Exploring Digital Twins of Nonlinear Systems through Meta-Modeling with Echo State Networks

Biopharma Is Going Digital … Bit by Bit

Echo state network (ESN), which efficiently models nonlinear dynamic systems, has been proposed as a special form of recurrent neural network. However, most of the proposed ESNs consist of complex reservoir structures, leading to excessive computational cost. Recently, minimum complexity ESNs were proposed and proved to exhibit high performance and low computational cost. In this paper, we propose a simple deterministic ESN with a loop reservoir, i.e., an ESN with an adjacent-feedback loop reservoir. The novel reservoir is constructed by introducing regular adjacent feedback based on the simplest loop reservoir. Only a single free parameter is tuned, which considerably simplifies the ESN construction. The combination of a simplified reservoir and fewer free parameters provides superior prediction performance. In the benchmark datasets and real-world tasks, our scheme obtains higher prediction accuracy with relatively low complexity, compared to the classic ESN and the minimum complexity ESN. Furthermore, we prove that all the linear ESNs with the simplest loop reservoir possess the same memory capacity, arbitrarily converging to the optimal value.

As a novel recurrent neural network (RNN), an echo state network (ESN) that utilizes a reservoir with many randomly connected internal units and only trains the readout, avoids increased complexity of training procedures faced by traditional RNN. The ESN can cope with complex nonlinear systems because of its dynamical properties and has been applied in hydrological forecasting and load forecasting. Due to the linear regression algorithm usually adopted by generic ESN to train the output weights, an ill-conditioned solution might occur, degrading the generalization ability of the ESN. In this study, the ESN with Bayesian regularization (BESN) is proposed for short-term power production forecasting of small hydropower (SHP) plants. According to the Bayesian theory, the weights distribution in space is considered and the optimal output weights are obtained by maximizing the posterior probabilistic distribution. The evidence procedure is employed to gain optimal hyperparameters for the BESN model. The recorded data obtained from the SHP plants in two different counties, located in Yunnan Province, China, are utilized to validate the proposed model. For comparison, the feed-forward neural networks with Levenberg-Marquardt algorithm (LM-FNN) and the generic ESN are also employed. The results indicate that BESN outperforms both LM-FNN and ESN.

Echo state network (ESN) has recently attracted increasing interests because of its superior capability in modeling nonlinear dynamic systems. In the conventional echo state network model, its dynamic reservoir (DR) has a random and sparse topology, which is far from the real biological neural networks from both structural and functional perspectives. We hereby propose three novel types of echo state networks with new dynamic reservoir topologies based on complex network theory, i.e., with a small-world topology, a scale-free topology, and a mixture of small-world and scale-free topologies, respectively. We then analyze the relationship between the dynamic reservoir structure and its prediction capability. We utilize two commonly used time series to evaluate the prediction performance of the three proposed echo state networks and compare them to the conventional model. We also use independent and identically distributed time series to analyze the short-term memory and prediction precision of these echo state networks. Furthermore, we study the ratio of scale-free topology and the small-world topology in the mixed-topology network, and examine its influence on the performance of the echo state networks. Our simulation results show that the proposed echo state network models have better prediction capabilities, a wider spectral radius, but retain almost the same short-term memory capacity as compared to the conventional echo state network model. We also find that the smaller the ratio of the scale-free topology over the small-world topology, the better the memory capacities.

The echo state network (ESN) employs a huge reservoir with sparsely and randomly connected internal nodes and only trains the output weights, which avoids the suboptimal problem, exploding and vanishing gradients, high complexity and other disadvantages faced by traditional recurrent neural network (RNN) training. In light of the outstanding adaption to nonlinear dynamical systems, ESN has been applied into a wide range of applications. However, in the era of Big Data, with an enormous amount of data being generated continuously every day, the data are often distributed and stored in real applications, and thus the centralized ESN training process is prone to being technologically unsuitable. In order to achieve the requirement of Big Data applications in the real world, in this study we propose an algorithm and its implementation for distributed ESN training. The mentioned algorithm is based on the parallel particle swarm optimization (P-PSO) technique and the implementation uses Spark, a famous large-scale data processing framework. Four extremely large-scale datasets, including artificial benchmarks, real-world data and image data, are adopted to verify our framework on a stretchable platform. Experimental results indicate that the proposed work is accurate in the era of Big Data, regarding speed, accuracy and generalization capabilities.

Echo state networks (ESNs), as efficient and powerful computational models for approximating nonlinear dynamical systems, have been successfully applied in financial time series forecasting. Reservoir constructions in standard ESNs rely on trials and errors in real applications due to a series of randomized model building stages. A novel form of ESN with deterministically constructed reservoir is competitive with standard ESN by minimal complexity and possibility of optimizations for ESN specifications. In this paper, forecasting performances of deterministic ESNs are investigated in stock price prediction applications. The experiment results on two benchmark datasets (Shanghai Composite Index and S&P500) demonstrate that deterministic ESNs outperform standard ESN in both accuracy and efficiency, which indicate the prospect of deterministic ESNs for financial prediction.

Echo State Networks (ESNs) are recurrent neural networks that map an input signal to a high-dimensional dynamical system, called reservoir, and possess adaptive output weights. The output weights are trained such that the ESN’s output signal fits the desired target signal. Classical reservoirs are sparse and randomly connected networks. In this article, we investigate the effect of different network topologies on the performance of ESNs. Specifically, we use two types of networks to construct clustered reservoirs of ESN: the clustered Erdös–Rényi and the clustered Barabási-Albert network model. Moreover, we compare the performance of these clustered ESNs (CESNs) and classical ESNs with the random reservoir by employing them to two different tasks: frequency filtering and the reconstruction of chaotic signals. By using a clustered topology, one can achieve a significant increase in the ESN’s performance.

