Nonlinear Memory Research Articles

Effects of COVID-19 on electric energy consumption in Turkey and ANN-based short-term forecasting

: Due to the coronavirus, millions of people worldwide carry out their work, education, shopping, culture, and entertainment activities from their homes now using the advantages of today's technology. Apart from this, patient care and follow-up are carried out with the help of electronic equipment especially in the institutions where health services are provided. It is important to provide a reliable electricity supply for humanity so that people can perform all these services. In this study, the outlook of energy in Turkey was examined. The current energy consumption and investments were examined. Then, the precautions by the government in the pandemic period according to the occurrence and spread of COVID-19 in the country are given in chronological order. The actual electricity consumption data were obtained daily across the country, after all these precautions. It was observed that electricity consumption decreased significantly, especially on restricted days. It is inarguable that energy consumption estimation should be made in the short term so that the energy sector is not adversely affected by this situation. In this study, more accurate short-term consumption forecasting methods were developed during the COVID-19 pandemic period: nonlinear autoregressive (NARX) and long short-term memory (LSTM) artificial neural networks (ANNs). Between January and April 2019 electrical consumption data were used to train and validate the forecast prediction. The NARX and LSTM are potential candidates for effective forecasting of electricity consumption. However, the obtained LSTM results suggest that the proposed method performs better than the NARX ANN.

Multistep Wind Speed Forecasting Based on a Hybrid Model of VMD and Nonlinear Autoregressive Neural Network

Reducing the costs of wind power requires reasonable wind farm operation and maintenance strategies, and then to develop these strategies, the 24-hour ahead forecasting of wind speed is necessary. However, existing prediction work is mostly limited to 5 hours. This work developed a diurnal forecasting methodology for the regional wind farm according to real-life data of the supervisory control and data acquisition (SCADA) system of a wind farm from Jiangxi Province. The methodology used the variational mode decomposition (VMD) to extract wind characteristics, and then, the characteristics were put in the nonlinear autoregressive neural network (Narnet) and long short-term memory network (LSTM) for prediction; the forecast results of VMD-Narnet and VMD-LSTM are compared with the actual wind speed. The comparison results indicate that compared with the LSTM, the Narnet improves the accuracy by 61.90% in 24 hours on wind speed forecasting, and the predicted time horizon was improved by 6.8 hours. This work strongly supports the development of wind farm operation and maintenance strategies and provides a foundation for the reduction of wind power costs.

Data-Driven Trajectory Prediction of Grid Power Frequency Based on Neural Models

Frequency in power systems is a real-time information that shows the balance between generation and demand. Good system frequency observation is vital for system security and protection. This paper analyses the system frequency response following disturbances and proposes a data-driven approach for predicting it by using machine learning techniques like Nonlinear Auto-regressive (NAR) Neural Networks (NN) and Long Short Term Memory (LSTM) networks from simulated and measured Phasor Measurement Unit (PMU) data. The proposed method uses a horizon-window that reconstructs the frequency input time-series data in order to predict the frequency features such as Nadir. Simulated scenarios are based on the gradual inertia reduction by including non-synchronous generation into the Nordic 32 test system, whereas the PMU collected data is taken from different locations in the Nordic Power System (NPS). Several horizon-windows are experimented in order to observe an adequate margin of prediction. Scenarios considering noisy signals are also evaluated in order to provide a robustness index of predictability. Results show the proper performance of the method and the adequate level of prediction based on the Root Mean Squared Error (RMSE) index.

Blow-up rates for a higher-order semilinear parabolic equation with nonlinear memory term

ABSTRACT In this paper, we establish blow-up rates for a higher-order semilinear parabolic equation with nonlocal in time nonlinearity with no positive assumption on the solution. We also give Liouville-type theorem for higher-order semilinear parabolic equation with infinite memory nonlinear term which plays the main tools to prove our blow-up rate result. Finally, we study the well-posedness of mild solutions.

