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Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks. While NSDEs are known to make accurate predictions, their uncertainty quantification properties have been…

We study the decentralized online regularized linear regression algorithm over random time-varying graphs. At each time step, every node runs an online estimation algorithm consisting of an innovation term processing its own new…

We propose a novel second-order optimization framework for training the emerging deep continuous-time models, specifically the Neural Ordinary Differential Equations (Neural ODEs). Since their training already involves expensive gradient…

We present a novel model Graph Neural Stochastic Differential Equations (Graph Neural SDEs). This technique enhances the Graph Neural Ordinary Differential Equations (Graph Neural ODEs) by embedding randomness into data representation using…

Long-term traffic flow forecasting plays a crucial role in intelligent transportation as it allows traffic managers to adjust their decisions in advance. However, the problem is challenging due to spatio-temporal correlations and complex…

Addressing the challenges of irregularity and concept drift in streaming time series is crucial for real-world predictive modelling. Previous studies in time series continual learning often propose models that require buffering long…

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 (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…

Non-uniform sampling arises when an experimenter does not have full control over the sampling characteristics of the process under investigation. Moreover, it is introduced intentionally in algorithms such as Bayesian optimization and…

We explore how neural differential equations (NDEs) may be trained on highly resolved fluid-dynamical models of unresolved scales providing an ideal framework for data-driven parameterizations in climate models. NDEs overcome some of the…

We consider the so-called $\natural$-model. It is an one-default model which gives the conditional law of a random time with respect to a reference filtration. This model has been studied in the case where the parameters are continuous. In…

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…

Using neural networks to solve partial differential equations (PDEs) is gaining popularity as an alternative approach in the scientific computing community. Neural networks can integrate different types of information into the loss…

Continuous-depth neural networks can be viewed as deep limits of discrete neural networks whose dynamics resemble a discretization of an ordinary differential equation (ODE). Although important steps have been taken to realize the…

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.…

Online continual learning (OCL) methods adapt to changing environments without forgetting past knowledge. Similarly, online time series forecasting (OTSF) is a real-world problem where data evolve in time and success depends on both rapid…

Learning network dynamics from the empirical structure and spatio-temporal observation data is crucial to revealing the interaction mechanisms of complex networks in a wide range of domains. However, most existing methods only aim at…

Established recurrent neural networks are well-suited to solve a wide variety of prediction tasks involving discrete sequences. However, they do not perform as well in the task of dynamical system identification, when dealing with…

Obesity is a serious public health concern world-wide, which increases the risk of many diseases, including hypertension, stroke, and type 2 diabetes. To tackle this problem, researchers across the health ecosystem are collecting diverse…

Flow matching has emerged as a powerful framework for generative modeling, offering computational advantages over diffusion models by leveraging deterministic Ordinary Differential Equations (ODEs) instead of stochastic dynamics. While…