Related papers: Machine Learning of Nonlinear Dynamical Systems wi…

Artificial neural networks are algorithms which have been developed to tackle a range of computational problems. These range from modelling brain function to making predictions of time-dependent phenomena to solving hard (NP-complete)…

Brains need to predict how the body reacts to motor commands. It is an open question how networks of spiking neurons can learn to reproduce the non-linear body dynamics caused by motor commands, using local, online and stable learning…

Unknown nonlinear dynamics can limit the performance of model-based feedforward control. The aim of this paper is to develop a feedforward control framework for systems with unknown, typically nonlinear, dynamics. To address the unknown…

The paper investigates nonlinear system identification using system output data at various linearized operating points. A feed-forward multi-layer Artificial Neural Network (ANN) based approach is used for this purpose and tested for two…

The ability of a feed-forward neural network to learn and classify different states of polymer configurations is systematically explored. Performing numerical experiments, we find that a simple network model can, after adequate training,…

A very popular model in machine learning is the feedforward neural network (FFN). The FFN can approximate general functions and mitigate the curse of dimensionality. Here we introduce FFNs which represent sections of holomorphic line…

Feed-forward neural networks (FNNs) work as standard building blocks in applying artificial intelligence (AI) to the physical world. They allow learning the dynamics of unknown physical systems (e.g., biological and chemical) {to predict…

We study a non-linear dynamical system on networks inspired by the pitchfork bifurcation normal form. The system has several interesting interpretations: as an interconnection of several pitchfork systems, a gradient dynamical system and…

We propose a hierarchical training algorithm for standard feed-forward neural networks that adaptively extends the network architecture as soon as the optimization reaches a stationary point. By solving small (low-dimensional) optimization…

This paper introduces a machine learning approach to take a nonlinear differential-equation model that exhibits qualitative agreement with a physical experiment over a range of parameter values and produce a hybrid model that also exhibits…

We fully characterize a large class of feedforward neural networks in terms of truncation maps. As an application, we show how a ReLU neural network can implement a feature map which separates concentric data.

Replicating chaotic characteristics of non-linear dynamics by machine learning (ML) has recently drawn wide attentions. In this work, we propose that a ML model, trained to predict the state one-step-ahead from several latest historic…

A single dynamical system with time-delayed feedback can emulate networks. This property of delay systems made them extremely useful tools for Machine Learning applications. Here we describe several possible setups, which allow emulating…

Time-delay mappings constructed using neural networks have proven successful in performing nonlinear system identification; however, because of their discrete nature, their use in bifurcation analysis of continuous-time systems is limited.…

We propose a novel learning method for multilayered neural networks which uses feedforward supervisory signal and associates classification of a new input with that of pre-trained input. The proposed method effectively uses rich input…

A computer model of the feed-forward neural network with the hidden layer is developed to reconstruct physical field investigated by the fiber-optic measuring system. The Gaussian distributions of some physical quantity are selected as…

This work proposes a data-driven approach for bifurcation analysis in nonlinear systems when the governing differential equations are not available. Specifically, regularized regression with barrier terms is used to learn a homeomorphism…

Machine learning algorithms, and more in particular neural networks, arguably experience a revolution in terms of performance. Currently, the best systems we have for speech recognition, computer vision and similar problems are based on…

For performing successful measurements within limited experimental time, efficient use of preliminary data plays a crucial role. This work shows that a simple feedforward type neural networks approach for learning preliminary experimental…

Higher order artificial neurons whose outputs are computed by applying an activation function to a higher order multinomial function of the inputs have been considered in the past, but did not gain acceptance due to the extra parameters and…