Related papers: To Infinity and Beyond: Some ODE and PDE Case Stud…
Ordinary differential equations (ODEs) are widely used to model biological, (bio-)chemical and technical processes. The parameters of these ODEs are often estimated from experimental data using ODE-constrained optimisation. This article…
The study of existence and uniqueness of solutions became important due to the lack of general formula for solving nonlinear ordinary differential equations (ODEs). Compact form of existence and uniqueness theory appeared nearly 200 years…
This work develops a class of probabilistic algorithms for the numerical solution of nonlinear, time-dependent partial differential equations (PDEs). Current state-of-the-art PDE solvers treat the space- and time-dimensions separately,…
Computing modular coincidences can show whether a given substitution system, which is supported on a point lattice in R^d, consists of model sets or not. We prove the computatibility of this problem and determine an upper bound for the…
This work proposes a discretization of the acoustic wave equation with possibly oscillatory coefficients based on a superposition of discrete solutions to spatially localized subproblems computed with an implicit time discretization. Based…
We study the approximation of general multiobjective optimization problems with the help of scalarizations. Existing results state that multiobjective minimization problems can be approximated well by norm-based scalarizations. However, for…
Engineering long-running computing systems that achieve their goals under ever-changing conditions pose significant challenges. Self-adaptation has shown to be a viable approach to dealing with changing conditions. Yet, the capabilities of…
Given the complexity of modern software systems, it is of great importance that such systems be able to autonomously modify themselves, i.e., self-adapt, with minimal human supervision. It is critical that this adaptation both results in…
In General Relativity a space-time $M$ is regarded singular if there is an obstacle that prevents an incomplete curve in $M$ to be continued. Usually, such a space-time is completed to form $\bar{M} = M \cup \partial M$ where $\partial M$…
In edge computing deployments, where devices may be in close proximity to each other, these devices may offload similar computational tasks (i.e., tasks with similar input data for the same edge computing service or for services of the same…
We show a general method allowing the solution calculation, in the form of a power series, for a very large class of nonlinear Ordinary Differential Equations (ODEs), namely the real analytic $\sigma\pi$-ODEs (and, more in general, the real…
Efficiently and accurately simulating partial differential equations (PDEs) in and around arbitrarily defined geometries, especially with high levels of adaptivity, has significant implications for different application domains. A key…
Probabilistic forecasting of irregularly sampled time series is crucial in domains such as healthcare and finance, yet it remains a formidable challenge. Existing Neural Controlled Differential Equation (Neural CDE) approaches, while…
Neural networks have the ability to serve as universal function approximators, but they are not interpretable and don't generalize well outside of their training region. Both of these issues are problematic when trying to apply standard…
In this vision paper, we explore the challenges and opportunities of a form of computation that employs an empirical (rather than a formal) approach, where the solution of a computational problem is returned as empirically most likely…
We address the following question of partial desingularization preserving normal crossings. Given an algebraic (or analytic) variety X in characteristic zero, can we find a finite sequence of blowings-up preserving the normal-crossings…
A large number of engineering, science and computational problems have yet to be solved in a computationally efficient way. One of the emerging challenges is how evolving technologies grow towards autonomy and intelligent decision making.…
We develop a general method for extending Markov processes to a larger state space such that the added points form a polar set. The so obtained extension is an improvement on the standard trivial extension in which case the process is made…
Partial differential equation (PDE)-constrained optimization, where an optimization problem is subject to PDE constraints, arises in various applications such as design, control, and inference. Solving such problems is computationally…
We present a framework for analyzing the exact dynamics of a class of online learning algorithms in the high-dimensional scaling limit. Our results are applied to two concrete examples: online regularized linear regression and principal…