Related papers: Neural ODEs with stochastic vector field mixtures

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…

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.…

We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic…

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…

Deep learning provides accurate collaborative filtering models to improve recommender system results. Deep matrix factorization and their related collaborative neural networks are the state-of-art in the field; nevertheless, both models…

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…

Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they…

Stochastic regularization of neural networks (e.g. dropout) is a wide-spread technique in deep learning that allows for better generalization. Despite its success, continuous-time models, such as neural ordinary differential equation (ODE),…

We introduce steerable neural ordinary differential equations on homogeneous spaces $M=G/H$. These models constitute a novel geometric extension of manifold neural ordinary differential equations (NODEs) that transport associated feature…

The emergence of organized multiscale patterns resulting from convection is ubiquitous, observed throughout different cloud types. The reproduction of such patterns by general circulation models remains a challenge due to the complex nature…

Ordinary differential equations (ODEs), via their induced flow maps, provide a powerful framework to parameterize invertible transformations for the purpose of representing complex probability distributions. While such models have achieved…

Data-driven modeling of dynamical systems is a crucial area of machine learning. In many scenarios, a thorough understanding of the model's behavior becomes essential for practical applications. For instance, understanding the behavior of a…

Neural fields, which represent signals as a function parameterized by a neural network, are a promising alternative to traditional discrete vector or grid-based representations. Compared to discrete representations, neural representations…

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…

Mixture models are probabilistic models aimed at uncovering and representing latent subgroups within a population. In the realm of network data analysis, the latent subgroups of nodes are typically identified by their connectivity…

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…

Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in…

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…

Since the advent of the ``Neural Ordinary Differential Equation (Neural ODE)'' paper, learning ODEs with deep learning has been applied to system identification, time-series forecasting, and related areas. Exploiting the diffeomorphic…

A general class of dynamical systems which can be trained to operate in classification and generation modes are introduced. A procedure is proposed to plant asymptotic stationary attractors of the deterministic model. Optimizing the…