Identification of partial differential equations from noisy data with integrated knowledge discovery and embedding using evolutionary neural networks

Identification of underlying partial differential equations(PDEs)for complex systems remains a formidable challenge.In the present study,a robust PDE identification method is proposed,demonstrating the ability to extract accurate governing equations under noisy conditions without prior knowledge.Specifically,the proposed method combines gene expression programming,one type of evolutionary algorithm capable of generating unseen terms based solely on basic operators and functional terms,with symbolic regression neural networks.These networks are designed to represent explicit functional expressions and optimize them with data gradients.In particular,the specifically designed neural networks can be easily transformed to physical constraints for the training data,embedding the discovered PDEs to further optimize the metadata used for iterative PDE identification.The proposed method has been tested in four canonical PDE cases,validating its effectiveness without preliminary information and confirming its suitability for practical applications across various noise levels.

肺微小脑膜上皮样结节——认知进展与争论

肺微小脑膜上皮样结节(minute pulmonary meningothelial-like nodules,MPMNs)是一种与脑膜上皮有相似病理学特征的肺部良性小病灶,和恶性肿瘤有相似的影像学表现,可在临床上导致误诊。关于MPMNs的发病机制尚未达成共识,有观点认为MPMNs可能是一种反应性增生,也有观点认为MPMNs与中枢神经系统脑膜瘤有共同的起源和分子机制。了解MPMNs的特征,深入研究其发病机制,有助于提高对该病的认识和诊断水平。本文就MPMNs的临床、病理、影像学特点以及鉴别诊断和发病机制进行综述,并全面分析了其发病机制的研究进展,对进一步探索提出展望。

磁性纳米Fe_(3)O_(4)制备及在酵母RNA提取分析中的应用

磁珠法提取核酸是新冠病毒核酸检测的关键一环。基于此,以安全无毒的酵母RNA为对象,开发了一个涉及多学科化学知识交叉的综合实验,包括Fe_(3)O_(4)纳米磁珠制备与表征、RNA提取方法建立与机制探究、实际样品应用等。本实验既能锻炼学生综合运用化学知识和实验手段解决实际问题的能力,又能引导学生关注公共事件,培养其社会责任感。

A Model Output Machine Learning Method for Grid Temperature Forecasts in the Beijing Area

In this paper, the model output machine learning (MOML) method is proposed for simulating weather consultation, which can improve the forecast results of numerical weather prediction (NWP). During weather consultation, the forecasters obtain the final results by combining the observations with the NWP results and giving opinions based on their experience. It is obvious that using a suitable post-processing algorithm for simulating weather consultation is an interesting and important topic. MOML is a post-processing method based on machine learning, which matches NWP forecasts against observations through a regression function. By adopting different feature engineering of datasets and training periods, the observational and model data can be processed into the corresponding training set and test set. The MOML regression function uses an existing machine learning algorithm with the processed dataset to revise the output of NWP models combined with the observations, so as to improve the results of weather forecasts. To test the new approach for grid temperature forecasts, the 2-m surface air temperature in the Beijing area from the ECMWF model is used. MOML with different feature engineering is compared against the ECMWF model and modified model output statistics (MOS) method. MOML shows a better numerical performance than the ECMWF model and MOS, especially for winter. The results of MOML with a linear algorithm, running training period, and dataset using spatial interpolation ideas, are better than others when the forecast time is within a few days. The results of MOML with the Random Forest algorithm, year-round training period, and dataset containing surrounding gridpoint information, are better when the forecast time is longer.

Machine Learning−based Weather Support for the 2022 Winter Olympics

1.A key support for the 2022 Winter Olympics The XXIV Olympic Winter Games are scheduled to take place from 4 to 22 February 2022,followed by the Paralympic Games from 4 to 13 March,in Beijing and towns in the neighboring Hebei Province,China.Weather plays an extremely important role in the outcome of the games(Chen et al.,2018).It can not only cause a difference between a medal or not,but affect the safety of athletes.Success of the Winter Olympics will greatly depend on weather conditions at the outdoor competition venues,dealing with many weather elements including the snow surface temperature,apparent temperature,gust wind speed,snow,visibility,etc.To ensure that the scheduled games go smoothly,it is imperative to have hourly or even every 10-minutely forecasts as well as updated weather-related risk assessments at the venues for the next 240 hours.So far,the Beijing/Hebei Meteorological Observatory has already started intelligent weather forecasting at 3-km resolution based on the results of numerical weather prediction(NWP)models.However,these experiments have suggested that the current forecasting techniques are incapable of capturing the complex mountain weather variations around some venues.The forecasting capability of NWP is constrained partly by limited knowledge of the local weather mechanisms.

