Machine learning of partial differential equations from noise data

Machine learning of partial differential equations(PDEs)from data is a potential breakthrough for addressing the lack of physical equations in complex dynamic systems.Recently,sparse regression has emerged as an attractive approach.However,noise presents the biggest challenge in sparse regression for identifying equations,as it relies on local derivative evaluations of noisy data.This study proposes a simple and general approach that significantly improves noise robustness by projecting the evaluated time derivative and partial differential term into a subspace with less noise.This method enables accurate reconstruction of PDEs involving high-order derivatives,even from data with considerable noise.Additionally,we discuss and compare the effects of the proposed method based on Fourier subspace and POD(proper orthogonal decomposition)subspace.Generally,the latter yields better results since it preserves the maximum amount of information.

Symmetric Learning Data Augmentation Model for Underwater Target Noise Data Expansion

An important issue for deep learning models is the acquisition of training of data.Without abundant data from a real production environment for training,deep learning models would not be as widely used as they are today.However,the cost of obtaining abundant real-world environment is high,especially for underwater environments.It is more straightforward to simulate data that is closed to that from real environment.In this paper,a simple and easy symmetric learning data augmentation model(SLDAM)is proposed for underwater target radiate-noise data expansion and generation.The SLDAM,taking the optimal classifier of an initial dataset as the discriminator,makes use of the structure of the classifier to construct a symmetric generator based on antagonistic generation.It generates data similar to the initial dataset that can be used to supplement training data sets.This model has taken into consideration feature loss and sample loss function in model training,and is able to reduce the dependence of the generation and expansion on the feature set.We verified that the SLDAM is able to data expansion with low calculation complexity.Our results showed that the SLDAM is able to generate new data without compromising data recognition accuracy,for practical application in a production environment.

Influence of image data set noise on classification with a convolutional network

To evaluate the influence of data set noise, the network in network(NIN) model is introduced and the negative effects of different types and proportions of noise on deep convolutional models are studied. Different types and proportions of data noise are added to two reference data sets, Cifar-10 and Cifar-100. Then, this data containing noise is used to train deep convolutional models and classify the validation data set. The experimental results show that the noise in the data set has obvious adverse effects on deep convolutional network classification models. The adverse effects of random noise are small, but the cross-category noise among categories can significantly reduce the recognition ability of the model. Therefore, a solution is proposed to improve the quality of the data sets that are mixed into a single noise category. The model trained with a data set containing noise is used to evaluate the current training data and reclassify the categories of the anomalies to form a new data set. Repeating the above steps can greatly reduce the noise ratio, so the influence of cross-category noise can be effectively avoided.

Picture-Neutrosophic Trusted Safe Semi-Supervised Fuzzy Clustering for Noisy Data

Clustering is a crucial method for deciphering data structure and producing new information.Due to its significance in revealing fundamental connections between the human brain and events,it is essential to utilize clustering for cognitive research.Dealing with noisy data caused by inaccurate synthesis from several sources or misleading data production processes is one of the most intriguing clustering difficulties.Noisy data can lead to incorrect object recognition and inference.This research aims to innovate a novel clustering approach,named Picture-Neutrosophic Trusted Safe Semi-Supervised Fuzzy Clustering(PNTS3FCM),to solve the clustering problem with noisy data using neutral and refusal degrees in the definition of Picture Fuzzy Set(PFS)and Neutrosophic Set(NS).Our contribution is to propose a new optimization model with four essential components:clustering,outlier removal,safe semi-supervised fuzzy clustering and partitioning with labeled and unlabeled data.The effectiveness and flexibility of the proposed technique are estimated and compared with the state-of-art methods,standard Picture fuzzy clustering(FC-PFS)and Confidence-weighted safe semi-supervised clustering(CS3FCM)on benchmark UCI datasets.The experimental results show that our method is better at least 10/15 datasets than the compared methods in terms of clustering quality and computational time.

Multiple Data Augmentation Strategy for Enhancing the Performance of YOLOv7 Object Detection Algorithm

The object detection technique depends on various methods for duplicating the dataset without adding more images.Data augmentation is a popularmethod that assists deep neural networks in achieving better generalization performance and can be seen as a type of implicit regularization.Thismethod is recommended in the casewhere the amount of high-quality data is limited,and gaining new examples is costly and time-consuming.In this paper,we trained YOLOv7 with a dataset that is part of the Open Images dataset that has 8,600 images with four classes(Car,Bus,Motorcycle,and Person).We used five different data augmentations techniques for duplicates and improvement of our dataset.The performance of the object detection algorithm was compared when using the proposed augmented dataset with a combination of two and three types of data augmentation with the result of the original data.The evaluation result for the augmented data gives a promising result for every object,and every kind of data augmentation gives a different improvement.The mAP@.5 of all classes was 76%,and F1-score was 74%.The proposed method increased the mAP@.5 value by+13%and F1-score by+10%for all objects.

Research on Real-time Monitoring of Abnormal Seismic Noise

The noise data in vertical component records of 85 seismic stations in Fujian Province during 2012 is used as the research object in this paper. The noise data is divided into fiveminute segments to calculate the power spectra. The high reference line and low reference line of station are then identified by drawing a probability density function graph( PDF)using the power spectral probability density function. Moreover, according to the anomalies of PDF graphs in 85 seismic stations,the abnormal noise is divided into four categories: dropped packet, low noise, high noise, and median noise anomalies.Afterwards,four selection methods are found by the high or low noise reference line of the stations,and the system of real-time monitoring of seismic noise is formed by combining the four selection methods. Noise records of 85 seismic stations in Fujian Province in July2013 are selected for verification,and the results show that the anomalous noise-recognition system could reach a 90% success rate at most stations and the effect of selection are very good. Therefore,it could be applied to the seismic noise real-time monitoring in stations.

ADAPTIVE FUSION ALGORITHMS BASED ON WEIGHTED LEAST SQUARE METHOD

Weighted fusion algorithms, which can be applied in the area of multi-sensor data fusion, are advanced based on weighted least square method. A weighted fusion algorithm, in which the relationship between weight coefficients and measurement noise is established, is proposed by giving attention to the correlation of measurement noise. Then a simplified weighted fusion algorithm is deduced on the assumption that measurement noise is uncorrelated. In addition, an algorithm, which can adjust the weight coefficients in the simplified algorithm by making estimations of measurement noise from measurements, is presented. It is proved by emulation and experiment that the precision performance of the multi-sensor system based on these algorithms is better than that of the multi-sensor system based on other algorithms.