Related papers: Embedding and Approximation Theorems for Echo Stat…

In this paper we introduce a new framework to train an Echo State Network to predict real valued time-series. The method consists in projecting the output of the internal layer of the network on a space with lower dimensionality, before…

Learning workable representations of dynamical systems is becoming an increasingly important problem in a number of application areas. By leveraging recent work connecting deep neural networks to systems of differential equations, we…

Since many real world networks are evolving over time, such as social networks and user-item networks, there are increasing research efforts on dynamic network embedding in recent years. They learn node representations from a sequence of…

Supralinear and sublinear pre-synaptic and dendritic integration is considered to be responsible for nonlinear computation power of biological neurons, emphasizing the role of nonlinear integration as opposed to nonlinear output…

A new learning algorithm for Evolving Cascade Neural Networks (ECNNs) is described. An ECNN starts to learn with one input node and then adding new inputs as well as new hidden neurons evolves it. The trained ECNN has a nearly minimal…

Modeling the dynamics of the formation and evolution of protostellar disks as well as the history of stellar mass accretion typically involve the numerical solution of complex systems of coupled differential equations. The resulting mass…

In this paper, we explore the predictive capabilities of echo state networks (ESNs) for the generalized Kuramoto-Sivashinsky (gKS) equation, an archetypal nonlinear PDE that exhibits spatiotemporal chaos. Our research focuses on predicting…

Classical network embeddings create a low dimensional representation of the learned relationships between features across nodes. Such embeddings are important for tasks such as link prediction and node classification. In the current paper,…

Slinky, a helical elastic rod, is a seemingly simple structure with unusual mechanical behavior; for example, it can walk down a flight of stairs under its own weight. Taking Slinky as a test-case, we propose a physics-informed deep…

Network embedding leverages the node proximity manifested to learn a low-dimensional node vector representation for each node in the network. The learned embeddings could advance various learning tasks such as node classification, network…

Structural network embedding is a crucial step in enabling effective downstream tasks for complex systems that aims to project a network into a lower-dimensional space while preserving similarities among nodes. We introduce a simple and…

Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization. However, many real-world networks…

The celebrated Takens' embedding theorem provides a theoretical foundation for reconstructing the full state of a dynamical system from partial observations. However, the classical theorem assumes that the underlying system is deterministic…

Information networks are ubiquitous and are ideal for modeling relational data. Networks being sparse and irregular, network embedding algorithms have caught the attention of many researchers, who came up with numerous embeddings algorithms…

Neural networks are emerging as a tool for scalable data-driven simulation of high-dimensional dynamical systems, especially in settings where numerical methods are infeasible or computationally expensive. Notably, it has been shown that…

In real-world applications such as emotion recognition from recorded brain activity, data are captured from electrodes over time. These signals constitute a multidimensional time series. In this paper, Echo State Network (ESN), a recurrent…

A core challenge in the interpretation of deep neural networks is identifying commonalities between the underlying algorithms implemented by distinct networks trained for the same task. Motivated by this problem, we introduce DYNAMO, an…

We report about probabilistic likelihood estimates that are performed on time series using an echo state network with orthogonal recurrent connectivity. The results from tests using synthetic stochastic input time series with temporal…

We consider a neural network with adapting synapses whose dynamics can be analitically computed. The model is made of $N$ neurons and each of them is connected to $K$ input neurons chosen at random in the network. The synapses are…

Graph Echo State Networks (GESN) have already demonstrated their efficacy and efficiency in graph classification tasks. However, semi-supervised node classification brought out the problem of over-smoothing in end-to-end trained deep…