10/9/2025 Per Pettersson, https://www.norceresearch.no/en/persons/per-pettersson/677

Title: Adaptive stratified sampling for uncertainty propagation: Application to large-scale CO2 storage and other non-smooth PDE solutions

Abstract: Permanent CO2 storage has been repeatedly identified by the International Panel on Climate Change as a necessary technology to limit global warming to two degrees. Offshore CO2 storage under the seafloor, where vast storage space is available, is subject to uncertainties that can only be reliably estimated by means of numerical simulation. Many existing sampling methods for uncertainty propagation, including the multilevel Monte Carlo method, multi-fidelity methods and Quasi-Monte Carlo methods, have been established as general-purpose procedures for problems where a hierarchy of models can easily be generated (i.e., grids of different coarseness) or displaying sufficient parameter dependence smoothness. However, these techniques may not provide performance gains when there is a non-smooth, in particular discontinuous, parameter dependence. An alternative means to obtain variance reduction in these cases is oﬀered by stratified sampling methods.

In this talk, we will discuss various ideas on adaptive stratified sampling methods tailored to applications with a discontinuous or localized parameter dependence, suitable for CO2 storage amoong other applications. The stochastic domain is adaptively stratified using local variance estimates, and the samples are sequentially allocated to the strata for asymptotically optimal variance reduction. The proposed methodology is demonstrated on discontinuous test cases from computational fluid mechanics and CO2 storage in subsurface reservoirs, exhibiting up to two orders of magnitude speedup compared to standard Monte Carlo methods. Finally, a realistic test case of large-scale CO2 storage is presented for the Smeaheia formation in the North Sea, where we combine stochastic upscaling of physical parameters with adaptive stratified sampling to quantify uncertainties related to leakage through the Vette fault with a stochastic model informed by data and geological expertise.

27/8/2025 Stefano De Marchi, https://www.math.unipd.it/~demarchi/

Title: Variably Scaled Persistence Kernels (VSPKs) for persistent homology applications

Abstract: In recent years, various kernels have been proposed in persistent homology to deal with persistence diagrams in supervised learning approaches. In this talk, we consider the idea of Variably Scaled Kernels (VSK) for approximating functions and data and interpret them in the framework of persistent homology. We call the new kernels Variably Scaled Persistence Kernels (VSPKs). These kernels have been then tested in different classification experiments showing that they can improve, in some cases, the performance and efficiency of existing standard kernels.

Short bio: Stefano De Marchi is a full professor of numerical analysis at the University of Padova. His research spans from theoretical aspects of multivariate polynomial approximation, kernel-based approximation, and rational approximation to applications to image reconstruction by kernels, "fake nodes" and classification by SVM with persistent kernels. He discovered the "Padua points" for bivariate polynomial interpolation and cubature on the square and, more recently, he studied the "Variably Scaled Discontinuous Kernels" for approximating discontinuous functions. He is the author of more than 130 papers, managing editor of Dolomites Research Notes on Approximation, associate editor of BIT Numerical Mathematics and a member of many editorial boards. He founded the Italian Network on Approximation (RITA) and is the Italian Mathematical Union's Coordinator of the topical group on Approximation Theory and Applications.

11/6/2025 Tom Britton, https://www.su.se/profiles/tbrit-1.182592

Title: Improving the use of contact studies in infectious disease modelling

Abstract: Social contact studies, investigating how many, and with whom, individuals tend to have close contact with, have been used to improve modelling of the potential for spread of infections in the community considered. The main output from such studies is an age-structured contact matrix $M$ describing the average number of contacts between individuals of different age-groups. $M$ often shows that social mixing is assortative with respect to age, and that younger age-groups have more contacts overall. What is lost when summarizing contact surveys with the matrix $M$ is the heterogeneity within age-groups. In the talk I will describe how this can be taken into account, and what the consequences are on the potential for the spread of infections. (Joint work with Frank Ball).

4/6/2025 Josefin Larsson, https://www.kth.se/profile/josla

Title: Supernova explosions

Abstract: The most massive stars in the universe end their lives with a supernova (SN) explosion. In the explosion, the outer layers of the star are ejected, while the core collapses to form a compact neutron star or black hole. There are many open questions regarding these events, including how the explosions are triggered and how the properties of the stars, explosions and compact objects are connected. In this talk I will give an overview methods used to study SNe, ranging from detailed analysis of the 3D morphology of individual nearby objects to studies of very large samples of distant SNe. Over the last decades, the number of SNe discovered every year has increased from single digits to over a thousand, and upcoming facilities will bring the rate to hundreds of thousands, which presents new opportunities and challenges to the field. I will discuss methods used for SN detection and classification, and give examples of research projects where we have used large data sets to search for rare interesting events.

