Related papers: Embedding Capabilities of Neural ODEs
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…
Neural ordinary differential equations (neural ODEs) are a popular type of deep learning model that operate with continuous-depth architectures. To assess how well such models perform on unseen data, it is crucial to understand their…
Dynamic Network Embedding (DNE) has recently attracted considerable attention due to the advantage of network embedding in various fields and the dynamic nature of many real-world networks. An input dynamic network to DNE is often assumed…
In this work, we investigate a method for simulation-free training of Neural Ordinary Differential Equations (NODEs) for learning deterministic mappings between paired data. Despite the analogy of NODEs as continuous-depth residual…
Learning continuous-time dynamics on complex networks is crucial for understanding, predicting and controlling complex systems in science and engineering. However, this task is very challenging due to the combinatorial complexities in the…
Recent work in deep learning focuses on solving physical systems in the Ordinary Differential Equation or Partial Differential Equation. This current work proposed a variant of Convolutional Neural Networks (CNNs) that can learn the hidden…
Neural networks are a popular tool for modeling sequential data but they generally do not treat time as a continuous variable. Neural ODEs represent an important exception: they parameterize the time derivative of a hidden state with a…
Neural Ordinary Differential Equations (NODEs) use a neural network to model the instantaneous rate of change in the state of a system. However, despite their apparent suitability for dynamics-governed time-series, NODEs present a few…
We suggest a universal map capable to recover a behavior of a wide range of dynamical systems given by ODEs. The map is built as an artificial neural network whose weights encode a modeled system. We assume that ODEs are known and prepare…
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…
Neural Ordinary Differential Equations (Neural ODEs) represent continuous-time dynamics with neural networks, offering advancements for modeling and control tasks. However, training Neural ODEs requires solving differential equations at…
Network embedding methods aim at learning low-dimensional latent representation of nodes in a network. These representations can be used as features for a wide range of tasks on graphs such as classification, clustering, link prediction,…
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…
Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…
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…
Neural Ordinary Differential Equations (ODE) are a promising approach to learn dynamic models from time-series data in science and engineering applications. This work aims at learning Neural ODE for stiff systems, which are usually raised…
To understand the fundamental trade-offs between training stability, temporal dynamics and architectural complexity of recurrent neural networks~(RNNs), we directly analyze RNN architectures using numerical methods of ordinary differential…
Complex nonlinear dynamics are ubiquitous in many fields. Moreover, we rarely have access to all of the relevant state variables governing the dynamics. Delay embedding allows us, in principle, to account for unobserved state variables.…
A wide range of scientific problems, such as those described by continuous-time dynamical systems and partial differential equations (PDEs), are naturally formulated on function spaces. While function spaces are typically…
Embedding learning, a.k.a. representation learning, has been shown to be able to model large-scale semantic knowledge graphs. A key concept is a mapping of the knowledge graph to a tensor representation whose entries are predicted by models…