Deep Learning Applied to Computational Mechanics:A Comprehensive Review,State of the Art,and the Classics

Three recent breakthroughs due to AI in arts and science serve as motivation:An award winning digital image,protein folding,fast matrix multiplication.Many recent developments in artificial neural networks,particularly deep learning(DL),applied and relevant to computational mechanics(solid,fluids,finite-element technology)are reviewed in detail.Both hybrid and pure machine learning(ML)methods are discussed.Hybrid methods combine traditional PDE discretizations with ML methods either(1)to help model complex nonlinear constitutive relations,(2)to nonlinearly reduce the model order for efficient simulation(turbulence),or(3)to accelerate the simulation by predicting certain components in the traditional integration methods.Here,methods(1)and(2)relied on Long-Short-Term Memory(LSTM)architecture,with method(3)relying on convolutional neural networks.Pure ML methods to solve(nonlinear)PDEs are represented by Physics-Informed Neural network(PINN)methods,which could be combined with attention mechanism to address discontinuous solutions.Both LSTM and attention architectures,together with modern and generalized classic optimizers to include stochasticity for DL networks,are extensively reviewed.Kernel machines,including Gaussian processes,are provided to sufficient depth for more advanced works such as shallow networks with infinite width.Not only addressing experts,readers are assumed familiar with computational mechanics,but not with DL,whose concepts and applications are built up from the basics,aiming at bringing first-time learners quickly to the forefront of research.History and limitations of AI are recounted and discussed,with particular attention at pointing out misstatements or misconceptions of the classics,even in well-known references.Positioning and pointing control of a large-deformable beam is given as an example.

Analysis of terrestrial water storage changes in the Shaan-Gan-Ning Region using GPS and GRACE/GFO

Both the Global Positioning System(GPS)and Gravity Recovery and Climate Experiment(GRACE)/GRACE Follow-On(GFO)provide effective tools to infer surface mass changes.In this paper,we combined GPS,GRACE/GFO spherical harmonic(SH)solutions and GRACE/GFO mascon solutions to analyze the total surface mass changes and terrestrial water storage(TWS)changes in the Shaan-Gan-Ning Region(SGNR)over the period from December 2010 to February 2021.To improve the reliability of GPS inversion results,an improved regularization Laplace matrix and monthly optimal regularization parameter estimation strategy were employed to solve the ill-posed problem.The results show that the improved Laplace matrix can suppress the edge effects better than that of the traditional Laplace matrix,and the corre-lation coefficient and standard deviation(STD)between the original signal and inversion results from the traditional and improved Laplace matrix are 0.84 and 0.88,and 17.49 mm and 15.16 mm,respectively.The spatial distributions of annual amplitudes and time series changes for total surface mass changes derived from GPS agree well with GRACE/GFO SH solutions and mascon solutions,and the correlation coefficients of total surface mass change time series between GPS and GRACE/GFO SH solutions,GPS and GRACE/GFO mascon solutions are 0.80 and 0.77.However,the obvious differences still exist in local regions.In addition,the seasonal characteristics,increasing and decreasing rate of TWS change time series derived from GPS,GRACE/GFO SH and mascon solutions agree well with the Global Land Data Assimilation System(GLDAS)hydrological model in the studied area,and generally consistent with the precipitation data.Meanwhile,TWS changes derived from GPS and GRACE mascon solutions in the SGNR are more reliable than those of GRACE SH solutions over the period from January 2016 to June 2017(the final operation phase of the GRACE mission).

An Efficient Deep Learning-based Content-based Image Retrieval Framework

The use of massive image databases has increased drastically over the few years due to evolution of multimedia technology.Image retrieval has become one of the vital tools in image processing applications.Content-Based Image Retrieval(CBIR)has been widely used in varied applications.But,the results produced by the usage of a single image feature are not satisfactory.So,multiple image features are used very often for attaining better results.But,fast and effective searching for relevant images from a database becomes a challenging task.In the previous existing system,the CBIR has used the combined feature extraction technique using color auto-correlogram,Rotation-Invariant Uniform Local Binary Patterns(RULBP)and local energy.However,the existing system does not provide significant results in terms of recall and precision.Also,the computational complexity is higher for the existing CBIR systems.In order to handle the above mentioned issues,the Gray Level Co-occurrence Matrix(GLCM)with Deep Learning based Enhanced Convolution Neural Network(DLECNN)is proposed in this work.The proposed system framework includes noise reduction using histogram equalization,feature extraction using GLCM,similarity matching computation using Hierarchal and Fuzzy c-Means(HFCM)algorithm and the image retrieval using DLECNN algorithm.The histogram equalization has been used for computing the image enhancement.This enhanced image has a uniform histogram.Then,the GLCM method has been used to extract the features such as shape,texture,colour,annotations and keywords.The HFCM similarity measure is used for computing the query image vector's similarity index with every database images.For enhancing the performance of this image retrieval approach,the DLECNN algorithm is proposed to retrieve more accurate features of the image.The proposed GLCM+DLECNN algorithm provides better results associated with high accuracy,precision,recall,f-measure and lesser complexity.From the experimental results,it is clearly observed that the proposed system provides efficient image retrieval for the given query image.

A numerical method to calculate dwell time for electron in semiconductor nanostructure

To some extent,the operational quickness of semiconductor devices depends on the transmission time of an electron through semiconductor nanostructures.However,the calculation of transmission time is very difficult,thanks to both the contentious definition of the transmission time in quantum mechanics and the complicated effective potential functions experienced by electrons in semiconductor devices.Here,based on an improved transfer matrix method to numerically solve the Schr?dinger equation and H G Winful’s relationship to calculate the dwell time,we develop a numerical approach to evaluate the transmission time of an electron in semiconductor devices.Compared to the exactly resolvable case of the rectangular potential barrier,the established numerical approach possesses high precision and small error,which may be employed to explore the dynamic response and operating speed of semiconductor devices.This proposed numerical method is successfully applied to the calculation of dwell time for an electron in double rectangular potential barriers and the dependence of transmission time on the number of potential barriers is revealed.

Efficient wireless multicast retransmission using network coding

In wireless multicast, network coding has recently attracted attentions as a substantial improvement to packet retransmission schemes. However, the problem of finding the optimal network code which minimizes the retransmissions is hard to solve or approximate. This paper presents two schemes to reduce the number of retransmissions for reliable multicast efficiently. One is retransmission using network coding based on improved Vandermonde matrix （VRNC）, the other is retransmission using network coding based on adaptive improved Vandermonde matrix （AVRNC）. Using VRNC scheme the sender selects the packets all receivers have lost and encodes them with improved Vandermonde matrix; when receivers receive enough encoded retransmission packets, all the lost packets can be recovered. With AVRNC scheme, the sender can obtain the recovery information from all the receivers after sending out per retransmission packet, and then the improved Vandermonde matrix can be updated, thus reducing the complexity of encoding and decoding. Our proposed schemes can achieve the theoretical lower bound assuming retransmission packets lossless, and approach the theoretical lower bound considering retransmission packets loss. Simulation results show that the proposed algorithms can efficiently reduce the number ofretransmissions, thus improving transmission efficiency.