Related papers: Computer algebra derives correct initial condition…
I describe a method for computer algebra that helps with laborious calculations typically encountered in theoretical microhydrodynamics. The program mimics how humans calculate by matching patterns and making replacements according to the…
We present a convergence proof of the projective integration method for a class of deterministic multi-dimensional multi-scale systems which are amenable to centre manifold theory. The error is shown to contain contributions associated with…
In many areas of engineering, nonlinear numerical analysis is playing an increasingly important role in supporting the design and monitoring of structures. Whilst increasing computer resources have made such formerly prohibitive analyses…
This paper presents a methodology that enables projection-based model reduction for black-box high-fidelity models such as commercial CFD codes. The methodology specifically addresses the situation where the high-fidelity model may be a…
For many problems, some of which are reviewed in the paper, popular algorithms like Douglas--Rachford (DR), ADMM, and FISTA produce approximating sequences that show signs of spiraling toward the solution. We present a meta-algorithm that…
This paper proposes an algorithm for solving structured optimization problems, which covers both the backward-backward and the Douglas-Rachford algorithms as special cases, and analyzes its convergence. The set of fixed points of the…
Slow-fast dynamical systems have two time scales and an explicit parameter representing the ratio of these time scales. Locally invariant slow manifolds along which motion occurs on the slow time scale are a prominent feature of slow-fast…
This work introduces a parametric simulation-free reduced order model for incompressible flows undergoing a Hopf bifurcation, leveraging the parametrisation method for invariant manifolds. Unlike data-driven approaches, this method operates…
Conditional diffusion models serve as the foundation of modern image synthesis and find extensive application in fields like computational biology and reinforcement learning. In these applications, conditional diffusion models incorporate…
This paper deals with the development of a Reduced-Order Model (ROM) to investigate haemodynamics in cardiovascular applications. It employs the use of Proper Orthogonal Decomposition (POD) for the computation of the basis functions and the…
We propose a new family of neural networks to predict the behaviors of physical systems by learning their underpinning constraints. A neural projection operator lies at the heart of our approach, composed of a lightweight network with an…
This chapter of the forthcoming Handbook of Graphical Models contains an overview of basic theorems and techniques from algebraic geometry and how they can be applied to the study of conditional independence and graphical models. It also…
In the sequential decision making setting, an agent aims to achieve systematic generalization over a large, possibly infinite, set of environments. Such environments are modeled as discrete Markov decision processes with both states and…
Conventional approaches to enhancing movement coordination, such as providing instructions and visual feedback, are often inadequate in complex motor tasks with multiple degrees of freedom (DoFs). To effectively address coordination…
In this work, inspired in the symbolic dynamic of chaotic systems and using machine learning techniques, a control strategy for complex systems is designed. Unlike the usual methodologies based on modeling, where the control signal is…
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…
In this paper we propose a model predictive control scheme for constrained fractional-order discrete-time systems. We prove that all constraints are satisfied at all time instants and we prescribe conditions for the origin to be an…
Valuation algebras abstract a large number of formalisms for automated reasoning and enable the definition of generic inference procedures. Many of these formalisms provide some notion of solution. Typical examples are satisfying…
This work introduces a new approach to reduce the computational cost of solving partial differential equations (PDEs) with convection-dominated solutions: model reduction with implicit feature tracking. Traditional model reduction…
Dimension reduction is a common strategy to study non-linear dynamical systems composed by a large number of variables. The goal is to find a smaller version of the system whose time evolution is easier to predict while preserving some of…