Related papers: Formalising the Continuous/Discrete Modeling Step
As the main contribution, this document provides a consistent discretization of a class of fixed-time stable systems, namely predefined-time stable systems. In the unperturbed case, the proposed approach allows obtaining not only a…
The majority of modern systems exhibit sophisticated concurrent behaviour, where several system components modify and observe the system state with fine-grained atomicity. Many systems (e.g., multi-core processors, real-time controllers)…
Model transformations play a fundamental role in model-driven software development. They can be used to solve or support central tasks, such as creating models, handling model co-evolution, and model merging. In the past, various…
The remarkable success of pretrain-then-finetune paradigm has led to a proliferation of available pre-trained models for vision tasks. This surge presents a significant challenge in efficiently choosing the most suitable pre-trained models…
Fine-tuning pretrained models has become a standard approach to adapting pretrained knowledge to improve the accuracy on new sparse, imbalance datasets. However, issues arise when optimization falls into a collapsed state, where the model…
Differential equations are frequently used in engineering domains, such as modeling and control of industrial systems, where safety and performance guarantees are of paramount importance. Traditional physics-based modeling approaches…
We are currently designing an object oriented model which describes static and dynamical knowledge in diff{\'e}rent domains. It provides a twin conceptual level. The internal level proposes: the object structure composed of sub-objects…
We study a catching-up algorithm for a class of differential inclusions driven by maximal monotone operators with continuous perturbations. Using a decomposition of the monotone operator into the closed convex hull of its single-valued part…
In current practice a formal analysis of hybrid system models is assertion-based. The work presented here is based on features that look beyond functional correctness toward a quantitative evaluation of behavioral attributes. A feature…
We introduce the technique of adaptive discretization to design an efficient model-based episodic reinforcement learning algorithm in large (potentially continuous) state-action spaces. Our algorithm is based on optimistic one-step value…
We introduce and analyze several aspects of a new model for cell differentiation. It assumes that differentiation of progenitor cells is a continuous process. From the mathematical point of view, it is based on partial differential…
Usually, given a continuous-time nonlinear model, a closed form solution for an exact discretization cannot be found explicitly, originating the need of approximating discrete-time models. This note studies the preservation of the Lipschitz…
Diffusion models have demonstrated remarkable performance in generating high-dimensional samples across domains such as vision, language, and the sciences. Although continuous-state diffusion models have been extensively studied both…
Neural Ordinary Differential Equations (ODEs) represent a significant advancement at the intersection of machine learning and dynamical systems, offering a continuous-time analog to discrete neural networks. Despite their promise, deploying…
A method of representation of a solution as segments of the series in powers of the step of the independent variable is expanded for solving complex systems of ordinary differential equations (ODE): the Lorenz system and other systems. A…
The evolution of local defects such as dislocations and cracks often determines the performance of engineering materials. For a proper description and understanding of these phenomena, one needs to descend to a very small scale, at which…
Mathematical models are used extensively for diverse tasks including analysis, optimization, and decision making. Frequently, those models are principled but imperfect representations of reality. This is either due to incomplete physical…
We study the dynamical evolution of the deposition interface using both discrete and continuous models for which shadowing effects are important. We explain why continuous and discrete models implying both only shadowing deposition do not…
The goal of this paper is to propose two nonlinear variational models for obtaining a refined motion estimation from an image sequence. Both the proposed models can be considered as a part of a generalized framework for an accurate…
Most of the engineering and physical systems are generally characterized by differential and difference equations based on their continuous-time and discrete-time dynamics, respectively. Moreover, these dynamical models are analyzed using…