Related papers: Toward the Fully Physics-Informed Echo State Netwo…

Echo-State Networks and Reservoir Computing have been studied for more than a decade. They provide a simpler yet powerful alternative to Recurrent Neural Networks, every internal weight is fixed and only the last linear layer is trained.…

Echo state networks (ESNs) have been recently proved to be universal approximants for input/output systems with respect to various $L ^p$-type criteria. When $1\leq p< \infty$, only $p$-integrability hypotheses need to be imposed, while in…

Since the advent of the ``Neural Ordinary Differential Equation (Neural ODE)'' paper, learning ODEs with deep learning has been applied to system identification, time-series forecasting, and related areas. Exploiting the diffeomorphic…

This article introduces Random Error Sampling-based Neuroevolution (RESN), a novel automatic method to optimize recurrent neural network architectures. RESN combines an evolutionary algorithm with a training-free evaluation approach. The…

The notion of an Evolutional Deep Neural Network (EDNN) is introduced for the solution of partial differential equations (PDE). The parameters of the network are trained to represent the initial state of the system only, and are…

We revisit the problem of physics-informed regression, and propose a method that directly computes the state at the prediction point, simultaneously with the derivative and curvature information of the existing samples. We frame each…

Estimating rate coefficients from complex chemical reactions is essential for advancing detailed chemistry. However, the stiffness inherent in real-world atmospheric chemistry systems poses severe challenges, leading to training instability…

We introduce Effective Field Neural Networks (EFNNs), a new architecture based on continued functions -- mathematical tools used in renormalization to handle divergent perturbative series. Our key insight is that neural networks can…

We present a data-driven model to reconstruct nonlinear dynamics from a very sparse times series data, which relies on the strength of the echo state network (ESN) in learning nonlinear representation of data. With an assumption of the…

This paper investigates the performance of Echo State Networks (ESNs) for univariate time series forecasting using a subset of the M4 Forecasting Competition dataset. Focusing on monthly and quarterly time series, we evaluate whether a…

Electromagnetic (EM) body models designed to predict Radio-Frequency (RF) propagation are time-consuming methods which prevent their adoption in strict real-time computational imaging problems, such as human body localization and sensing.…

Distribution System State Estimation (DSSE) is becoming increasingly important with the integration of Distributed Energy Resources (DERs) and the active operation of distribution networks (DNs), but it remains challenging due to the…

In this study, we use a reservoir computing based echo state network (ESN) to predict the collective burst synchronization of neurons. Specifically, we investigate the ability of ESN in predicting the burst synchronization of an ensemble of…

An evolution strategy (ES) variant based on a simplification of a natural evolution strategy recently attracted attention because it performs surprisingly well in challenging deep reinforcement learning domains. It searches for neural…

We discuss deep learning inference for the neutron star equation of state (EoS) using the real observational data of the mass and the radius. We make a quantitative comparison between the conventional polynomial regression and the neural…

Parametric optimal control problems governed by partial differential equations (PDEs) are widely found in scientific and engineering applications. Traditional grid-based numerical methods for such problems generally require repeated…

Neural differential equations offer a powerful framework for modeling continuous-time dynamics, but forecasting stiff biophysical systems remains unreliable. Standard Neural ODEs and physics informed variants often require orders of…

Spiking neural networks (SNNs) are well known as the brain-inspired models with high computing efficiency, due to a key component that they utilize spikes as information units, close to the biological neural systems. Although spiking based…

Physics-informed neural networks (PINNs) have proven to be a promising method for the rapid solving of partial differential equations (PDEs) in both forward and inverse problems. However, due to the smoothness assumption of functions…

Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…