The topic of the UMIT seminar series is computational science and its applications. Talks are given every second Friday during the semester, starting at 14.05. Do arrive at 14.00 and grab some coffee, cake, and company. The duration is usually 20-30 minutes.

Subscribe to umit-seminar@lists.umu.se for notification of future talks.

Calendar feed: https://www.canvas.umu.se/feeds/calendars/user_HMNTu5oVcipW7rrvD5IFrpbpVU40sbCYQ1HiP4UD.ics

2025 Friday November 7th - 14.05

Title: CutFEMs for Convection-Diffusion in Mixed-Dimensional Domains

Speaker: Shantiram Mahata, Mathematics, UmU

Abstract: In this talk, we focus on Cut Finite Element Methods (CutFEMs) for convection-diffusion in mixed-dimensional domains. Mixed-dimensional domains are unions of manifolds of different dimensions such that a d-dimensional component always resides on the boundary of a (d+1)-dimensional component. This type of domain models porous media with embedded intersecting fractures. We first consider in a fully coupled manner the convection-diffusion equations on this mixed-dimensional geometry and discuss the well-posedness result. We then design CutFEM based on a fixed background mesh that covers the domain, allowing the manifolds to cut through the mesh in a very general fashion. We consider a stabilized finite element formulation and discuss a priori error bounds with illustrating numerical examples.

This is a joint work with Erik Burman, Peter Hansbo, Mats G. Larson, and Karl Larsson.

2025 Friday August 29th - 14.10-16.00

Presentations of three UmU-projects funded by eSSENCE 2025-2026:

Talk #1 (14:10-14:45)

Speaker: Cristian Gudasz

Title: A novel method to transform the modeling of global lake ecosystem dynamics using Model Order Reduction

Abstract: As climate change and nutrient pollution intensify, linking local lake processes to global biogeochemical patterns is both urgent and complex. Process-based, climate-coupled models are the most robust means of integrating physical and ecosystem dynamics; yet applying them to 5.7 million lakes over decadal time scales is computationally prohibitive. We address this bottleneck with model order reduction (MOR), constructing reduced-order models (ROMs) from high-fidelity lake models based on partial differential equations (PDEs) to simulate physical dynamics with minimal loss of accuracy. ROMs of one-dimensional hydrodynamic models reproduce essential processes, vertical temperature structure and turbulence-driven mixing, at a fraction of the computational cost. This capability makes decadal, planet-scale simulations of lake dynamics feasible, thereby improving lake representation in Earth system models and transforming a long-standing computational barrier into a shared platform for synthesis, standardized evaluation, and theory building.

Talk #2 (14:45-15:20)

Speaker: Maria Hamrin

Title: Unveiling space weather hazards – 3D spatiotemporal reconstructions of ionospheric currents

Abstract: Space weather can seriously impact modern infrastructure in many ways. For example, rapid variations in ionospheric E region currents (90–150 km altitude) can generate Geomagnetically Induced Currents (GICs) in the ground, which may overload power grids and trigger blackouts. For instance, a 2003 geomagnetic storm-induced GIC caused a prolonged outage in Skåne, and a Carrington-level event today could cause unprecedented damage to our electrified society.

However, there are large gaps in the understanding of the spatiotemporal behaviour of the ionospheric currents due to a lack of in-situ observations since satellites rarely orbit the E region. Hence, studies must rely on remote ground or space based observations, far away in altitude. Fortunately, the new EISCAT 3D (E3D) radars will provide unique data from the relevant altitudes. For example, it will be the first radar facility to measure the 3D ion velocities needed for determining the currents.

To make the most of the E3D data, a method for reconstructing additional ionospheric data sets has been suggested (Stamm et al., 2023). It solves an inverse problem based on assumptions of the governing equations. However, this method has limitations: it assumes quasi‑neutrality and a static magnetic field (often invalid during geomagnetic substorms and storms), it cannot reconstruct the current density, and it suffers from boundary errors due to its finite‑difference approach. Our project will address these issues by incorporating the ideal Ohm’s law to allow quasi neutrality deviations, applying the finite element method to avoid boundary problems, and using an iterative technique and complementary ground and/or spacecraft data to reconstruct the magnetic field.

In the future, we will use our method to analyse the detailed spatiotemporal behaviour of the ionospheric E region currents, and we will use our new understanding in state-of-the art simulations of GICs in Sweden.

Talk #3 (15:20-15:55)

Speakers: Mats G Larson & Karl Larsson

Title: Finite Element Methods for Modern Computing Architectures and Machine Learning Applications

Abstract: In this talk, we outline how to implement a finite element solver that interoperates with modern machine-learning and differentiable-computing frameworks such as JAX. We demonstrate the approach on an inverse problem, where we incorporate observations of typical solution behavior to regularize the formulation, making an otherwise ill-posed problem solvable.

2025 Friday May 23rd - 14.05

Title: How do neural networks react to symmetries in the data?

