Related papers: On the relationship between ODEs and DBNs

Nonlinear differential equations are challenging to solve numerically and are important to understanding the dynamics of many physical systems. Deep neural networks have been applied to help alleviate the computational cost that is…

In this paper we present a family of algorithms that can simultaneously align and cluster sets of multidimensional curves measured on a discrete time grid. Our approach is based on a generative mixture model that allows non-linear time…

Deep neural networks (DNN) are versatile parametric models utilised successfully in a diverse number of tasks and domains. However, they have limitations---particularly from their lack of robustness and over-sensitivity to out of…

Direct Loss Minimization (DLM) has been proposed as a pseudo-Bayesian method motivated as regularized loss minimization. Compared to variational inference, it replaces the loss term in the evidence lower bound (ELBO) with the predictive log…

This paper presents, evaluates, and discusses a new software tool to automatically build Dynamic Bayesian Networks (DBNs) from ordinary differential equations (ODEs) entered by the user. The DBNs generated from ODE models can handle both…

In this paper, we study deep neural networks (DNNs) for solving high-dimensional evolution equations with oscillatory solutions. Different from deep least-squares methods that deal with time and space variables simultaneously, we propose a…

Deep generative models have achieved impressive success in recent years. Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs), as emerging families for generative model learning, have largely been considered as two…

Identifying causal relations among multi-variate time series is one of the most important elements towards understanding the complex mechanisms underlying the dynamic system. It provides critical tools for forecasting, simulations and…

Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…

Graph Neural Networks (GNNs) and differential equations (DEs) are two rapidly advancing areas of research that have shown remarkable synergy in recent years. GNNs have emerged as powerful tools for learning on graph-structured data, while…

Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise…

Network Embeddings (NEs) map the nodes of a given network into $d$-dimensional Euclidean space $\mathbb{R}^d$. Ideally, this mapping is such that `similar' nodes are mapped onto nearby points, such that the NE can be used for purposes such…

The intersection of machine learning and dynamical systems has generated considerable interest recently. Neural Ordinary Differential Equations (NODEs) represent a rich overlap between these fields. In this paper, we develop a continuous…

The performance of deep neural networks (DNN) is very sensitive to the particular choice of hyper-parameters. To make it worse, the shape of the learning curve can be significantly affected when a technique like batchnorm is used. As a…

This paper investigates two prominent probabilistic neural modeling paradigms: Bayesian Neural Networks (BNNs) and Mixture Density Networks (MDNs) for uncertainty-aware nonlinear regression. While BNNs incorporate epistemic uncertainty by…

The use of differential equations (ODE) is one of the most promising approaches to network inference. The success of ODE-based approaches has, however, been limited, due to the difficulty in estimating parameters and by their lack of…

Traditionally, learning the structure of a Dynamic Bayesian Network has been centralized, requiring all data to be pooled in one location. However, in real-world scenarios, data are often distributed across multiple entities (e.g.,…

The choice of activation function fundamentally shapes the representational capacity and parameter efficiency of deep neural networks, yet most widely used activations lack rigorous theoretical guarantees on these properties. We provide a…

Variational mean field approximations tend to struggle with contemporary overparametrized deep neural networks. Where a Bayesian treatment is usually associated with high-quality predictions and uncertainties, the practical reality has been…

Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the…