A station-data-based model residual machine learning method for fine-grained meteorological grid prediction

Fine-grained weather forecasting data,i.e.,the grid data with high-resolution,have attracted increasing attention in recent years,especially for some specific applications such as the Winter Olympic Games.Although European Centre for Medium-Range Weather Forecasts(ECMWF)provides grid prediction up to 240 hours,the coarse data are unable to meet high requirements of these major events.In this paper,we propose a method,called model residual machine learning(MRML),to generate grid prediction with high-resolution based on high-precision stations forecasting.MRML applies model output machine learning(MOML)for stations forecasting.Subsequently,MRML utilizes these forecasts to improve the quality of the grid data by fitting a machine learning(ML)model to the residuals.We demonstrate that MRML achieves high capability at diverse meteorological elements,specifically,temperature,relative humidity,and wind speed.In addition,MRML could be easily extended to other post-processing methods by invoking different techniques.In our experiments,MRML outperforms the traditional downscaling methods such as piecewise linear interpolation(PLI)on the testing data.

Meshless Surface Wind Speed Field Reconstruction Based on Machine Learning

We propose a novel machine learning approach to reconstruct meshless surface wind speed fields,i.e.,to reconstruct the surface wind speed at any location,based on meteorological background fields and geographical information.The random forest method is selected to develop the machine learning data reconstruction model(MLDRM-RF)for wind speeds over Beijing from 2015-19.We use temporal,geospatial attribute and meteorological background field features as inputs.The wind speed field can be reconstructed at any station in the region not used in the training process to cross-validate model performance.The evaluation considers the spatial distribution of and seasonal variations in the root mean squared error(RMSE)of the reconstructed wind speed field across Beijing.The average RMSE is 1.09 m s^(−1),considerably smaller than the result(1.29 m s^(−1))obtained with inverse distance weighting(IDW)interpolation.Finally,we extract the important feature permutations by the method of mean decrease in impurity(MDI)and discuss the reasonableness of the model prediction results.MLDRM-RF is a reasonable approach with excellent potential for the improved reconstruction of historical surface wind speed fields with arbitrary grid resolutions.Such a model is needed in many wind applications,such as wind energy and aviation safety assessments.

NeoHunter:Flexible software for systematically detecting neoantigens from sequencing data

Complicated molecular alterations in tumors generate various mutant peptides.Some of these mutant peptides can be presented to the cell surface and then elicit immune responses,and such mutant peptides are called neoantigens.Accurate detection of neoantigens could help to design personalized cancer vaccines.Although some computational frameworks for neoantigen detection have been proposed,most of them can only detect SNV-and indel-derived neoantigens.In addition,current frameworks adopt oversimplified neoantigen prioritization strategies.These factors hinder the comprehensive and effective detection of neoantigens.We developed NeoHunter,flexible software to systematically detect and prioritize neoantigens from sequencing data in different formats.NeoHunter can detect not only SNV-and indel-derived neoantigens but also gene fusion-and aberrant splicing-derived neoantigens.NeoHunter supports both direct and indirect immunogenicity evaluation strategies to prioritize candidate neoantigens.These strategies utilize binding characteristics,existing biological big data,and T-cell receptor specificity to ensure accurate detection and prioritization.We applied NeoHunter to the TESLA dataset,cohorts of melanoma and non-small cell lung cancer patients.NeoHunter achieved high performance across the TESLA cancer patients and detected 79%(27 out of 34)of validated neoantigens in total.SNV-and indel-derived neoantigens accounted for 90%of the top 100 candidate neoantigens while neoantigens from aberrant splicing accounted for 9%.Gene fusion-derived neoantigens were detected in one patient.NeoHunter is a powerful tool to‘catch all’neoantigens and is available for free academic use on Github(XuegongLab/NeoHunter).

