis of PDEs, structure-preserving schemes, arbitrary-order methods, discrete complexes, polytopal meshes, dissipative systems, entropy and energy structures

Confirmed Speakers | Title of the contribution |
---|---|

Marianne Bessemoulin-Chatard (CNRS, Univ. Nantes) | Discrete hypocoercivity for a nonlinear kinetic reaction model |

Stefano Bonetti (Politecnico di Milano) | Numerical modeling of wave propagation phenomena in thermo-poroelastic media via discontinuous Galerkin methods |

Simon Lemaire (Inria, University of Lille) | High-order polyhedral methods for eddy current testing simulation |

Robert Eymard (Université Gustave Eiffel) | Approximations of linear elliptic problems with irregular data on general simplicial grids |

Hana Mizerová (Comenius University in Bratislava) | Convergent numerical schemes for compressible fluid flow models |

Julien Moatti (TU Vienna) | An arbitrary-order entropic method for structure-preserving approximations of advection-diffusion |

Antoine Zurek (UTC, Compiègne) | Analysis of a numerical scheme for a nonlocal cross-diﬀusion system |

## Numerical methods for level-set and eikonal equations – theory and applications

##### Organizers: Jooyoung Hahn (Slovak University of Technology) and Karol Mikula (Slovak University of Technology)

The minisymposium focuses on the recent state-of-the-art research on level-set and eikonal equations and related topics with diverse applications such as image segmentation, sound propagation in 3D environments, 3D shape reconstruction, 3D printing, distance computation on a non-convex domain, crystalline mean curvature flow, and Earth gravity field modelling. Various numerical methods and related mathematical theories will be presented.

Confirmed Speakers | Title of the contribution |
---|---|

Laurent Cohen (Universite Paris Dauphine) | Fast marching and front propagation for image segmentation |

Silvia Tozza (University of Bologna) | Level-set method in Image Processing and 3D printing problems |

Marek Macák (Slovak University of Technology in Bratislava) | Earth gravity field modelling by using eikonal type boundary condition |

Norbert Požár (Kanazawa University) | Level set method for the crystalline mean curvature flow with forcing |

Samuel Potter (The Courant Institute, New York University) | Jet marching on unstructured meshes: algorithms and applications |

Jooyoung Hahn (Slovak University of Technology in Bratislava) | Eikonal boundary condition for level set method |