28/5/2025 Oscar Grånäs, https://www.uu.se/kontakt-och-organisation/personal?query=N6-743

Title: Challenges in simulating light-matter interactions from first-principles

Abstract: The direct manipulation of spins via light may provide a path toward ultrafast energy-efficient devices. However, there are several fundamental questions that remain open. One major difficulty is to distinguishing the microscopic processes that occur during ultrafast laser excitation in magnetic alloys experimentally. We approach this difficulty from first-principles simulations. However, the governing equations needs to capture dynamics on time-scales differing by 4-6 orders of magnitude, a challenge to model efficiently.

In this presentation, I give an overview of a computational framework to simulate the out-of-equilibrium conditions arising in ultrafast laser experiments, and how transient response functions may be extracted to facilitate comparison to experimental observables relating to magnetism and topological band features. Further, the method is applied to study laser-induced magnetization dynamics in a multi-component ferro-magnetic alloy. By combining theory and experiment, we disentangle the competition between three ultrafast light-induced processes that occur. Our combined approach enables a comprehensive microscopic interpretation of laser-induced magnetization dynamics on time scales shorter than 100 femtoseconds.

21/5/2025 Doghonay Arjmand, https://www.uu.se/en/contact-and-organisation/staff?query=N15-1365

Title: From Periodic Structures to General Media: Solving Elliptic PDEs on Infinite Domains

Abstract: Elliptic partial differential equations (PDEs) posed on unbounded domains naturally emerge in various contexts within engineering and applied sciences, particularly in the modelling of heterogeneous media such as composite materials and microscale magnetic structures. In this talk, we present a class of efficient numerical methods tailored to the accurate and scalable solution of such problems. Emphasis is placed on the treatment of infinite domains through techniques such as domain truncation, regularization, and coupled PDE-boundary integral formulations. We further examine the associated analytical foundations, with particular attention to the distinctions between periodic and non-periodic configurations with respect to their convergence rates.

14/5/2025 Monika Eisenmann, https://portal.research.lu.se/sv/persons/monika-eisenmann

Title: A fully discretized domain decomposition approach for semi-linear SPDEs

Abstract: In recent years, SPDEs have become a well-studied field in mathematics. With their increasing popularity, it has become important to efficiently approximate their solutions. Therefore, our goal is to develop a modern time-stepping method for SPDEs. We consider a fully discretized numerical scheme for parabolic stochastic partial differential equations. Our method is based on a non-iterative domain decomposition approach, which can help parallelize the code, leading to more efficient implementations.

The domain decomposition is integrated through an operator splitting approach, where each operator acts on a specific part of the domain. More precisely, we combine the implicit Euler method with the Douglas-Rachford splitting scheme. For an efficient space discretization of the underlying equation, we chose the discontinuous Galerkin method. We provide a strong space-time convergence result for this fully discretized scheme and verify our theoretical findings through numerical experiments.

This talk is based on a joint work with Eskil Hansen and Marvin Jans (both Lund University).

7/5/2025 Olof Runborg, https://www.csc.kth.se/~olofr/

Title: Solving Helmholtz Equation Using the Temporal Wave Equation

Abstract: We consider iterative methods for the Helmholtz equation that are based
on the related time domain wave equation. In each iteration, the
solution to the wave equation with a time-periodic forcing is computed
and filtered in time. For Dirichlet and Neumann problems the iteration
corresponds to a linear and coercive operator which, after
discretization, is recast as a positive definite linear system of
equations that can be solved with the conjugate gradient method. The
main benefit of using these iterations comes when considering large
scale problems. Implementing parallelized, high order methods that run
efficiently on big computers is typically easier to do for time domain
methods than for traditional Helmholtz solvers. We also show how the
iterations can be used to turn a multiscale method for the wave equation
into a multiscale method for the Helmholtz equation.

29/4/2025 Mayank Nautiyal, https://www.uu.se/kontakt-och-organisation/personal?query=N22-2267
10.15--11.30, Ångström Laboratory, room 100155
TDB 1/2-time seminar Note the time and place!

Title: Likelihood-free inference using Machine Learning

External reviewer: Ashkan Panahi, https://research.chalmers.se/person/ashkanp

Abstract: Simulation-based inference (SBI) is a powerful approach for parameter estimation in scientific domains where likelihood functions are intractable but forward simulations are feasible. This seminar presents two complementary generative modelling approaches developed to accelerate SBI workflows.

