Related papers: Neural DAEs: Constrained neural networks

Recently, deep residual networks have been successfully applied in many computer vision and natural language processing tasks, pushing the state-of-the-art performance with deeper and wider architectures. In this work, we interpret deep…

We propose the use of physics-informed neural networks for solving the shallow-water equations on the sphere in the meteorological context. Physics-informed neural networks are trained to satisfy the differential equations along with the…

We introduce Graph Neural Processes (GNP), inspired by the recent work in conditional and latent neural processes. A Graph Neural Process is defined as a Conditional Neural Process that operates on arbitrary graph data. It takes features of…

Nowadays Dynamic Adaptive Streaming over HTTP (DASH) is the most prevalent solution on the Internet for multimedia streaming and responsible for the majority of global traffic. DASH uses adaptive bit rate (ABR) algorithms, which select the…

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…

Current physics-informed (standard or deep operator) neural networks still rely on accurately learning the initial and/or boundary conditions of the system of differential equations they are solving. In contrast, standard numerical methods…

This study proposes a method to enhance neural network performance when training data and application data are not very similar, e.g., out of distribution problems, as well as pattern and regime shifts. The method consists of three main…

Although the spike-trains in neural networks are mainly constrained by the neural dynamics itself, global temporal constraints (refractoriness, time precision, propagation delays, ..) are also to be taken into account. These constraints are…

Neural networks (NN)-based learning algorithms are strongly affected by the choices of initialization and data distribution. Different optimization strategies have been proposed for improving the learning trajectory and finding a better…

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…

We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this second…

Today artificial neural networks are applied in various fields - engineering, data analysis, robotics. While they represent a successful tool for a variety of relevant applications, mathematically speaking they are still far from being…

Neural Ordinary Differential Equations (Neural ODEs) represent a significant breakthrough in deep learning, promising to bridge the gap between machine learning and the rich theoretical frameworks developed in various mathematical fields…

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 recursive Newton-Euler Algorithm (RNEA) is a popular technique for computing the dynamics of robots. RNEA can be framed as a differentiable computational graph, enabling the dynamics parameters of the robot to be learned from data via…

Electronic healthcare records are an important source of information which can be used in patient stratification to discover novel disease phenotypes. However, they can be challenging to work with as data is often sparse and irregularly…

Dynamic neural network is an emerging research topic in deep learning. Compared to static models which have fixed computational graphs and parameters at the inference stage, dynamic networks can adapt their structures or parameters to…

We propose to adapt segmentation networks with a constrained formulation, which embeds domain-invariant prior knowledge about the segmentation regions. Such knowledge may take the form of simple anatomical information, e.g., structure size…

We introduce a novel computational unit for neural networks that features multiple biases, challenging the traditional perceptron structure. This unit emphasizes the importance of preserving uncorrupted information as it is passed from one…

Modeling the traffic dynamics is essential for understanding and predicting the traffic spatiotemporal evolution. However, deriving the partial differential equation (PDE) models that capture these dynamics is challenging due to their…