Upcoming events

05 October 2023 16:00 till 17:00

[PDE & Applications seminar] Kerstin Lux-Gottschalk: The effect of parameter uncertainty on climate tipping points

Several subsystems of the Earth might undergo critical transitions under sustained anthropogenic forcing, i.e. these systems are at risk of passing a so-called tipping point (TP). That induces a drastic sudden change in the system’s phase portrait that is often irreversible. We approach these tipping phenomena through the lense of nonlinear dynamical systems theory. In particular, we use tools from bifurcation theory, which provides the mathematical framework for the creation and loss of equilibria as well as changes in their stability properties under variation of a deterministic control parameter. In this talk, I will address the question how uncertainty in model parameters affects the tipping behavior of the dynamical system in terms of the location of TPs and how they are approached. I will present a workflow for climate tipping points from a Bayesian inference on the uncertain model input parameter to the forward propagation of the obtained input probability distribution through the nonlinear dynamics turning the bifurcation curve into a random object [1]. I will show numerical results on a conceptual model of the Atlantic Meridional Overturning Circulation, which is one of the identified tipping elements. This talk covers joint work with Peter Ashwin (University of Exeter, UK), Richard Wood (Met Office, UK), and Christian K ̈uhn (Technical University of Munich, Germany).

25 January 2024 16:00 till 17:00

[PDE & Applications seminar] Daniele Avitabile: Uncertainty Quantification for Neurobiological Networks

This talk presents a framework for forward uncertainty quantification problems in spatially-extended neurobiological networks. We will consider networks in which the cortex is represented as a continuum domain, and local neuronal activity evolves according to an integro-differential equation, collecting inputs nonlocally, from the whole cortex. These models are sometimes referred to as neural field equations.

Large-scale brain simulations of such models are currently performed heuristically, and the numerical analysis of these problems is largely unexplored. In the first part of the talk I will summarise recent developments for the rigorous numerical analysis of projection schemes [1] for deterministic neural fields, which sets the foundation for developing Finite-Element and Spectral schemes for large-scale problems.

The second part of the talk will discuss the case of networks in the presence of uncertainties modelled with random data, in particular: random synaptic connections, external stimuli, neuronal firing rates, and initial conditions. Such problems give rise to random solutions, whose mean, variance, or other quantities of interest have to be estimated using numerical simulations. This so-called forward uncertainty quantification problem is challenging because it couples spatially nonlocal, nonlinear problems to large-dimensional random data.

I will present a family of schemes that couple a spatial projector for the spatial discretisation, to stochastic collocation for the random data. We will analyse the time- dependent problem with random data and the schemes from a functional analytic viewpoint, and show that the proposed methods can achieve spectral accuracy, provided the random data is sufficiently regular. We will showcase the schemes using several examples.

Acknowledgements This talk presents joint work with Francesca Cavallini (VU Amsterdam), Svetlana Dubinkina (VU Amsterdam), and Gabriel Lord (Radboud University).

[1] Avitabile D. (2023). Projection Methods for Neural Field Equations. https://www.danieleavitabile.com/projection-methods-for-neural-field-equations/