From Euler disk to phonon bottleneck effect: Excited state physics

The Euler disk,known since 1765,1 describes a solid disk that rotates on a smooth,firm surface,similar to a coin spun by a finger on a table,before its energy dissipates and it falls on the table.2 It represents a typical nonequilibrium excited state in classical physics.The most striking characteristic of an Euler disk is that it exhibits a sharply enhanced sound frequency when approaching the critical time,tc,after which the disk instantly ceases rotation and precession.At the excited-state-to-ground-state transition,its frequency abruptly changes from infinite to zero.This quasi-divergent and suddenly disappearing behavior is intriguing,revealing that this is a shared physical property in the microscopic quantum regime.

A New Explicit Symplectic Fourier Pseudospectral Method for Klein-Gordon-Schrodinger Equation

In this paper,we propose an explicit symplectic Fourier pseudospectral method for solving the Klein-Gordon-Schr odinger equation.The key idea is to rewrite the equation as an infinite-dimensional Hamiltonian system and discrete the system by using Fourier pseudospectral method in space and symplectic Euler method in time.After composing two different symplectic Euler methods for the ODEs resulted from semi-discretization in space,we get a new explicit scheme for the target equation which is of second order in space and spectral accuracy in time.The canonical Hamiltonian form of the resulted ODEs is presented and the new derived scheme is proved strictly to be symplectic.The new scheme is totally explicitwhereas symplectic scheme are generally implicit or semi-implicit.Linear stability analysis is carried and a necessary Courant-Friedrichs-Lewy condition is given.The numerical results are reported to test the accuracy and efficiency of the proposed method in long-term computing.

Rapid classification of copper concentrate by portable laser-induced breakdown spectroscopy combined with transfer learning and deep convolutional neural network

This paper investigates the combination of laser-induced breakdown spectroscopy〔LIBS〕and deep convolutional neural networks〔CNNs〕to classify copper concentrate samples using pretrained CNN models through transfer learning.Four pretrained CNN models were compared.The LIBS profiles were augmented into 2D matrices.Three transfer learning methods were tried.All the models got a high classification accuracy of>92%,with the highest at 96.2%for VGG16.These results suggested that the knowledge learned from machine vision by the CNN models can accelerate the training process and reduce the risk of overfitting.The results showed that deep CNN and transfer learning have great potential for the classification of copper concentrates by portable LIBS.

A SIXTH ORDER AVERAGED VECTOR FIELD METHOD

In this paper, based on the theory of rooted trees and B-series, we propose the concrete formulas of the substitution law for the trees of order = 5. With the help of the new substitution law, we derive a B-series integrator extending the averaged vector field （AVF） methods for general Hamiltonian system to higher order. The new integrator turns out to be order of six and exactly preserves energy for Hamiltonian systems. Numerical exper- iments are presented to demonstrate the accuracy and the energy-preserving property of the sixth order AVF method.

A Deep Spatio-Temporal Forecasting Model for Multi-Site Weather Prediction Post-Processing

In this paper, we propose a deep spatio-temporal forecasting model (DeepSTF) for multi-site weather prediction post-processing by using both temporal andspatial information. In our proposed framework, the spatio-temporal information ismodeled by a CNN (convolutional neural network) module and an encoder-decoderstructure with the attention mechanism. The novelty of our work lies in that our modeltakes full account of temporal and spatial characteristics and obtain forecasts of multiple meteorological stations simultaneously by using the same framework. We applythe DeepSTF model to short-term weather prediction at 226 meteorological stations inBeijing. It significantly improves the short-term forecasts compared to other widelyused benchmark models including the Model Output Statistics method. In order toevaluate the uncertainty of the model parameters, we estimate the confidence intervals by bootstrapping. The results show that the prediction accuracy of the DeepSTFmodel has strong stability. Finally, we evaluate the impact of seasonal changes and topographical differences on the accuracy of the model predictions. The results indicatethat our proposed model has high prediction accuracy.