The first approach, leverages conditional variational autoencoders (c-VAEs) to approximate complex posteriors efficiently using variational inference. We explore two variants of conditional VAEs — one that uses a learned prior conditioned on the observed data, and another that relies on a fixed standard Gaussian prior. The trade-offs between these approaches are evaluated in terms of modelling accuracy and computational efficiency across standard benchmark simulation tasks.

To address the limitations of VAE-based approaches—such as restrictive Gaussian assumptions, challenging training dynamics, and difficulty capturing complex multimodal distributions—we introduce ConDiSim, a conditional diffusion model for SBI. ConDiSim employs denoising diffusion probabilistic models (DDPMs) to approximate the posterior through iterative refinements, conditioned on observed data. This framework, enables richer generative capacity and more accurate mode coverage compared to VAEs.

We conclude the presentation with an outlook and future work.

28/4/2025 Aleksandr Karakulev, https://www.uu.se/kontakt-och-organisation/personal?query=N22-1436
14:15–-16:00, Ångström Laboratory, room 80109
TDB 1/2-time seminar Note the time and place!

Title: Learning from Imperfect Data at Scale: A Bayesian Approach

External reviewer: Ashkan Panahi, https://research.chalmers.se/person/ashkanp

Abstract: As modern machine learning models increasingly rely on large and complex data sets, dealing with data contamination — such as measurement errors, labeling mistakes, or adversarial inputs — has become a significant challenge. Manual cleaning is often impractical, and even small amounts of corrupted data can degrade performance. In this seminar, we present an adaptive method for robust learning, grounded in a Bayesian latent variable framework. The approach is broadly applicable through flexible likelihood modeling, resilient to various types of contamination, and does not require manual tuning. We demonstrate its utility across standard statistical tasks — regression, classification, and dimensionality reduction — and explore extensions to online learning, overparameterized/deep models, and federated learning, where it enables robust aggregation in the presence of heterogeneous and partially corrupted data.

Reference. For those interested in a more detailed exploration of the method and its applications, please refer to the full paper: https://arxiv.org/abs/2312.00585

23/4/2025 Karl Larsson, https://www.umu.se/personal/karl-larsson

Title: Solving inverse and ill-posed problems using stabilized finite elements, data, and machine learning

Abstract: In this talk, we consider two closely related examples of ill-posed PDE problems, illustrating two different approaches for solving such problems:

Ill-posed problems using stabilized finite elements, including stability and error estimates
Ill-posed problems using machine learning techniques for operator learning and processing of data

In the first example, we address an inverse problem that involves reconstructing the solution to a 2:nd order PDE with incomplete boundary data given measurements of the solution on a subdomain of the computational domain. Here, we take a classical numerical analysis approach and solve the problem in a detailed fashion using stabilized finite elements. Using higher regularity spline spaces leads to simplified formulations and potentially minimal multiplier space. We show that our formulation is inf-sup stable, and given appropriate a priori assumptions, we establish optimal order convergence.

In our second example, we address an inverse problem that involves reconstructing the solution to a nonlinear PDE with unknown boundary conditions. Instead of directly observing the boundary data, we are provided with two types of information: (1) a large dataset of boundary observations corresponding to typical solutions (collective data) and (2) a bulk measurement associated with a specific realization of the solution. Our goal is to utilize the collective data to inform the reconstruction of the boundary conditions for the specific case. Here, our approach is to employ machine learning techniques.

We first compress the high-dimensional boundary data using proper orthogonal decomposition (POD), representing the boundary observations as a linear combination of orthogonal modes. This step reduces the complexity of the data while retaining essential features. Next, we employ an auto-encoder to capture any underlying nonlinear structure in the expansion coefficients. The auto-encoder provides a nonlinear parametrization of the boundary data in a low-dimensional latent space, effectively learning a reduced representation of the collective data.

With this reduced representation, we train a neural network that maps the latent variables (representing the boundary conditions) to the solution of the PDE. The neural network serves as an efficient surrogate model, bypassing the need to solve the complete PDE repeatedly during the inverse reconstruction process.

To solve the inverse problem, we optimize a data-fitting objective over the latent space, adjusting the latent variables to minimize the discrepancy between the bulk measurement and the predicted solution. This optimization estimates the boundary conditions corresponding to the given bulk measurement, thus reconstructing the solution.

