Related papers: On Dominant Manifolds in Reservoir Computing Netwo…
This paper focuses on the construction of accurate and predictive data-driven reduced models of large-scale numerical simulations with complex dynamics and sparse training datasets. In these settings, standard, single-domain approaches may…
Recently, reinforcement learning models have achieved great success, completing complex tasks such as mastering Go and other games with higher scores than human players. Many of these models collect considerable data on the tasks and…
Classification of multivariate time series (MTS) has been tackled with a large variety of methodologies and applied to a wide range of scenarios. Reservoir Computing (RC) provides efficient tools to generate a vectorial, fixed-size…
Determining hidden shared patterns behind dynamic phenomena can be a game-changer in multiple areas of research. Here we present the principles and show a method to identify hidden shared dynamics from time series by a two-module,…
Ability of deep networks to extract high level features and of recurrent networks to perform time-series inference have been studied. In view of universality of one hidden layer network at approximating functions under weak constraints, the…
Reservoir Computing is a relatively new framework created to allow the usage of powerful but complex systems as computational mediums. The basic approach consists in training only a readout layer, exploiting the innate separation and…
We study the dynamics of discrete-time regulatory networks on random digraphs. For this we define ensembles of deterministic orbits of random regulatory networks, and introduce some statistical indicators related to the long-term dynamics…
Recurrent Neural Networks (RNNs) have shown great success in modeling time-dependent patterns, but there is limited research on their learned representations of latent temporal features and the emergence of these representations during…
Reservoir computing derived from recurrent neural networks is more applicable to real world systems than deep learning because of its low computational cost and potential for physical implementation. Specifically, physical reservoir…
An emerging paradigm proposes that neural computations can be understood at the level of dynamical systems that govern low-dimensional trajectories of collective neural activity. How the connectivity structure of a network determines the…
The extension of deep learning towards temporal data processing is gaining an increasing research interest. In this paper we investigate the properties of state dynamics developed in successive levels of deep recurrent neural networks…
The prediction of complex dynamics remains an open problem across many domains of physics, where nonlinearities and multiscale interactions severely limit the reliability of conventional forecasting methods. Quantum reservoir computing…
We show that connectivity within the high-dimensional recurrent layer of a reservoir network is crucial for its performance. To this end, we systematically investigate the impact of network connectivity on its performance, i.e., we examine…
Any model order reduced dynamical system that evolves a modal decomposition to approximate the discretized solution of a stochastic PDE can be related to a vector field tangent to the manifold of fixed rank matrices. The Dynamically…
Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has…
This study presents a novel representation learning model tailored for dynamic networks, which describes the continuously evolving relationships among individuals within a population. The problem is encapsulated in the dimension reduction…
Training reinforcement learning (RL) agents to control fluid dynamics systems is computationally expensive due to the high cost of direct numerical simulations (DNS) of the governing equations. Surrogate models offer a promising alternative…
The simulation of turbulent flow requires many degrees of freedom to resolve all the relevant times and length scales. However, due to the dissipative nature of the Navier-Stokes equations, the long-term dynamics are expected to lie on a…
We present a simple and scalable implementation of next-generation reservoir computing (NGRC) for modeling dynamical systems from time-series data. The method uses a pseudorandom nonlinear projection of time-delay embedded inputs, allowing…
Animals often demonstrate a remarkable ability to adapt to their environments during their lifetime. They do so partly due to the evolution of morphological and neural structures. These structures capture features of environments shared…