Global well-posedness for effectively damped wave models with nonlinear memory

In this paper, we study the Cauchy problem for a special family of effectively damped wave models with nonlinear memory on the right-hand side. Our goal is to prove global (in time) well-posedness results for Sobolev solutions. Due to the effective dissipation the model is parabolic like from the point of view of energy decay estimates of the corresponding linear Cauchy problem with vanishing right-hand side. For this reason there appears a Fujita type exponent as a threshold. Applying modern tools from Harmonic Analysis we prove several results by taking into consideration different regularity properties of the data.

Blow-up of energy solutions for the semilinear generalized Tricomi equation with nonlinear memory term

<abstract><p>In this paper, we investigate blow-up conditions for the semilinear generalized Tricomi equation with a general nonlinear memory term in $ \mathbb{R}^n $ by using suitable functionals and employing iteration procedures. Particularly, a new combined effect from the relaxation function and the time-dependent coefficient is found.</p></abstract>

Initial value problem for fractional Volterra integrodifferential pseudo-parabolic equations

In this paper, we investigate a initial value problem for the Caputo time-fractional pseudo-parabolic equations with fractional Laplace operator of order 0 < ν ≤ 1 and the nonlinear memory source term. For 0 < ν < 1, the problem will be considered on a bounded domain of ℝd. By some Sobolev embeddings and the properties of the Mittag-Leffler function, we will give some results on the existence and the uniqueness of mild solution for problem (1.1) below. When ν = 1, we will introduce some Lp − Lq estimates, and based on them we derive the global existence of a mild solution in the whole space ℝd.

Water Quality Prediction Using Artificial Intelligence Algorithms.

During the last years, water quality has been threatened by various pollutants. Therefore, modeling and predicting water quality have become very important in controlling water pollution. In this work, advanced artificial intelligence (AI) algorithms are developed to predict water quality index (WQI) and water quality classification (WQC). For the WQI prediction, artificial neural network models, namely nonlinear autoregressive neural network (NARNET) and long short-term memory (LSTM) deep learning algorithm, have been developed. In addition, three machine learning algorithms, namely, support vector machine (SVM), K-nearest neighbor (K-NN), and Naive Bayes, have been used for the WQC forecasting. The used dataset has 7 significant parameters, and the developed models were evaluated based on some statistical parameters. The results revealed that the proposed models can accurately predict WQI and classify the water quality according to superior robustness. Prediction results demonstrated that the NARNET model performed slightly better than the LSTM for the prediction of the WQI values and the SVM algorithm has achieved the highest accuracy (97.01%) for the WQC prediction. Furthermore, the NARNET and LSTM models have achieved similar accuracy for the testing phase with a slight difference in the regression coefficient (RNARNET = 96.17% and RLSTM = 94.21%). This kind of promising research can contribute significantly to water management.

Stochastic dynamic for an extensible beam equation with localized nonlinear damping and linear memory

In this paper, we concerned to prove the existence of a random attractor for the stochastic dynamical system generated by the extensible beam equation with localized non-linear damping and linear memory defined on bounded domain. First we investigate the existence and uniqueness of solutions, bounded absorbing set, then the asymptotic compactness. Longtime behavior of solutions is analyzed. In particular, in the non-autonomous case, the existence of a random attractor attractors for solutions is achieved.

Effect of directed aging on nonlinear elasticity and memory formation in a material

Disordered solids often change their elastic response as they slowly age. Using experiments and simulations, we study how aging disordered planar networks under an applied stress affects their nonlinear elastic response. We are able to modify dramatically the elastic properties of our systems in the nonlinear regime. Using simulations, we study two models for the microscopic evolution of properties of such a material; the first considers changes in the material strength, while the second considers distortions in the microscopic geometry. Both models capture different aspects of the experiments including the encoding of memories of the aging history of the system and the dramatic effects on the material's nonlinear elastic properties. Our results demonstrate how aging can be used to create complex elastic behavior in the nonlinear regime.Received 15 August 2020Accepted 22 October 2020DOI:https://doi.org/10.1103/PhysRevResearch.2.043231Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAgingElasticityMemoryPoisson ratioPhysical SystemsAmorphous materialsNetworksPolymers & Soft MatterCondensed Matter, Materials & Applied Physics

Application of deep neural techniques in predictive modelling for the estimation of Escherichia coli growth rate.