2/4/2025 Carl Nettelblad, https://www.uu.se/kontakt-och-organisation/personal?query=N6-1341

Title: Single particle imaging phase retrieval – a sort of convex optimization problem

Abstract: In several imaging domains, diffraction patterns can be recorded. What one typically wants to understand is the structure of the original object – to reconstruct the object in “real space” from “diffraction space”. A step in doing this is to go from imaged intensities to a representation of the full complex-valued wavefunction with amplitudes and phases. A typical optical detector will only record intensities or photon counts, but not the phase. Phase retrieval algorithms have generally assumed these values to be exact, while any actual image has some noise. Furthermore, the phase retrieval problem is non-convex, meaning that an iterative optimization approach can converge towards a local optimum.

I will discuss a convex relaxation of this problem that I introduced to allow us to pre-process noisy intensities to a version that is supposed to fulfill the original problem exactly. While not making phase-retrieval itself non-convex, this approach makes convergence of the non-convex problem more reliable and accurate. A problem being mathematically convex does not guarantee efficient convergence in practice, though. To achieve this, we use accelerated first-order methods, using the open-source MATLAB toolbox TFOCS. There are also additional challenges introduced by aspects of the discretization of the Fourier transform and non-negativity constraints in general, especially when the optimum lies on that boundary in many dimensions.

Finally, as an early Easter egg, maybe there is almost a closed-form solution to the phase retrieval problem?!

26/3/2025 Kurt Otto, https://www.uu.se/kontakt-och-organisation/personal?query=XX3695

Title: The Italian algebraists and the French connection

Abstract: The topic is solving cubic equations with real coefficients.
The focus is on the derivation of solution formulas. The Italian algebraists
(Ferro, Tartaglia, Cardano, Ferrari, Bombelli) and the French mathematician
François Viète struggled with the problem during the century 1515--1615.

12/3/2025 Dave Zachariah, https://www.uu.se/en/contact-and-organisation/staff?query=N13-1398

Title: Data consistency and the role of uncertainty quantification in science

Abstract: In scientific inference problems, the underlying statistical modeling assumptions have a crucial impact on the end results. In this paper we discuss a general criterion to evaluate the consistency of a set of parametric statistical models with respect to observed data. This is achieved by automatically gauging the models’ ability to generate data that is similar to the observed data. It is applicable to a broad range of inference problems with varying data types, ranging from independent univariate data to high-dimensional time-series. We also raise the need for calibrated and intersubjective notions of uncertainty quantification in science.

5/3/2025 Eddie Wadbro, https://www.kau.se/en/researchers/eddie-wadbro

Title: Material distribution topology optimization for boundary effect dominated problems

Abstract: In the classical design optimization using the material distribution method (density-based topology optimization), a material indicator function represents the presence or absence of material within the domain. The first part of this talk introduces the fundamentals of material distribution topology optimization, focusing on mathematical morphology, non-linear filters, and length scale control.

To use the material distribution approach for boundary-effect-dominated problems, we need to identify the boundary of the design at each iteration. The two main methods to achieve this are (i) the traditional approach that uses a boundary strip indicator function defined on the elements of the computational mesh and (ii) a recent approach that uses a boundary indicator function defined on the mesh faces (edges in 2D and facets in 3D). This talk highlights the latter approaches and presents two model problems for which this approach is suitable and produces optimized designs with excellent performance.

4/3/2025 Divya Shridar and Zhenlu Sun ("TDB 1/4 seminar")

Speaker: Divya Shridar, https://www.uu.se/en/contact-and-organisation/staff?query=N23-2658

Title: Investigating pathogen surveillance through wastewater metagenomics

Abstract: Antibiotic resistance (AMR) is one of the greatest threats to public health globally. To guide treatment decision-making, it is imperative that there is ample information on the specific antimicrobial resistant pathogens that are prevalent within the community. Given the laborious and expensive nature of traditional surveillance, this project aims to develop novel techniques for assessing resistance severity from wastewater samples and metagenomic sequencing. Specifically, the infectious agent of Escherichia Coli (E. Coli) is of interest, given its pervasiveness globally and the implications of its pathogenic antibiotic-resistant variants spanning from gastrointestinal infections to sepsis and pneumonia, to name a few. As the most common pathogen found in the human body, much research has been conducted on E. Coli over the years. However, the surveillance of antibiotic resistant E. Coli through wastewater has been limited.

Wastewater epidemiology quantifies pathogens in communal wastewater samples to assess their prevalence in the population and predict imminent outbreaks. It has been successful for several viruses, but targeting bacterial pathogens has proved more difficult. To predict epidemiological outcomes from bacterial quantities in wastewater, molecular markers that can separate commensal and pathogenic strains are required for the data to be clinically informative. This requires an interdisciplinary approach with classic microbiological cultivation, molecular biological processing, next-generation sequencing, bioinformatic analysis, and computational data modelling.

