IEEE

Unified Framework for Evaluating Numerical Integration Methods Through Characteristic Root Distortion in Linear Ordinary Differential Equations

Abstract: Analytically solving complex or large-scale differential equations is often difficult or even impossible, making numerical integration methods indispensable. However, as all numerical ...
C&EN

Modeling Chemical Reaction Networks Using Neural Ordinary Differential Equations

Creative Commons (CC): This is a Creative Commons license. Attribution (BY): Credit must be given to the creator. In chemical reaction network theory, ordinary differential equations are used to model ...
acm.org

On the numerical solution of an N-point boundary value problem for linear ordinary differential equations

A method for the numerical solution of the n-point boundary value problem for homogeneous linear ordinary differential equations is developed. The method requires two Runge-Kutta integrations over the ...
Frontiers

Applying neural ordinary differential equations for analysis of hormone dynamics in Trier Social Stress Tests

1 Department of Pharmacology and Systems Physiology, University of Cincinnati College of Medicine, Cincinnati, OH, United States 2 Department of Psychiatry and Behavioral Neuroscience, University of ...
PNAS

Bridging the gap between models based on ordinary, delayed, and fractional differentials equations through integral kernels

This study centers on incorporating memory effects (the impact of past events on current states) into mathematical models for population dynamics. It introduces a framework based on the gamma ...
Frontiers

HiDeS: a higher-order-derivative-supervised neural ordinary differential equation for multi-robot systems and opinion dynamics

This paper addresses the limitations of current neural ordinary differential equations (NODEs) in modeling and predicting complex dynamics by introducing a novel framework called ...
IEEE

Neural Ordinary Differential Equations for Nonlinear System Identification

Abstract: Neural ordinary differential equations (NODE) have been recently proposed as a promising approach for nonlinear system identification tasks. In this work, we systematically compare their ...