A Hybrid Method Using HAVOK Analysis and Machine Learning for Predicting Chaotic Time Series.

The prediction of chaotic time series systems has remained a challenging problem in recent decades. A hybrid method using Hankel Alternative View Of Koopman (HAVOK) analysis and machine learning (HAVOK-ML) is developed to predict chaotic time series. HAVOK-ML simulates the time series by reconstructing a closed linear model so as to achieve the purpose of prediction. It decomposes chaotic dynamics into intermittently forced linear systems by HAVOK analysis and estimates the external intermittently forcing term using machine learning. The prediction performance evaluations confirm that the proposed method has superior forecasting skills compared with existing prediction methods.

A Framework for Four-Dimensional Variational Data Assimilation Based on Machine Learning.

The initial field has a crucial influence on numerical weather prediction (NWP). Data assimilation (DA) is a reliable method to obtain the initial field of the forecast model. At the same time, data are the carriers of information. Observational data are a concrete representation of information. DA is also the process of sorting observation data, during which entropy gradually decreases. Four-dimensional variational assimilation (4D-Var) is the most popular approach. However, due to the complexity of the physical model, the tangent linear and adjoint models, and other processes, the realization of a 4D-Var system is complicated, and the computational efficiency is expensive. Machine learning (ML) is a method of gaining simulation results by training a large amount of data. It achieves remarkable success in various applications, and operational NWP and DA are no exception. In this work, we synthesize insights and techniques from previous studies to design a pure data-driven 4D-Var implementation framework named ML-4DVAR based on the bilinear neural network (BNN). The framework replaces the traditional physical model with the BNN model for prediction. Moreover, it directly makes use of the ML model obtained from the simulation data to implement the primary process of 4D-Var, including the realization of the short-term forecast process and the tangent linear and adjoint models. We test a strong-constraint 4D-Var system with the Lorenz-96 model, and we compared the traditional 4D-Var system with ML-4DVAR. The experimental results demonstrate that the ML-4DVAR framework can achieve better assimilation results and significantly improve computational efficiency.

Analysis on leading-fiber-induced Doppler noise in interferometric FBG sensor arrays using polarization switching and PGC hybrid processing method.

The random disturbance in the leading fiber is considered as a vital noise source in the practical interferometric fiber Bragg grating (FBG) sensor array, which is usually interrogated by periodic laser pulse pair. As the two interrogation laser pluses propagate through the leading fiber in a time-sharing manner, the leading fiber disturbance could cause undesired demodulated phase noises to both the polarization state and the pulse-interval, which are summarized as the polarization fading induced noise and the Doppler noise, respectively. This paper focused on the Doppler noise under the demodulation scheme of polarization switching (PS) and phase generated carrier (PGC) hybrid processing method. A model describing the transformation from arbitrary leading fiber stretching to sensor phase background was presented. The complexity was that the Doppler noise was coupled with the birefringence states, as verified by both simulation and experiment. In response to this issue, a two-stage Doppler noise suppression method was proposed, which is based on the PS and PGC hybrid processing and a reference sensor. A processing procedure was presented where the polarization synthesis must be performed before and the reference sensor was considered. Otherwise, the suppression algorithm will be completely invalid due to the mutual coupling of the Doppler noise and the birefringence. Experimental results showed that only after the first stage of polarization synthesis, identical Doppler noise in the two TDM channels could be obtained, with an amplitude error of 0.02 dB. The second stage involved non-sensitive reference sensor subtraction, which achieved a maximum suppression of about 30 dB, which was the highest to be best of our knowledge. The two-stage Doppler noise suppression method was tested for sinusoidal and wideband leading fiber disturbances, providing a solution for practical interferometric FBG array applications.

Photo-induced enhancement of the power factor of Cu2S thermoelectric films.

Element doping is commonly used to adjust the carrier concentrations in semiconductors such as thermoelectric materials. However, the doping process unavoidably brings in defects or distortions in crystal lattices, which further strongly affects the physical properties of the materials. In this work, high energy photons have been used to activate the carriers in Cu2S thermoelectric films. As a result, the carrier concentrations, and the respective electrical conductivity as well as Seebeck coefficient are further changed. The photon-induced electrical transport properties are further analyzed utilizing a Parallel circuit model. Due to the realization of optimized carrier concentrations by photon activation, the power factor of Cu2S film is improved more than 900 times as compared with the dark data. As compared to the traditional doping process, the approach using photon activation can realize the tuning of carrier concentrations without affecting crystal lattice. This method provides an opportunity to investigate the intrinsic physical properties of semiconductor materials without involving traditional element doping process that usually brings in additional lattice defects or distortions.

Couple of the variational iteration method and fractional-order Legendre functions method for fractional differential equations.

We present a new numerical method to get the approximate solutions of fractional differential equations. A new operational matrix of integration for fractional-order Legendre functions (FLFs) is first derived. Then a modified variational iteration formula which can avoid "noise terms" is constructed. Finally a numerical method based on variational iteration method (VIM) and FLFs is developed for fractional differential equations (FDEs). Block-pulse functions (BPFs) are used to calculate the FLFs coefficient matrices of the nonlinear terms. Five examples are discussed to demonstrate the validity and applicability of the technique.

Crystalline structures and misfit strain inside Er silicide nanocrystals self-assembled on Si(001) substrates.

The morphology and crystalline structure of Er silicide nanocrystals self-assembled on the Si(001) substrate were investigated using scanning tunneling microscopy (STM) and transmission electron microscopy (TEM). It was found that the nanowires and nanorods formed at 630 °C has dominant hexagonal AlB(2)-type structure, while inside the nanoislands self-organized at 800 °C the tetragonal ThSi(2)-type structure is prevalent. The lattice analysis via cross-sectional high-resolution TEM demonstrated that internal misfit strain plays an important role in controlling the growth of nanocrystals. With the relaxation of strain, the nanoislands could evolve from a pyramid-like shape into a truncated-hut-like shape.