Related papers: Structure-Preserving Neural Ordinary Differential …

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,…

Many engineered physical processes exhibit nonlinear but asymptotically stable dynamics that converge to a finite set of equilibria determined by control inputs. Identifying such systems from data is challenging: stable dynamics provide…

Deep neural networks have become invaluable tools for supervised machine learning, e.g., classification of text or images. While often offering superior results over traditional techniques and successfully expressing complicated patterns in…

Neural Ordinary Differential Equations (NODEs) have proven to be a powerful modeling tool for approximating (interpolation) and forecasting (extrapolation) irregularly sampled time series data. However, their performance degrades…

By interpreting the forward dynamics of the latent representation of neural networks as an ordinary differential equation, Neural Ordinary Differential Equation (Neural ODE) emerged as an effective framework for modeling a system dynamics…

Ordinary differential equations (ODEs) provide a powerful framework for modeling dynamic systems arising in a wide range of scientific domains. However, most existing ODE methods focus on a single system, and do not adequately address the…

Neural ordinary differential equations (ODEs) have attracted much attention as continuous-time counterparts of deep residual neural networks (NNs), and numerous extensions for recurrent NNs have been proposed. Since the 1980s, ODEs have…

This work presents the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in both steady and transient form. Implicit time integration is used in the case of the transient form. A…

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…

The laws of physics have been written in the language of dif-ferential equations for centuries. Neural Ordinary Differen-tial Equations (NODEs) are a new machine learning architecture which allows these differential equations to be learned…

The high computational cost associated with solving for detailed chemistry poses a significant challenge for predictive computational fluid dynamics (CFD) simulations of turbulent reacting flows. These models often require solving a system…

Neural ordinary differential equations (NODE) have been proposed as a continuous depth generalization to popular deep learning models such as Residual networks (ResNets). They provide parameter efficiency and automate the model selection…

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…

We present a novel approach (DyNODE) that captures the underlying dynamics of a system by incorporating control in a neural ordinary differential equation framework. We conduct a systematic evaluation and comparison of our method and…

Neural Ordinary Differential Equations (NODEs) are a new class of models that transform data continuously through infinite-depth architectures. The continuous nature of NODEs has made them particularly suitable for learning the dynamics of…

Deep neural networks can be fragile and sensitive to small input perturbations that might cause a significant change in the output. In this paper, we employ contraction theory to improve the robustness of neural ODEs (NODEs). A dynamical…

Modeling dynamical systems is crucial across the science and engineering fields for accurate prediction, control, and decision-making. Recently, machine learning (ML) approaches, particularly neural ordinary differential equations (NODEs),…

Accurate modeling of spatiotemporal dynamics is crucial to understanding complex phenomena across science and engineering. However, this task faces a fundamental challenge when the governing equations are unknown and observational data are…

In future power systems, the detailed structure and dynamics may not always be fully known. This is due to an increasing number of distributed energy resources, such as photovoltaic generators, battery storage systems, heat pumps and…

Understanding how complex systems respond to perturbations, such as whether they will remain stable or what their most sensitive patterns are, is a fundamental challenge across science and engineering. Traditional stability and receptivity…