Langtangen Seminar

Figure represents cutting scientific computing as done by Numerical Analysis and Scientific Computing members at Simula. — Figure: Finite element simulation of the neuronal, astrocytic and extracellular ionic landscape; Benedusi, Ellingsrud, Herlyng and Rognes (2024). (Scientific paper: https://epubs.siam.org/doi/10.1137/24M1644717)

Named in honour of Professor Hans Petter Langtangen, the Langtangen Seminar on Scientific Computing series is part of Simula's continued efforts to be at the forefront of scientific computing. Through this seminar series, we aim to showcase internationally renowned researchers who will not only present their latest, cutting-edge work, but also share their personal insights on the future of the field.

The seminars will be online and viewable via zoom on Tuesday at 15:00 (Central European Time). Some presentations will become available on YouTube on this channel.

Schedule

April 29: Carola Schönlieb, University of Cambridge
May 6: Siddhartha Mishra, Eidgenössische Technische Hochschule Zürich
May 13: Aslak Tveito, Simula Research Laboratory

Upcoming Seminar

When: Tuesday 29 April 2025 at 15:00
Where: Join online via Zoom
Who: Carola Schönlieb, University of Cambridge

Mathematical imaging and structure-preserving deep learning

Abstract:
Images are a rich source of beautiful mathematical formalism and analysis.

Associated mathematical problems arise in functional and non-smooth analysis, the theory and numerical analysis of nonlinear partial differential equations, inverse problems, harmonic, stochastic, and statistical analysis, and optimization, just to name a few. Applications of mathematical imaging are profound and arise in biomedicine, material sciences, astronomy, digital humanities, as well as many technological developments such as autonomous driving, facial screening and many more.

In this talk I will discuss my perspective onto mathematical imaging, share my fascination and vision for the subject. I will then zoom into structure-preserving deep learning and its relevance for solving inverse imaging problems.

Join the Zoom webinar.

More information

This seminar is organised by Marie E. Rognes & Thomas M. Surowiec.

Join the Zoom webinar.

Past seminars in this series

Enforcing conservation laws and dissipation inequalities via auxiliary variables
Patrick E. Farrell, University of Oxford

Abstract:
We propose a general strategy for enforcing multiple conservation laws and dissipation inequalities in the numerical solution of initial value problems. The key idea is to represent the conservation law or dissipation inequality by means of its associated test function; we introduce auxiliary variables representing the projection onto a discrete test set, and modify the equation to use these new variables. We demonstrate the ideas by generalizing to arbitrary order the energy-dissipating and helicity-tracking scheme of Rebholz for the incompressible Navier–Stokes equations, and by devising a novel time discretization of the compressible Navier–Stokes equations that for the first time conserves mass, momentum, and energy, while probably dissipating entropy.

Modeling neurodegenerative disease
Paola F. Antonietti from Politecnico di Milano

Abstract:
Neurodegenerative diseases (NDs) are complex disorders that mainly affect neurons in the brain and nervous system, resulting in progressive functional decline and structural deterioration. A common pathological hallmark among various NDs is the accumulation of disease-specific misfolded and aggregated proteins, such as amyloid-beta and tau in Alzheimer's disease and α-synuclein in Parkinson's disease. This talk centers on the mathematical and numerical modeling of the fundamental mechanisms that drive and sustain neurodegeneration.

First, we discuss the dynamics of misfolded protein modeling using increasingly complex mathematical models. We develop and analyze high-order discontinuous Galerkin methods on polyhedral grids (PolyDG) to simulate these processes accurately. In the second part of the talk, we present mathematical and computational models of waste clearance mechanisms in the brain, which are critical to the onset and progression of neurodegenerative diseases (NDs). Specifically, we investigate glymphatic and cerebrospinal fluid dynamics and their roles in neurodegenerative processes. Furthermore, we discuss modeling seizure dynamics, focusing on their interplay with pathological protein accumulation. We present numerical simulations based on patient-specific brain geometries reconstructed from clinical imaging data, providing insights into the complex interactions involved in neurodegeneration.

Control and Machine Learning
Enrique Zuazua, Friedrich-Alexander-Universität Erlangen-Nürnberg

Abstract:
Systems control, or cybernetics—a term first coined by Ampère and later popularized by Norbert Wiener—refers to the science of control and communication in animals and machines. The pursuit of this field dates back to antiquity, driven by the desire to create machines that autonomously perform human tasks, thereby enhancing freedom and efficiency.

The objectives of control systems closely parallel those of modern Artificial Intelligence (AI), illustrating both the profound unity within Mathematics and its extraordinary capacity to describe natural phenomena and drive technological innovation.

In this lecture, we will explore the connections between these mathematical disciplines and their broader implications. We will also discuss our recent work addressing two fundamental questions: Why does Machine Learning perform so effectively? And how can data-driven insights be integrated into the classical applied mathematics framework, particularly in the context of Partial Differential Equations (PDE) and numerical methods? This effort is leading us to a new emerging field of PDE+D(ata) in parallel to the development of new Digital Twins technologies.