Physics-Informed Echo State Networks

  title={Physics-Informed Echo State Networks},
  author={Nguyen Anh Khoa Doan and Wolfgang Polifke and Luca Magri},
  journal={J. Comput. Sci.},

Chaotic systems learning with hybrid echo state network/proper orthogonal decomposition based model

The hybrid-ESN-B approach is seen to provide the best prediction accuracy, outperforming the other hybrid approach, the POD/Galerkin projection ROM, and the data-only ESN, especially when using ESNs with a small number of neurons.

Robust Optimization and Validation of Echo State Networks for learning chaotic dynamics

Short- and long-term predictions of chaotic flows and extreme events: a physics-constrained reservoir computing approach

We propose a physics-constrained machine learning method—based on reservoir computing—to time-accurately predict extreme events and long-term velocity statistics in a model of chaotic flow. The

Data-driven prediction and control of extreme events in a chaotic flow

A data-driven methodology for the prediction and control of extreme events in a chaotic shear system based on echo state networks, which are a type of reservoir computing that learn temporal correlations within a time-dependent dataset.

Auto-Encoded Reservoir Computing for Turbulence Learning

The Auto-Encoded Reservoir-Computing approach is able to both learn the time-accurate dynamics of the turbulent flow and predict its first-order statistical moments.

A machine-learning approach for long-term prediction of experimental cardiac action potential time series using an autoencoder and echo state networks

The proposed AE-ESN approach is evaluated using synthetic and experimental voltage time series from cardiac cells, which exhibit nonlinear and chaotic behavior, and yields mean absolute errors in predicted voltage 6-14 times smaller when forecasting approximately 20 future action potentials for the datasets considered.

Chain-structure time-delay reservoir computing for synchronizing chaotic signal and an application to secure communication

A novel scheme of secure communication is further designed, in which the “smart” receiver can synchronize to the chaotic signal used for encryption in an adaptive manner, and sheds light on developing machine learning-based signal processing and communication applications.

CD-ROM: Complementary Deep-Reduced Order Model

The proposed model, called CD-ROM (Complementary Deep Reduced Order Model) is able to retain information from past states of the system and use it to correct the imperfect reduced dynamics of POD-Galerkin models.

CD-ROM: Complemented Deep-Reduced Order Model

The present CD-ROM approach is based on an interpretable continuous memory formulation, derived from simple hypotheses on the behavior of partially observed dynamical systems, and can hence be simulated using most classical time stepping schemes.



Echo State Networks with Self-Normalizing Activations on the Hyper-Sphere

A model of ESNs is proposed that eliminates critical dependence on hyper-parameters, resulting in networks that provably cannot enter a chaotic regime and, at the same time, denotes nonlinear behavior in phase space characterized by a large memory of past inputs, comparable to the one of linear networks.

Harnessing Nonlinearity: Predicting Chaotic Systems and Saving Energy in Wireless Communication

We present a method for learning nonlinear systems, echo state networks (ESNs). ESNs employ artificial recurrent neural networks in a way that has recently been proposed independently as a learning

Hybrid Forecasting of Chaotic Processes: Using Machine Learning in Conjunction with a Knowledge-Based Model

A general method is proposed that leverages the advantages of these two approaches by combining a knowledge-based model and a machine learning technique to build a hybrid forecasting scheme, and is able to accurately predict for a much longer period of time than either its machine-learning component or its model-based component alone.

Reservoir computing approaches to recurrent neural network training

A Practical Guide to Applying Echo State Networks

Practical techniques and recommendations for successfully applying Echo State Network, as well as some more advanced application-specific modifications are presented.

Reynolds averaged turbulence modelling using deep neural networks with embedded invariance

This paper presents a method of using deep neural networks to learn a model for the Reynolds stress anisotropy tensor from high-fidelity simulation data and proposes a novel neural network architecture which uses a multiplicative layer with an invariant tensor basis to embed Galilean invariance into the predicted anisotropic tensor.

A Comprehensive Physics-Informed Machine Learning Framework for Predictive Turbulence Modeling

Although an increased availability of computational resources has enabled high-fidelity simulations of turbulent flows, the RANS models are still the dominant tools for industrial applications.

Data-assisted reduced-order modeling of extreme events in complex dynamical systems

A novel hybrid framework that complements an imperfect reduced order model, with data-streams that are integrated though a recurrent neural network (RNN) architecture is developed, showing that the blended approach has improved performance compared with methods that use either data streams or the imperfect model alone.

Deep learning of vortex-induced vibrations

A new paradigm of inference in fluid mechanics for coupled multi-physics problems enables velocity and pressure quantification from flow snapshots in small subdomains and can be exploited for flow control applications and also for system identification.