Related papers: Time Dependence in Non-Autonomous Neural ODEs
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) have emerged as a novel network architecture that bridges dynamical systems and deep learning. However, the gradient obtained with the continuous adjoint method in the vanilla neural ODE…
We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a…
In artificial neural networks, weights are a static representation of synapses. However, synapses are not static, they have their own interacting dynamics over time. To instill weights with interacting dynamics, we use a model describing…
Neural ordinary differential equations are an attractive option for modelling temporal dynamics. However, a fundamental issue is that the solution to an ordinary differential equation is determined by its initial condition, and there is no…
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…
Continuous-depth neural networks, such as Neural ODEs, have refashioned the understanding of residual neural networks in terms of non-linear vector-valued optimal control problems. The common solution is to use the adjoint sensitivity…
Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an…
Neural ordinary differential equations (neural ODEs) are a popular family of continuous-depth deep learning models. In this work, we consider a large family of parameterized ODEs with continuous-in-time parameters, which include…
The neural Ordinary Differential Equation (ODE) model has shown success in learning complex continuous-time processes from observations on discrete time stamps. In this work, we consider the modeling and forecasting of time series data that…
Neural controlled differential equations (CDEs) are the continuous-time analogue of recurrent neural networks, as Neural ODEs are to residual networks, and offer a memory-efficient continuous-time way to model functions of potentially…
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…
Artificial neural networks, widely recognised for their role in machine learning, are now transforming the study of ordinary differential equations (ODEs), bridging data-driven modelling with classical dynamical systems and enabling the…
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…
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…
Neural ordinary differential equations (Neural ODEs) is a class of machine learning models that approximate the time derivative of hidden states using a neural network. They are powerful tools for modeling continuous-time dynamical systems,…
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…
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…
Time series modeling and analysis have become critical in various domains. Conventional methods such as RNNs and Transformers, while effective for discrete-time and regularly sampled data, face significant challenges in capturing the…
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…