Related papers: On Numerical Integration in Neural Ordinary Differ…

Neural Ordinary Differential Equations replace the right-hand side of a conventional ODE with a neural net, which by virtue of the universal approximation theorem, can be trained to the representation of any function. When we do not know…

Deformable image registration (DIR) is crucial in medical image analysis, enabling the exploration of biological dynamics such as organ motions and longitudinal changes in imaging. Leveraging Neural Ordinary Differential Equations (ODE) for…

Physics-informed neural networks (PINNs) and their variants have been very popular in recent years as algorithms for the numerical simulation of both forward and inverse problems for partial differential equations. This article aims to…

This paper proposes a novel inverse kinematics (IK) solver of articulated robotic systems for path planning. IK is a traditional but essential problem for robot manipulation. Recently, data-driven methods have been proposed to quickly solve…

Neural Ordinary Differential Equations (Neural ODEs) are the continuous analog of Residual Neural Networks (ResNets). We investigate whether the discrete dynamics defined by a ResNet are close to the continuous one of a Neural ODE. We first…

A concept of using Neural Ordinary Differential Equations(NODE) for Transfer Learning has been introduced. In this paper we use the EfficientNets to explore transfer learning on CIFAR-10 dataset. We use NODE for fine-tuning our model. Using…

Neural Ordinary Differential Equations (ODEs) have been successful in various applications due to their continuous nature and parameter-sharing efficiency. However, these unique characteristics also introduce challenges in training,…

Ordinary differential equations (ODEs), via their induced flow maps, provide a powerful framework to parameterize invertible transformations for the purpose of representing complex probability distributions. While such models have achieved…

Embedding nonlinear dynamical systems into artificial neural networks is a powerful new formalism for machine learning. By parameterizing ordinary differential equations (ODEs) as neural network layers, these Neural ODEs are…

Deep learning has become a pivotal technology in fields such as computer vision, scientific computing, and dynamical systems, significantly advancing these disciplines. However, neural Networks persistently face challenges related to…

Learned iterative reconstruction algorithms for inverse problems offer the flexibility to combine analytical knowledge about the problem with modules learned from data. This way, they achieve high reconstruction performance while ensuring…

Deep Learning has emerged as one of the most significant innovations in machine learning. However, a notable limitation of this field lies in the ``black box" decision-making processes, which have led to skepticism within groups like…

Nonlinear operators with long distance spatiotemporal dependencies are fundamental in modeling complex systems across sciences, yet learning these nonlocal operators remains challenging in machine learning. Integral equations (IEs), which…

Rapidly developing machine learning methods has stimulated research interest in computationally reconstructing differential equations (DEs) from observational data which may provide additional insight into underlying causative mechanisms.…

Machines of all kinds from vehicles to industrial equipment are increasingly instrumented with hundreds of sensors. Using such data to detect anomalous behaviour is critical for safety and efficient maintenance. However, anomalies occur…

The identification of a mathematical dynamics model is a crucial step in the designing process of a controller. However, it is often very difficult to identify the system's governing equations, especially in complex environments that…

Fractional-order differential equations (FDEs) enhance traditional differential equations by extending the order of differential operators from integers to real numbers, offering greater flexibility in modeling complex dynamical systems…

A neural ordinary differential equation (neural ODE) is a machine learning model that is commonly described as a continuous-depth generalization of a residual network (ResNet) with a single residual block, or conversely, the ResNet can be…

Neural ordinary differential equations (NODE) have garnered significant attention for their design of continuous-depth neural networks and the ability to learn data/feature dynamics. However, for high-dimensional systems, estimating…

When learning dynamical systems from data, embedding physical structure can constrain the solution space and improve generalization, but many physics-informed models assume access to the full system state. This limits their use in partially…