To develop a predictive model for Escherichia coli using deep neural networks. Batch experiments are conducted at different temperatures closer to optimum value (36·5°C, 37°C, 37·5°C, 38°C and 38·5°C) to obtain the growth curves of E .coli K-12. Two primary models namely modified Gompertz and new logistic are chosen. Three secondary models namely Gaussian, nonlinear autoregressive eXogenous (NARX) model and long short-term memory (LSTM) are developed. The novelty in this paper is the development of secondary models using artificial neural network (ANN) and deep network. The performance measures chosen to compare the developed primary and secondary models are correlation coefficient (R2 ), root-mean-square error (RMSE) and accuracy factor (Af ). Results show that modified Gompertz model has better R2 (0·99) and RMSE (0·019) when compared to new logistic model. Also, the deep network model outperforms other secondary models. Based on the primary and novel secondary model, a predictive model (tertiary model) is developed with improved accuracy and is validated. The proposed predictive model exhibit good validation results in terms of RMSE and R2 values and can be applied for determining the growth rate of E. coli at a particular temperature value. The proposed model can be used in food processing industries during enzyme production such as Chymosin, to predict the growth rate of E. coli as a function of temperature. Also, the developed LSTM and NARX models can be used to predict maximum specific growth rate of other microbial strains with proper training.

A New Expanded Mixed Finite Element Method for Parabolic Integro-Differential Equations with Nonlinear Memory

A new extended mixed finite element method (MFEM) is suggested for parabolic integrodifferential equations (PIDEs) with nonlinear memory. On the contrary, of the extended mixed scheme, the modern extended mixed element system refers to an asymmetric positive well known and the two gradient equation as well as the flux equation can be isolated from the scalar undefined equation. The presence and uniqueness of the semi-discrete system can be confirmed and error estimates can be achieved for semidiscrete. Fully discrete can be said to be discretization.

Attractors for a quasilinear viscoelastic equation with nonlinear damping and memory

In this paper, the long time behavior of a quasilinear viscoelastic equation with nonlinear damping is considered. Under suitable assumptions, the existence of global attractors is established.

Markov Decision Process Based Design of SWIPT Systems: Non-Linear EH Circuits, Memory, and Impedance Mismatch

In this paper, we study simultaneous wireless information and power transfer (SWIPT) systems employing practical non-linear energy harvester (EH) circuits. Since the voltage across the reactive elements of realistic EH circuits cannot drop or rise instantaneously, EHs have memory which we model with a Markov decision process (MDP). Moreover, since an analytical model that accurately models all non-linear effects and the unavoidable impedance mismatch of EHs is not tractable, we propose a learning based model for the EH circuit. We optimize the input signal distribution for maximization of the harvested power under a constraint on the minimum mutual information between transmitter (TX) and information receiver (IR). We distinguish the cases where the MDP state is known and not known at TX and IR. When the MDP state is known, the formulated optimization problem for the harvested power is convex. In contrast, if TX and IR do not know the MDP state, the resulting optimization problem is non-convex and solved via alternating optimization, which is shown to yield a limit point of the problem. Our simulation results reveal that the rate-power region of the considered SWIPT system depends on the symbol duration, the EH input power level, the EH impedance mismatch, and the type of EH circuit. In particular, a shorter symbol duration enables higher bit rates at the expense of a significant decrease in the average harvested power. Furthermore, whereas half-wave rectifiers outperform full-wave rectifiers in the low and medium input power regimes, full-wave rectifiers are preferable if the input power at the EH is high.

Tractable nonlinear memory functions as a tool to capture and explain dynamical behaviors.

Mathematical approaches from dynamical systems theory are used in a range of fields. This includes biology where they are used to describe processes such as protein-protein interaction and gene regulatory networks. As such networks increase in size and complexity, detailed dynamical models become cumbersome, making them difficult to explore and decipher. This necessitates the application of simplifying and coarse graining techniques to derive explanatory insight. Here we demonstrate that Zwanzig-Mori projection methods can be used to arbitrarily reduce the dimensionality of dynamical networks while retaining their dynamical properties. We show that a systematic expansion around the quasi-steady-state approximation allows an explicit solution for memory functions without prior knowledge of the dynamics. The approach not only preserves the same steady states but also replicates the transients of the original system. The method correctly predicts the dynamics of multistable systems as well as networks producing sustained and damped oscillations. Applying the approach to a gene regulatory network from the vertebrate neural tube, a well-characterized developmental transcriptional network, identifies features of the regulatory network responsible for its characteristic transient behavior. Taken together, our analysis shows that this method is broadly applicable to multistable dynamical systems and offers a powerful and efficient approach for understanding their behavior.