At this quarter-time seminar, we will discuss the investigation thus far as to if wastewater metagenomics can and should be used for surveillance of antimicrobial resistant E. coli.

Speaker: Zhenlu Sun, https://www.uu.se/en/contact-and-organisation/staff?query=N22-2419

Title: Graph-based Machine Learning for Intrusion Detection

Abstract: Intrusion detection systems (IDS) are widely used to identify anomalies in computer networks and raise alarms on intrusive behaviors. ML-based IDSs generally take network traces or host logs as input to extract patterns from individual samples, whereas the inter-dependencies of network are often not captured and learned, which may result in large amounts of uncertain predictions, false positives, and false negatives. Moreover, the behaviors of normal users and attackers changes dynamically in the computer systems and networks, how to effectively detect anomalous behaviors in real-time is another challenge that need to be further studied.

Graph machine learning, especially Graph Neural Networks (GNNs), have been gaining more attentions due to the ability to effectively learn the hidden representation of node and topological information of graph-structured data. In the seminar, we will first give an introduction to intrusion detection and GNN. Next, we will present two projects in which graph-based approaches are studied to address the challenges in intrusion detection. Lastly, we will discuss the future works.

12/2/2025 Jonas Nycander, https://www.su.se/profiles/nycan-1.182533

Title: Modeling internal waves in the global ocean

Abstract: Vertical mixing by breaking internal waves is crucial for the ocean
circulation. The mixing transports heat to the abyss, and without it
the deep waters would be largely stagnant. The internal waves are too
short to be resolved in ocean general circulation models, and the
mixing they cause must therefore be parameterized, which requires
dedicated computations. Internal waves are excited by tidal currents
over rough bottom topography. This process can be computed numerically,
by using wave theory and observationally based data for the tidal
currents, the density stratification and the bottom topography. A
complicating factor is that the excitation is strongest where the
topography is very steep, so that nonlinear effects are essential.
I will describe how these computations are done in various parts of
the ocean, and how the results are implemented in parameteriations
in general ocean circulation models.

5/2/2025 Anders Szepessy, https://www.kth.se/profile/szepessy

Title: Convergence for adaptive resampling of random features

Abstract: The machine learning random Fourier feature method for data in high dimension is computationally and theoretically attractive since the optimization is based on a convex standard least squares problem and independent sampling of Fourier frequencies. The challenge is to sample the Fourier frequencies well. I will prove convergence of a data adaptive method based on resampling that samples the frequencies asymptotically optimally as the number of nodes and amount of data tend to infinity. Numerical results based on resampling and random walk steps together with approximations of the least squares problem by conjugate gradient iterations confirm the analysis.

29/1/2025 Behnaz Pirzamanbein, https://portal.research.lu.se/sv/persons/behnaz-pirzamanbein

Title: POLLENOMICS: Decoding the Farming History of Europe Using Advanced Statistics to Combine Ancient DNA with Paleo-Pollen Data

Abstract: In this seminar, I will talk about one of my research projects which is called Pollenomics. The study uniquely combines advanced continental-scale data from two distinct sources: pollen-based land cover (PbLC) and ancient DNA (aDNA), developing a novel statistical model for spatiotemporal reconstructions of past land use across Europe. The aDNA data serves as a proxy for human habitation, differentiating anthropogenic and natural land cover from PbLC reconstruction. This will be accomplished using a Bayesian hierarchical model that combines compositional data, Gaussian Markov random fields and point process models.

This groundbreaking approach gives insights into the environmental impacts of Holocene human migration and subsistence practices, and marks a major advancement in understanding human-environmental dynamics over millennia.

17/1/2025 (TDB 1/2-time seminar)

Gesina Menz, https://www.uu.se/kontakt-och-organisation/personal?query=N21-2101

Title: Investigating Cellular Signalling During Embryonal Development

Abstract: The topic of this talk is the investigation of cellular signalling during embryo development using the Hes1-Notch signalling pathway. Specifically, the talk will explore the modelling of this pathway using both ordinary differential equation (ODE) and reaction-diffusion master equation (RDME) models to examine the differences between deterministic and stochastic modelling. The focus will be on highlighting the trade-offs in these models: capturing both oscillatory in time behaviour and stationary spatial patterning, while balancing mathematical tractability with realistic, individual cell models.