23 citations · 106 across the 22 of their papers we have counts for
24 papers
SABLE: Scalable Affine Bayesian Latent-space Exploration
Erik Bodin, Lisa Maria Kreusser, Donney Fan +3
Complex objects such as engineering designs and proteins are often difficult to optimise because their design spaces exhibit high-dimensional structure and objective evaluations ar…
Learning efficient and provably convergent splitting methods
L. M. Kreusser, H. E. Lockyer, E. H. Müller +1
Splitting methods are widely used for solving initial value problems (IVPs) due to their ability to simplify complicated evolutions into more manageable subproblems which can be so…
Parallel-in-Time Solutions with Random Projection Neural Networks
Marta M. Betcke, Lisa Maria Kreusser, Davide Murari
This paper considers one of the fundamental parallel-in-time methods for the solution of ordinary differential equations, Parareal, and extends it by adopting a neural network as a…
Equidistribution-based training of Free Knot Splines and ReLU Neural Networks
Simone Appella, Simon Arridge, Chris Budd +2
We consider the problem of univariate nonlinear function approximation using shallow neural networks (NN) with a rectified linear unit (ReLU) activation function. We show that the…
A general formulation of reweighted least squares fitting
Carlotta Giannelli, Sofia Imperatore, Lisa Maria Kreusser +3
We present a generalized formulation for reweighted least squares approximations. The goal of this article is twofold: firstly, to prove that the solution of such problem can be ex…
Closing the ODE-SDE gap in score-based diffusion models through the Fokker-Planck equation
Teo Deveney, Jan Stanczuk, Lisa Maria Kreusser +2
Score-based diffusion models have emerged as one of the most promising frameworks for deep generative modelling, due to their state-of-the art performance in many generation tasks…
Generalised Gillespie Algorithms for Simulations in a Rule-Based Epidemiological Model Framework
David Alonso, Steffen Bauer, Markus Kirkilionis +2
Rule-based models have been successfully used to represent different aspects of the COVID-19 pandemic, including age, testing, hospitalisation, lockdowns, immunity, infectivity, be…
-Convergence of an Ambrosio-Tortorelli approximation scheme for image segmentation
Irene Fonseca, Lisa Maria Kreusser, Carola-Bibiane Schönlieb +1
Given an image , the aim of minimising the Mumford-Shah functional is to find a decomposition of the image domain into sub-domains and a piecewise smooth approximation of…
Models for information propagation on graphs
Oliver R. A. Dunbar, Charles M. Elliott, Lisa Maria Kreusser
We propose and unify classes of different models for information propagation over graphs. In a first class, propagation is modelled as a wave which emanates from a set of \emph{kno…
A Rule-Based Epidemiological Modelling Framework
David Alonso, Steffen Bauer, Markus Kirkilionis +2
Motivated by chemical reaction rules, we introduce a rule-based epidemiological framework for the systematic mathematical modelling of future pandemics. Here we stress that we do n…
Wasserstein GANs Work Because They Fail (to Approximate the Wasserstein Distance)
Jan Stanczuk, Christian Etmann, Lisa Maria Kreusser +1
Wasserstein GANs are based on the idea of minimising the Wasserstein distance between a real and a generated distribution. We provide an in-depth mathematical analysis of differenc…
Autophosphorylation and the dynamics of the activation of Lck
Lisa Maria Kreusser, Alan D. Rendall
Lck (lymphocyte-specific protein tyrosine kinase) is an enzyme which plays a number of important roles in the function of immune cells. It belongs to the Src family of kinases whic…
Mean-field optimal control for biological pattern formation
Martin Burger, Lisa Maria Kreusser, Claudia Totzeck
We propose a mean-field optimal control problem for the parameter identification of a given pattern. The cost functional is based on the Wasserstein distance between the probabilit…
On anisotropic diffusion equations for label propagation
Lisa Maria Kreusser, Marie-Therese Wolfram
In many problems in data classification one wishes to assign labels to points in a point cloud with a certain number of them being already correctly labeled. In this paper, we prop…
Equilibria of an anisotropic nonlocal interaction equation: Analysis and numerics
José A. Carrillo, Bertram Düring, Lisa Maria Kreusser +1
In this paper, we study the equilibria of an anisotropic, nonlocal aggregation equation with nonlinear diffusion which does not possess a gradient flow structure. Here, the anisotr…
Detection of high codimensional bifurcations in variational PDEs
Lisa Maria Kreusser, Robert I McLachlan, Christian Offen
We derive bifurcation test equations for A-series singularities of nonlinear functionals and, based on these equations, we propose a numerical method for detecting high codimension…
A Deterministic Gradient-Based Approach to Avoid Saddle Points
Lisa Maria Kreusser, Stanley J. Osher, Bao Wang
Loss functions with a large number of saddle points are one of the major obstacles for training modern machine learning models efficiently. First-order methods such as gradient des…
Auxin transport model for leaf venation
Jan Haskovec, Henrik Jönsson, Lisa Maria Kreusser +1
The plant hormone auxin controls many aspects of the development of plants. One striking dynamical feature is the self-organisation of leaf venation patterns which is driven by hig…
Rigorous Continuum Limit for the Discrete Network Formation Problem
Jan Haskovec, Lisa Maria Kreusser, Peter Markowich
Motivated by recent physics papers describing the formation of biological transport networks we study a discrete model proposed by Hu and Cai consisting of an energy consumption fu…
Stability analysis of line patterns of an anisotropic interaction model
José A. Carrillo, Bertram Düring, Lisa Maria Kreusser +1
Motivated by the formation of fingerprint patterns we consider a class of interacting particle models with anisotropic, repulsive-attractive interaction forces whose orientations d…
ODE and PDE based modeling of biological transportation networks
Jan Haskovec, Lisa Maria Kreusser, Peter Markowich
We study the global existence of solutions of a discrete (ODE based) model on a graph describing the formation of biological transportation networks, introduced by Hu and Cai. We p…
An Anisotropic Interaction Model for Simulating Fingerprints
Bertram Düring, Carsten Gottschlich, Stephan Huckemann +2
Evidence suggests that both the interaction of so-called Merkel cells and the epidermal stress distribution play an important role in the formation of fingerprint patterns during p…
Pattern formation of a nonlocal, anisotropic interaction model
Martin Burger, Bertram Düring, Lisa Maria Kreusser +2
We consider a class of interacting particle models with anisotropic, repulsive-attractive interaction forces whose orientations depend on an underlying tensor field. An example of…
Trend to equilibrium for a delay Vlasov-Fokker-Planck equation and explicit decay estimates
Axel Klar, Lisa Kreusser, Oliver Tse
In this paper, a delay Vlasov-Fokker-Planck equation associated to a stochastic interacting particle system with delay is investigated analytically. Under certain restrictions on t…