Control and enhancement of photo-induced refractive index modifications in fused silica

A thorough study of the femtosecond photo-inscription of optical waveguides in fused silica is presented. Quantitative phase microscopy was used to study the variation of the index contrast of the waveguides as a function of the writing conditions. It is revealed that waveguides based exclusively on Type I refractive index modifications are difficult to form for pulses longer than 300 fs. We show that this limitation can be circumvented by scanning the laser beam multiple times at low pulse energy. We also demonstrate that by equally multiplying the scan speed and the number of passes, the index contrast can be increased, which was not expected for the low-repetition-rate regime. Based on the nonlinear ionization memory, we propose an explanation for this phenomenon. For shorter pulses, multiple passes of the beam allowed for the formation of waveguides with an enhanced index contrast while preserving the morphology and uniformity of Type I modifications. Index contrasts up to 9 × 10−3 in Heraeus F300 fused silica are reported. Using this method, waveguides that exhibits single mode operation at wavelengths of 405, 633, 980 and 1550 nm were successfully inscribed.

Interplay effects on blow-up of weakly coupled systems for semilinear wave equations with general nonlinear memory terms

In this paper, we study weakly coupled systems for semilinear wave equations with distinct nonlinear memory terms in general forms, and the corresponding single semilinear equation with general nonlinear memory terms. Thanks to fixed point theory, we prove local (in time) existence of solutions with the L1 assumption on the memory kernels. Then, blow-up results for energy solutions are derived by applying iteration methods associated with slicing procedure. We investigate interactions on the blow-up conditions under different decreasing assumptions on the memory term. Particularly, a new threshold for the kernels on interplay effect is found. Additionally, we give some applications of our results on semilinear wave equations and acoustic wave equations.

Large Time Behavior for Inhomogeneous Damped Wave Equations with Nonlinear Memory

We investigate the large time behavior for the inhomogeneous damped wave equation with nonlinear memory ϕtt(t,ω)−Δϕ(t,ω)+ϕt(t,ω)=1Γ(1−ρ)∫0t(t−σ)−ρ|ϕ(σ,ω)|qdσ+μ(ω),t>0, ω∈RN imposing the condition (ϕ(0,ω),ϕt(0,ω))=(ϕ0(ω),ϕ1(ω))inRN, where N≥1, q>1, 0<ρ<1, ϕi∈Lloc1(RN), i=0,1, μ∈Lloc1(RN) and μ≢0. Namely, it is shown that, if ϕ0,ϕ1≥0, μ∈L1(RN) and ∫RNμ(ω)dω>0, then for all q>1, the considered problem has no global weak solution.

Estimating the Memory Parameter for Non-Linear Time Series with Wavelets

The asymptotic theory for the memory parameter estimator constructed from log-regression with wavelets is incomplete for 1/f processes that are not necessarily Gaussian or linear. Such a theory is necessary due to the importance of non-Gaussian and nonlinear long memory models in describing financial time series. To fill this gap, we prove that under an assumption which can be implied by ergodicity and additional ones, the estimator is asymptotically consistent. Then, we apply this estimation method to several economic/financial time series. Our results indicate that a long memory exists in U.S. economic policy uncertainties and we provide possible explanations.

Blow-up results for effectively damped wave models with nonlinear memory

<p style="text-indent:20px;">In this paper, we study the Cauchy problem for a special family of effectively damped wave models with nonlinear memory on the right-hand side. Our goal is to prove blow-up results for local (in time) Sobolev solutions. Due to the effective dissipation the model is parabolic like from the point of view of energy decay estimates of the corresponding linear Cauchy problem with vanishing right-hand side. For this reason we apply the test function method for proving our results.</p>