This paper introduces an Electrical Submersible Pump (ESP) model based on the Echo State Network (ESN) neural network. ESPs are commonly used in oil extraction, and their performance is influenced by a variety of factors, making accurate modeling crucial for optimizing operations and maintenance. ESN is a type of recurrent neural network with unique dynamic memory capabilities, making it suitable for handling time-series data and modeling nonlinear dynamic systems. The article details the ESN network structure and its application in the ESP model, including how to use ESN to predict performance parameters and diagnose faults in ESPs. Compared with traditional models, the ESN model shows significant advantages in prediction accuracy and computational efficiency. The results indicate that the ESN-based ESP model can effectively simulate the dynamic behavior of ESPs, providing a powerful tool for real-time monitoring and fault prevention of ESPs.

Deterministic echo state network (ESN) models integrated with particle swarm optimization (PSO) are proposed to improve the accuracy and efficiency of stock price forecasting. ESNs have been successfully applied to financial time series forecasting because of their efficient and powerful computational ability in approximating nonlinear dynamical systems. However, reservoir construction in standard ESNs is primarily driven by a series of randomized model-building stages, because of which both researchers and practitioners have to rely on a series of trials and errors to determine parameters. An ESN with a deterministically constructed reservoir is comparable in performance to a standard ESN and has minimal complexity as well as potential for optimizations with regard to ESN parameters. In this paper, forecasting performances of the proposed PSO-DESN models are compared with those of standard ESNs for stock price prediction on the benchmark dataset of S&P 500. The comparison results demonstrate that the proposed PSO-DESNs exhibit better performance in stock price forecasting in terms of both accuracy and efficiency, thereby verifying the potential of PSO-DESNs for financial predictions.

Reservoir computing (RC) is considered as a suitable alternative for descending gradient methods in recursive neural networks (RNNs) training. The echo state network (ESN) is a platform for RC and nonlinear system simulation in the cloud environment with many external users. In the past researches, the highest eigenvalue of reservoir connection weight (spectral radius) was used to predict reservoir dynamics. Some researchers have illustrated; the characteristics of scale-free and small-world can improve the approximation capability in echo state networks; however, recent studies have shown importance of the infrastructures such as clusters and the stability criteria of these reservoirs as altered. In this research, we suggest a high clustered ESN called HCESN that its internal neurons are interconnected in form of clusters. Each of the clusters contains one backbone and a number of local nodes. We implemented a classical clustering algorithm, called K-means, and three optimization algorithms including genetic algorithm (GA), differential evolution (DE), and particle swarm optimization (PSO) to improve the clustering efficiency of the new reservoir and compared them with each other. For investigating the spectral radius and predictive power of the resulting reservoirs, we also applied them to the laser time series and the Mackey-Glass dynamical system. It is demonstrated that new clustered reservoirs have some specifications of biologic neural systems and complex networks like average short path length, high clustering coefficient, and power-law distribution. The empirical results illustrated that the ESN based on PSO could strikingly enhance echo state property (ESP) and obtains less chaotic time series prediction error compared with other works and the original version of ESN. Therefore, it can approximate nonlinear dynamical systems and predict the chaotic time series.

Optimizing simple deterministically constructed cycle reservoir network with a Redundant Unit Pruning Auto-Encoder algorithm

Echo state networks (ESNs) are a novel form of recurrent neural networks (RNNs) that provide an efficient and powerful computational model approximating nonlinear dynamical systems. A unique feature of an ESN is that a large number of neurons (the "reservoir") are used, whose synaptic connections are generated randomly, with only the connections from the reservoir to the output modified by learning. Why a large randomly generated fixed RNN gives such excellent performance in approximating nonlinear systems is still not well understood. In this brief, we apply random matrix theory to examine the properties of random reservoirs in ESNs under different topologies (sparse or fully connected) and connection weights (Bernoulli or Gaussian). We quantify the asymptotic gap between the scaling factor bounds for the necessary and sufficient conditions previously proposed for the echo state property. We then show that the state transition mapping is contractive with high probability when only the necessary condition is satisfied, which corroborates and thus analytically explains the observation that in practice one obtains echo states when the spectral radius of the reservoir weight matrix is smaller than 1.

Participation and influence of citizens are crucial requirements to ensure sustainable and responsible land use planning. Notwithstanding, both documented and anecdotal evidence indicate that citizens’ influence in planning is still limited, especially in the agenda-setting phase. One explanation is that the design of geospatial tools and participation in land use planning is often limited to elites and experts and less to ordinary citizens. Recent studies propose that digital twins could ensure sustainable and responsible land use planning where the influence of citizens can be significantly observed. Adapting Kingdon's multiple streams framework to include elements of sociotechnical artefacts, this study aims to test this assertion and verify how citizens interacting with government institutions at different levels can employ digital twins to find agenda status for their land use issues and proposals. This study employed a systematic review following the PRISMA process to identify 34 articles about applying digital twins for citizen participation in planning decision-making. The study reveals that to improve the participation and influence of citizens, the development of digital twins needs to be citizen-centric. Data from digital twins should be presented in a form non-experts can understand. Qualities for digital twins to promote citizen participation include being interactive and user-friendly, smooth visualisation and immersive experience, inclusiveness, and privacy-oriented. In line with Kingdon’s framework, citizens could frame, convince, and propose land use interventions. The findings also reveal two ways of citizen participation: (1) providing data for developing digital twins and (2) utilising digital twins to analyse and identify key land use challenges and to push forward land use claims and proposals within a policy system.

Real-time Error Compensation Transfer Learning with Echo State Networks for Enhanced Wind Power Prediction

Echo-state network based adaptive fuzzy sliding-mode consensus control scheme for nonlinear multi-agent systems with external disturbances.