Publications related to Delay differential equation

Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

Alfio Quarteroni, Francesco Regazzoni, Stefano Pagani

Predicting the evolution of systems with spatio-temporal dynamics in response to external stimuli is essential for scientific progress. Traditional equations-based approaches leverage first principles through the numerical approximation of differential equ ...

Nature Portfolio2024

From low-rank retractions to dynamical low-rank approximation and back

Daniel Kressner, Axel Elie Joseph Séguin, Gianluca Ceruti

In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...

Springer2024

Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains

Rafael Vazquez Hernandez

Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline models is not well s ...

WORLD SCIENTIFIC PUBL CO PTE LTD2023

Analysis of a Class of Multilevel Markov Chain Monte Carlo Algorithms Based on Independent Metropolis–Hastings

Fabio Nobile, Juan Pablo Madrigal Cianci

In this work, we present, analyze, and implement a class of multilevel Markov chain Monte Carlo(ML-MCMC) algorithms based on independent Metropolis--Hastings proposals for Bayesian inverse problems. In this context, the likelihood function involves solving ...

2023

High order geometric methods with splines: fast solution with explicit time-stepping for Maxwell equations

Bernard Kapidani, Rafael Vazquez Hernandez

We introduce a high-order spline geometric approach for the initial boundary value problem for Maxwell's equations. The method is geometric in the sense that it discretizes in structure preserving fashion the two de Rham sequences of differential forms inv ...

2023

Analysis-aware defeaturing of complex geometries with Neumann features

Pablo Antolin Sanchez, Ondine Gabrielle Chanon

Local modifications of a computational domain are often performed in order to simplify the meshing process and to reduce computational costs and memory requirements. However, removing geometrical features of a domain often introduces a non-negligible error ...

Hoboken2023

A Shape Derivative Approach to Domain Simplification

Annalisa Buffa, Jochen Peter Hinz, Ondine Gabrielle Chanon, Alessandra Arrigoni

The objective of this study is to address the difficulty of simplifying the geometric model in which a differential problem is formulated, also called defeaturing, while simultaneously ensuring that the accuracy of the solution is maintained under control. ...

Oxford2023

Gradient-based optimisation of the conditional-value-at-risk using the multi-level Monte Carlo method

Fabio Nobile, Sundar Subramaniam Ganesh

In this work, we tackle the problem of minimising the Conditional-Value-at-Risk (CVaR) of output quantities of complex differential models with random input data, using gradient-based approaches in combination with the Multi-Level Monte Carlo (MLMC) method ...

2022

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Delay differential equation

Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

From low-rank retractions to dynamical low-rank approximation and back

Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains

Analysis of a Class of Multilevel Markov Chain Monte Carlo Algorithms Based on Independent Metropolis–Hastings

High order geometric methods with splines: fast solution with explicit time-stepping for Maxwell equations

Analysis-aware defeaturing of complex geometries with Neumann features

Low-Rank Tensor Methods for High-Dimensional Problems

Diff3DHPE: A Diffusion Model for 3D Human Pose Estimation

A Shape Derivative Approach to Domain Simplification

Gradient-based optimisation of the conditional-value-at-risk using the multi-level Monte Carlo method

Graph Chatbot

Chat with Graph Search

Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

A Shape Derivative Approach to Domain Simplification

Analysis of a Class of Multilevel Markov Chain Monte Carlo Algorithms Based on Independent Metropolis–Hastings

Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains

From low-rank retractions to dynamical low-rank approximation and back

High order geometric methods with splines: fast solution with explicit time-stepping for Maxwell equations

Analysis-aware defeaturing of complex geometries with Neumann features

Low-Rank Tensor Methods for High-Dimensional Problems

Gradient-based optimisation of the conditional-value-at-risk using the multi-level Monte Carlo method

Diff3DHPE: A Diffusion Model for 3D Human Pose Estimation