52 citations · 270 across the 19 of their papers we have counts for
21 papers
Learning PDE Dynamics between Submanifolds Using Green's Observation Operators
Jan Tauberschmidt, Jephte Abijuru, Samuel Okon +5
Many physical systems are driven and observed only on lower-dimensional submanifolds of a larger spatial domain, while their dynamics are governed by the ambient medium occupying t…
How to beat a Bayesian adversary
Zihan Ding, Kexin Jin, Jonas Latz +1
Deep neural networks and other modern machine learning models are often susceptible to adversarial attacks. Indeed, an adversary may often be able to change a model's prediction th…
Subsampling Error in Stochastic Gradient Langevin Diffusions
Kexin Jin, Chenguang Liu, Jonas Latz
The Stochastic Gradient Langevin Dynamics (SGLD) are popularly used to approximate Bayesian posterior distributions in statistical learning procedures with large-scale data. As opp…
Can Physics-Informed Neural Networks beat the Finite Element Method?
Tamara G. Grossmann, Urszula Julia Komorowska, Jonas Latz +1
Partial differential equations play a fundamental role in the mathematical modelling of many processes and systems in physical, biological and other sciences. To simulate such proc…
Subsampling in ensemble Kalman inversion
Matei Hanu, Jonas Latz, Claudia Schillings
We consider the Ensemble Kalman Inversion which has been recently introduced as an efficient, gradient-free optimisation method to estimate unknown parameters in an inverse setting…
Losing momentum in continuous-time stochastic optimisation
Kexin Jin, Jonas Latz, Chenguang Liu +1
The training of modern machine learning models often consists in solving high-dimensional non-convex optimisation problems that are subject to large-scale data. In this context, mo…
Joint reconstruction-segmentation on graphs
Jeremy Budd, Yves van Gennip, Jonas Latz +2
Practical image segmentation tasks concern images which must be reconstructed from noisy, distorted, and/or incomplete observations. A recent approach for solving such tasks is to…
Gaussian random fields on non-separable Banach spaces
Yury Korolev, Jonas Latz, Carola-Bibiane Schönlieb
We study Gaussian random fields on certain Banach spaces and investigate conditions for their existence. Our results apply inter alia to spaces of Radon measures and Hölder functio…
Gradient flows and randomised thresholding: sparse inversion and classification
Jonas Latz
Sparse inversion and classification problems are ubiquitous in modern data science and imaging. They are often formulated as non-smooth minimisation problems. In sparse inversion,…
A Continuous-time Stochastic Gradient Descent Method for Continuous Data
Kexin Jin, Jonas Latz, Chenguang Liu +1
Optimization problems with continuous data appear in, e.g., robust machine learning, functional data analysis, and variational inference. Here, the target function is given as an i…
Classification and image processing with a semi-discrete scheme for fidelity forced Allen--Cahn on graphs
Jeremy Budd, Yves van Gennip, Jonas Latz
This paper introduces a semi-discrete implicit Euler (SDIE) scheme for the Allen-Cahn equation (ACE) with fidelity forcing on graphs. Bertozzi and Flenner (2012) pioneered the use…
Error analysis for probabilities of rare events with approximate models
Fabian Wagner, Jonas Latz, Iason Papaioannou +1
The estimation of the probability of rare events is an important task in reliability and risk assessment. We consider failure events that are expressed in terms of a limit-state fu…
Analysis of Stochastic Gradient Descent in Continuous Time
Jonas Latz
Stochastic gradient descent is an optimisation method that combines classical gradient descent with random subsampling within the target functional. In this work, we introduce the…
Generalized Parallel Tempering on Bayesian Inverse Problems
Jonas Latz, Juan P. Madrigal-Cianci, Fabio Nobile +1
In the current work we present two generalizations of the Parallel Tempering algorithm, inspired by the so-called continuous-time Infinite Swapping algorithm. Such a method, found…
Multilevel Sequential Importance Sampling for Rare Event Estimation
Fabian Wagner, Jonas Latz, Iason Papaioannou +1
The estimation of the probability of rare events is an important task in reliability and risk assessment. We consider failure events that are expressed in terms of a limit state fu…
Multilevel adaptive sparse Leja approximations for Bayesian inverse problems
Ionut-Gabriel Farcas, Jonas Latz, Elisabeth Ullmann +2
Deterministic interpolation and quadrature methods are often unsuitable to address Bayesian inverse problems depending on computationally expensive forward mathematical models. Whi…
On the well-posedness of Bayesian inverse problems
Jonas Latz
The subject of this article is the introduction of a new concept of well-posedness of Bayesian inverse problems. The conventional concept of (Lipschitz, Hellinger) well-posedness i…
A practical example for the non-linear Bayesian filtering of model parameters
Matthieu Bulté, Jonas Latz, Elisabeth Ullmann
In this tutorial we consider the non-linear Bayesian filtering of static parameters in a time-dependent model. We outline the theoretical background and discuss appropriate solvers…
Bayesian parameter identification in Cahn-Hilliard models for biological growth
Christian Kahle, Kei Fong Lam, Jonas Latz +1
We consider the inverse problem of parameter estimation in a diffuse interface model for tumour growth. The model consists of a fourth-order Cahn-Hilliard system and contains three…
Fast sampling of parameterised Gaussian random fields
Jonas Latz, Marvin Eisenberger, Elisabeth Ullmann
Gaussian random fields are popular models for spatially varying uncertainties, arising for instance in geotechnical engineering, hydrology or image processing. A Gaussian random fi…
Multilevel Sequential Monte Carlo for Bayesian Inverse Problems
Jonas Latz, Iason Papaioannou, Elisabeth Ullmann
The identification of parameters in mathematical models using noisy observations is a common task in uncertainty quantification. We employ the framework of Bayesian inversion: we c…