Enhanced photon communication through Bayesian estimation with an SNSPD array

Laser communication using photons should consider not only the transmission environment’s effects,but also the performance of the single-photon detector used and the photon number distribution.Photon communication based on the superconducting nanowire single-photon detector(SNSPD)is a new technology that addresses the current sensitivity limitations at the level of single photons in deep space communication.The communication’s bit error rate(BER)is limited by dark noise in the space environment and the photon number distribution with a traditional single-pixel SNSPD,which is unable to resolve the photon number distribution.In this work,an enhanced photon communication method was proposed based on the photon number resolving function of four-pixel array SNSPDs.A simulated picture transmission was carried out,and the error rate in this counting mode can be reduced by 2 orders of magnitude when compared with classical optical communication.However,in the communication mode using photon-enhanced counting,the four-pixel response amplitude for counting was found to restrain the communication rate,and this counting mode is extremely dependent on the incident light intensity through experiments,which limits the sensitivity and speed of the SNSPD array’s performance advantage.Therefore,a BER theoretical calculation model for laser communication was presented using the Bayesian estimation algorithm in order to analyze the selection of counting methods for information acquisition under different light intensities and to make better use of the SNSPD array’s high sensitivity and speed and thus to obtain a lower BER.The counting method and theoretical model proposed in this work refer to array SNSPDs in the deep space field.

Multi-SymplecticMethod for the Zakharov-Kuznetsov Equation

A newscheme for the Zakharov-Kuznetsov(ZK)equationwith the accuracy order of O(△t^(2)+△x+△y^(2))is proposed.The multi-symplectic conservation property of the new scheme is proved.The backward error analysis of the newmulti-symplectic scheme is also implemented.The solitary wave evolution behaviors of the Zakharov-Kunetsov equation is investigated by the new multi-symplectic scheme.The accuracy of the scheme is analyzed.

Collector efficiency for hydrosol deep-bed filtration of non-Brownian particles at low and finite Reynolds numbers

Aqueous filtration systems with granular media are increasingly implemented as a unit operation for the treatment of urban waters.Many of these aqueous filtration systems are designed with coarse granular media and are therefore subject to finite granular Reynolds numbers(Reg).In contrast to the Reg conditions generated by such designs,current hydrosol filtration models,such as the Yao and RT models,rely on a flow solution that is derived within the Stokes limit at low Reg.In systems that are subject to these finite and higher Reg regimes,the collector efficiency has not been examined.Therefore,in this study,we develop a 3D periodic porosity-compensated face-centered cubic sphere(PCFCC)computational fluid dynamics(CFD)model,with the surface interactions incorporated,to investigate the collector efficiency for Reg ranging from 0.01 to 20.Particle filtration induced by interception and sedimentation is examined for non-Brownian particlesfanging from 1 to 100 μm under favorable surface interactions for particle adhesion.The results from the CFD-based PCFCC model agreed well with those of the classical RT and Yao models for Reg<1.Based on 3150 simulations from the PCFCC model,we developed a new correlation for vertical aqueous filtration based on a modified gravitation number,NG^*,for the initial deep-bed filtration efficiency at lower yet finite(0.01 to 20)Reg.The proposed PCFCC model has low computational cost and is extensibile from vertical to horizontal filtration at low and finite Reg.

Reduction of mercury(Ⅱ)by electrons contained in carbon dots:An environmentally friendly cold vapor generation for mercury analysis

In this work,the reduction of mercury ions(Hg2+)to elemental mercury(Hg0)was easily achieved using highly reductive carbon dots(r-CDs),which synthesized from sucrose by a simple and cost-effective method.After a careful mechanistic study,the reduction was probably accomplished with the large numbers of electrons contained in r-CDs rather than the oxidation of its functional groups.Additionally,a3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide(MTT)assay showed that the r-CDs were nontoxic to wildlife and human beings.Consequently,the r-CDs were used as an alternative to toxic reductants(SnCl2 or NaBH4)for the sensitive and in situ determination of mercury by cold vapor gene ration(CVG)coupled to a miniature point discharge optical emission spectrometer(μPD-OES).Limit of detection of 0.05μg/L was obtained for Hg2+,with relative standard deviation(RSD)less than 5.4%at a concentration of 5μg/L.The accuracy of r-CDs induced CVG-μPD-OES was validated by the determination of mercury in a certified reference material(DOLT-5,dogfish liver)and five natural water samples collected from different rivers and lakes in Chengdu City,Since r-CDs are nontoxic and prepared from abundant and inexpensive sucrose,the r-CDs induced CVG-μPD-OES retains the great potential for the inexpensive and enviro nmentally friendly field analysis of mercury in natural water.The accuracy of the proposed method was validated by the analysis of a certified reference material and several water samples with satisfactory results.