Related papers: Neural ODE control for classification, approximati…

Most deep neural networks use simple, fixed activation functions, such as sigmoids or rectified linear units, regardless of domain or network structure. We introduce differential equation units (DEUs), an improvement to modern neural…

Neural ordinary differential equations (ODEs) have been attracting increasing attention in various research domains recently. There have been some works studying optimization issues and approximation capabilities of neural ODEs, but their…

A key appeal of the recently proposed Neural Ordinary Differential Equation (ODE) framework is that it seems to provide a continuous-time extension of discrete residual neural networks. As we show herein, though, trained Neural ODE models…

Optimal control problems with nonsmooth objectives and nonlinear partial differential equation (PDE) constraints are challenging, mainly because of the underlying nonsmooth and nonconvex structures and the demanding computational cost for…

Deep neural networks (DNNs) are vulnerable to small adversarial perturbations of the inputs, posing a significant challenge to their reliability and robustness. Empirical methods such as adversarial training can defend against particular…

Identifying dynamical systems from experimental data is a notably difficult task. Prior knowledge generally helps, but the extent of this knowledge varies with the application, and customized models are often needed. Neural ordinary…

Objective. Precise control of neural systems is essential to experimental investigations of how the brain controls behavior and holds the potential for therapeutic manipulations to correct aberrant network states. Model predictive control,…

An extensive body of empirical research has revealed remarkable regularities in the acquisition, organization, deployment, and neural representation of human semantic knowledge, thereby raising a fundamental conceptual question: what are…

Automated medical image segmentation plays a key role in quantitative research and diagnostics. Convolutional neural networks based on the U-Net architecture are the state-of-the-art. A key disadvantage is the hard-coding of the receptive…

Neural networks can be fragile to input noise and adversarial attacks. In this work, we consider Convolutional Neural Ordinary Differential Equations (NODEs), a family of continuous-depth neural networks represented by dynamical systems,…

The uncertainty in human driving behaviors leads to stop-and-go instabilities in freeway traffic. The traffic dynamics are typically modeled by the Aw-Rascle-Zhang (ARZ) Partial Differential Equation (PDE) models, in which the relaxation…

OD matrix estimation is a critical problem in the transportation domain. The principle method uses the traffic sensor measured information such as traffic counts to estimate the traffic demand represented by the OD matrix. The problem is…

Scientific machine learning is an emerging field that broadly describes the combination of scientific computing and machine learning to address challenges in science and engineering. Within the context of differential equations, this has…

Deep learning has arguably achieved tremendous success in recent years. In simple words, deep learning uses the composition of many nonlinear functions to model the complex dependency between input features and labels. While neural networks…

While tumor dynamic modeling has been widely applied to support the development of oncology drugs, there remains a need to increase predictivity, enable personalized therapy, and improve decision-making. We propose the use of Tumor Dynamic…

We investigate the expressive power of deep residual neural networks idealized as continuous dynamical systems through control theory. Specifically, we consider two properties that arise from supervised learning, namely universal…

Recently, domain-uniform stabilizability and detectability has been the central assumption %in order robustness results on the to ensure robustness in the sense of exponential decay of spatially localized perturbations in optimally…

Recent research in deep learning has shown that neural networks can learn differential equations governing dynamical systems. In this paper, we adapt this concept to Virtual Analog (VA) modeling to learn the ordinary differential equations…

Physics-Informed Neural Networks (PINNs) and Neural Ordinary Differential Equations (NODEs) represent two distinct machine learning frameworks for modeling nonlinear neuronal dynamics. This study systematically evaluates their performance…

We propose a reduced-order modeling approach for nonlinear, parameter-dependent ordinary differential equations (ODE). Dimensionality reduction is achieved using nonlinear maps represented by autoencoders. The resulting low-dimensional ODE…