Speaker: Axel Flinth, Mathematics, UmU

Abstract: There is an ongoing debate on how symmetries in data should be handled when training neural networks. Should one take them into account when designing the neural network architecture, or should one just trust the neural networks to find them? In this talk, I will present a framework in which these questions can be naturally addressed. We will see that the geometry of the neural network architecture will dictate how it will react to symmetries in the data.

This talk is based on joint work with Fredrik Ohlsson and Oskar Nordenfors.

2025 Friday April 25th - 14.05

Title: Predicting interactions in dynamic networks with distributed adaptive stochastic gradient optimization

Speaker: Martin Rosvall, IceLab/Physics, UmU

Abstract: Predicting future interactions or novel links in networks is an indispensable tool with many applications across diverse domains, including drug repurposing based on genetic networks, money laundering detection in financial systems, and recommendation systems using transactional data. Among the many techniques developed for link prediction, those leveraging the networks' community structure have proven highly effective. For example, the recently proposed MapSim predicts links based on a similarity measure derived from the code structure of the map equation, an information-theoretic community-detection objective function that operates on network flows. The map equation benefits from Infomap, its fast optimization method widely regarded as one of the best network-clustering algorithms. However, we developed Infomap for static networks. While its stochastic greedy search algorithm excels at identifying reliable communities in network snapshots, Infomap cannot effectively integrate new data or adapt to smooth transitions over time in continuously evolving relational networks. This shortcoming raises a computational challenge: How can we equip the map equation framework with a computationally efficient optimization method to enable adaptive analysis of dynamic networks, leveraging evolving relational data to predict future interactions and uncover novel links in real time?

2025 Friday April 4th - 13.00 (note the time)

Title: Data-driven construction of basis sets and atomic potentials

Speaker: Valera Veryazov, Lunds Universitet

Abstract: The traditional approach to constructing atomic basis sets and model potentials is based on atomic calculations and energy minimization. This project, now sponsored by eSSENCE, explores an alternative strategy:
replacing energy minimization with the minimization of the difference between computed and reference electron density. The optimization of parameters used in the basis sets and in atomic potentials is performed using machine learning techniques.

2025 Friday March 28th - 14.05

Title: Structural Rigidity Using Combinatorics and Group Theory

Speaker: Klara Stokes, Mathematics and Mathematical Statistics, UmU

Abstract: Structural rigidity is the study of when a structure made of fixed-length bars and flexible joints holds its shape or can move. This area lies at the crossroads of geometry and combinatorics and traditionally uses tools from algebra and geometry to analyze different types of structures, such as bar-joint frameworks and tensegrities. In this talk, I’ll present an alternative viewpoint—using graphs and group theory to study rigidity. By focusing on the role of symmetry and structure, this approach offers a more intuitive and flexible way to understand when and why a framework is rigid. I’ll introduce the main ideas through simple examples and explain how this perspective connects to other themes in mathematics.

2025 Friday February 21st - 14.05

Title: Topology optimization of decoupling networks for antenna arrays

Speaker: Pan Lu, Computing Science, UmU

Abstract: Near-field coupling between closely placed antennas is unavoidable, and it is a well-known challenge in designing compact systems for wireless communications. Traditional decoupling techniques usually rely on human expertise and require considerable design effort. In this work, we employ a density-based topology optimization approach to design decoupling networks for metallic antenna arrays. The design problem is formulated as a multi-objective optimization problem, including maximizing the radiated energy and minimizing the reflected energy. The antennas are replaced by their time-domain impulse responses to improve computational efficiency and enable the usage of gradient-based optimization methods. We implement an in-house 3D finite difference time domain (FDTD) solver for the time-domain Maxwell's equations, and the simulations are performed on HPC2N. We will present two design examples of the decoupling feeding network for a two-element antenna array, which are manufactured and validated experimentally.

2025 Friday February 7th - 14.05

Title: PDE Solution Operator Learning Using Energy Minimization and MLPs

Speaker: Carl Lundholm, Mathematics and Mathematical Statistics, UmU

Abstract: We develop and evaluate a method for learning solution operators to nonlinear problems governed by partial differential equations. The approach is based on a finite element discretization and aims at representing the solution operator by an MLP that takes latent variables as input. The latent variables will typically correspond to parameters in a parametrization of input data such as boundary conditions, coefficients, and right-hand sides. The loss function is most often an energy functional and we formulate efficient parallelizable training algorithms based on assembling the energy locally on each element. For large problems, the learning process can be made more efficient by using only a small fraction of randomly chosen elements in the mesh in each iteration. The approach is evaluated on several relevant test cases, where learning the solution operator turns out to be beneficial compared to classical numerical methods.

The work is a collaboration with Mats G. Larson, Anna Persson, Erik Burman, and Karl Larsson.

Links to preprints: https://arxiv.org/abs/2412.04596, https://arxiv.org/abs/2412.04409

2025 Friday January 24th - 14.00

Title: Advanced Learning for Machine Automation

Speaker: Prof. Reza Ghabcheloo, Tampere University

Abstract: Reza is professor in autonomous mobile machines at Tampere University, Faculty of Engineering and Natural Sciences, unit Automation Technology and Mechanical Engineering.