Related papers: Modular Neural Ordinary Differential Equations

Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with representative datasets. Recently, an augmented framework has been…

The idea of neural Ordinary Differential Equations (ODE) is to approximate the derivative of a function (data model) instead of the function itself. In residual networks, instead of having a discrete sequence of hidden layers, the…

We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary…

Neural ODEs (NODEs) are continuous-time neural networks (NNs) that can process data without the limitation of time intervals. They have advantages in learning and understanding the evolution of complex real dynamics. Many previous works…

Recently, Neural Ordinary Differential Equations has emerged as a powerful framework for modeling physical simulations without explicitly defining the ODEs governing the system, but instead learning them via machine learning. However, the…

Neural networks have the ability to serve as universal function approximators, but they are not interpretable and don't generalize well outside of their training region. Both of these issues are problematic when trying to apply standard…

Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with some representative datasets. Recently, an augmented framework has been…

The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin.…

Modeling complex systems using standard neural ordinary differential equations (NODEs) often faces some essential challenges, including high computational costs and susceptibility to local optima. To address these challenges, we propose a…

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…

Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…

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…

Neural ordinary differential equations (NODEs) presented a new paradigm to construct (continuous-time) neural networks. While showing several good characteristics in terms of the number of parameters and the flexibility in constructing…

We show that Neural Ordinary Differential Equations (ODEs) learn representations that preserve the topology of the input space and prove that this implies the existence of functions Neural ODEs cannot represent. To address these…

Deep learning has an increasing impact to assist research, allowing, for example, the discovery of novel materials. Until now, however, these artificial intelligence techniques have fallen short of discovering the full differential equation…

Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics and engineering to medicine and economics. These systems cannot be properly modelled and simulated with standard…

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 predictive performance with current state-of-the-art…

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…

Neural ordinary differential equations (neural ODEs) can effectively learn dynamical systems from time series data, but their behavior on graph-structured data remains poorly understood, especially when applied to graphs with different size…

In this study, we propose parameter-varying neural ordinary differential equations (NODEs) where the evolution of model parameters is represented by partition-of-unity networks (POUNets), a mixture of experts architecture. The proposed…