Related papers: Progressive Growing of Neural ODEs
We propose a Dynamical System (DS) approach to learn complex, possibly periodic motion plans from kinesthetic demonstrations using Neural Ordinary Differential Equations (NODE). To ensure reactivity and robustness to disturbances, we…
Classical neural ordinary differential equations (ODEs) are powerful tools for approximating the log-density functions in high-dimensional spaces along trajectories, where neural networks parameterize the velocity fields. This paper…
Ordinary differential equations (ODEs) can provide mechanistic models of temporally local changes of processes, where parameters are often informed by external knowledge. While ODEs are popular in systems modeling, they are less established…
We introduce a provably stable variant of neural ordinary differential equations (neural ODEs) whose trajectories evolve on an energy functional parametrised by a neural network. Stable neural flows provide an implicit guarantee on…
Combinations of neural ODEs with recurrent neural networks (RNN), like GRU-ODE-Bayes or ODE-RNN are well suited to model irregularly observed time series. While those models outperform existing discrete-time approaches, no theoretical…
Time series with non-uniform intervals occur in many applications, and are difficult to model using standard recurrent neural networks (RNNs). We generalize RNNs to have continuous-time hidden dynamics defined by ordinary differential…
A novel way of using neural networks to learn the dynamics of time delay systems from sequential data is proposed. A neural network with trainable delays is used to approximate the right hand side of a delay differential equation. We relate…
Neural ordinary differential equations (NODEs) treat computation of intermediate feature vectors as trajectories of ordinary differential equation parameterized by a neural network. In this paper, we propose a novel model, delay…
Ordinary differential equations (ODEs) are a conventional way to describe the observed dynamics of physical systems. Scientists typically hypothesize about dynamical behavior, propose a mathematical model, and compare its predictions to…
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 ODE Processes approach the problem of meta-learning for dynamics using a latent variable model, which permits a flexible aggregation of contextual information. This flexibility is inherited from the Neural Process framework and…
Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…
The well-known generalization problem hinders the application of artificial neural networks in continuous-time prediction tasks with varying latent dynamics. In sharp contrast, biological systems can neatly adapt to evolving environments…
Differential equations are used to model problems that originate in disciplines such as physics, biology, chemistry, and engineering. In recent times, due to the abundance of data, there is an active search for data-driven methods to learn…
The order/dimension of models derived on the basis of data is commonly restricted by the number of observations, or in the context of monitored systems, sensing nodes. This is particularly true for structural systems (e.g., civil or…
Fractional-order differential equations (FDEs) enhance traditional differential equations by extending the order of differential operators from integers to real numbers, offering greater flexibility in modeling complex dynamical systems…
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,…
Optimal control problems naturally arise in many scientific applications where one wishes to steer a dynamical system from a certain initial state $\mathbf{x}_0$ to a desired target state $\mathbf{x}^*$ in finite time $T$. Recent advances…
Proper orthogonal decomposition (POD) allows reduced-order modeling of complex dynamical systems at a substantial level, while maintaining a high degree of accuracy in modeling the underlying dynamical systems. Advances in machine learning…
To better understand and improve the behavior of neural networks, a recent line of works bridged the connection between ordinary differential equations (ODEs) and deep neural networks (DNNs). The connections are made in two folds: (1) View…