Related papers: Tensor Network Framework for Forecasting Nonlinear…

Recurrent neural networks have gained widespread use in modeling sequential data. Learning long-term dependencies using these models remains difficult though, due to exploding or vanishing gradients. In this paper, we draw connections…

The present study represents a data-driven turbulent model with Galilean invariance preservation based on machine learning algorithm. The fully connected neural network (FCNN) and tensor basis neural network (TBNN) [Ling et al. (2016)] are…

The nonlinear nature of chaotic systems results in extreme sensitivity to initial conditions and highly intricate dynamical behaviors, posing fundamental challenges for accurately predicting their evolution. To overcome the limitation that…

I present a data-driven predictive modeling tool that is applicable to high-dimensional chaotic systems with unstable periodic orbits. The basic idea is using deep neural networks to learn coordinate transformations between the trajectories…

This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…

The identification of nonlinear dynamics from observations is essential for the alignment of the theoretical ideas and experimental data. The last, in turn, is often corrupted by the side effects and noise of different natures, so…

Several Tensor Basis Neural Network (TBNN) frameworks aimed at enhancing turbulence RANS modeling have recently been proposed in the literature as data-driven constitutive models for systems with known invariance properties. However,…

We propose a hybrid meta-learning framework for forecasting and anomaly detection in nonlinear dynamical systems characterized by nonstationary and stochastic behavior. The approach integrates a physics-inspired simulator that captures…

Short-term demand forecasting models commonly combine convolutional and recurrent layers to extract complex spatiotemporal patterns in data. Long-term histories are also used to consider periodicity and seasonality patterns as time series…

Tensor networks have been successfully applied in simulation of quantum physical systems for decades. Recently, they have also been employed in classical simulation of quantum computing, in particular, random quantum circuits. This paper…

This paper suggests parametrically transformed nested error regression models (TNERM), which transform the data flexibly to follow the normal linear mixed regression. We provide a procedure for estimating consistently the parameters of the…

A large-scale dynamic network (LDN) is a source of data in many big data-related applications due to their large number of entities and large-scale dynamic interactions. They can be modeled as a high-dimensional incomplete (HDI) tensor that…

The prediction of periodical time-series remains challenging due to various types of data distortions and misalignments. Here, we propose a novel model called Temporal embedding-enhanced convolutional neural Network (TeNet) to learn…

Recently, a general data driven numerical framework has been developed for learning and modeling of unknown dynamical systems using fully- or partially-observed data. The method utilizes deep neural networks (DNNs) to construct a model for…

Recurrent neural networks (RNNs) have recently been extensively applied to model the time-evolution in fluid dynamics, weather predictions, and even chaotic systems thanks to their ability to capture temporal dependencies and sequential…

We propose a neural network model with transient chaos, or a transiently chaotic neural network (TCNN) as an approximation method for combinatorial optimization problem, by introducing transiently chaotic dynamics into neural networks.…

We explore the influence of precision of the data and the algorithm for the simulation of chaotic dynamics by neural networks techniques. For this purpose, we simulate the Lorenz system with different precisions using three different neural…

In the domain of sequence modelling, Recurrent Neural Networks (RNN) have been capable of achieving impressive results in a variety of application areas including visual question answering, part-of-speech tagging and machine translation.…

Networks are powerful tools for modeling interactions in complex systems. While traditional networks use scalar edge weights, many real-world systems involve multidimensional interactions. For example, in social networks, individuals often…

The capabilities of recurrent neural networks and Koopman-based frameworks are assessed in the prediction of temporal dynamics of the low-order model of near-wall turbulence by Moehlis et al. (New J. Phys. 6, 56, 2004). Our results show…