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

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Theoretical & Applied Mechanics Letters 2024年第2期14卷 90-97页

作者： Hanyu Zhou haochen li Yaomin Zhao HEDPS Center for Applied Physics and Technologyand College of EngineeringPeking UniversityBeijing 100871China State Key Laboratory for Turbulence and Complex Systems College of EngineeringPeking UniversityBeijing 100871China

Identification of underlying partial differential equations(PDEs)for complex systems remains a formidable *** the present study,a robust PDE identification method is proposed,demonstrating the ability to extract accurate governing equations under noisy conditions without prior ***,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 are designed to represent explicit functional expressions and optimize them with data *** 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 *** 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.

关键词： PDE discovery Gene Expression Programming Deep Learning Knowledge embedding

A SIXTH ORDER AVERAGED VECTOR FIELD METHOD

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Journal of Computational Mathematics 2016年第5期34卷 479-498页

作者： haochen li Yushun Wang Mengzhao Qin Jiangsu Key Laboratory for NSLSCS School of Mathematical Sciences Nanjing Normal University Jiangsu 210023 China Lsec Academy of Mathematics and System Sciences Chinese Academy of Science PoBox 2719 Beijing China

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.

关键词： Hamiltonian systems B-series Energy=preserving method Sixth order AVFmethod Substitution law.

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

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Applied Mathematics and Mechanics(English Edition) 2022年第2期43卷 155-166页

作者： Chuansai ZHOU haochen li Chen YU Jiangjiang XIA Pingwen ZHANG School of Mathematical Sciences Peking UniversityBeijing100871China School of Science Beijing University of Posts and TelecommunicationsBeijing100876China Institute of Atmospheric Physics Chinese Academy of SciencesBeijing100029China

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 *** 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 *** this paper,we propose a method,called model residual machine learning(MRML),to generate grid prediction with high-resolution based on high-precision stations *** applies model output machine learning(MOML)for stations ***,MRML utilizes these forecasts to improve the quality of the grid data by fitting a machine learning(ML)model to the *** demonstrate that MRML achieves high capability at diverse meteorological elements,specifically,temperature,relative humidity,and wind *** addition,MRML could be easily extended to other post-processing methods by invoking different *** our experiments,MRML outperforms the traditional downscaling methods such as piecewise linear interpolation(Pli)on the testing data.

关键词： machine learning(ML) post-processing fine-grained weather forecasting model residual machine learning(MRML)

Multi-SymplecticMethod for the Zakharov-Kuznetsov Equation

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Advances in Applied Mathematics and Mechanics 2015年第1期7卷 58-73页

作者： haochen li Jianqiang Sun Mengzhao Qin Department of Mathematics College of Information Science and TechnologyHainan UniversityHainan 570228China School of Mathematical Science Nanjing Normal UniversityJiangsu 210023China LSEC Academy of Mathematics and System SciencesChinese Academy of ScienceBeijing 100190China

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

关键词： The Zakharov-Kuznetsov equation multi-symplectic method backward error analysis.

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

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Advances in Applied Mathematics and Mechanics 2018年第1期10卷 242-260页

作者： Yanhong Yang Yongzhong Song haochen li Yushun Wang Jiangsu Key Laboratory for NSLSCS Institute of MathematicsSchool of Mathematical SciencesNanjing Normal UniversityNanjing 210023China Department of Mathematics College of TaizhouNanjing Normal UniversityTaizhou 225300China LMAM CAPT and School of Mathematical SciencesPekingUniversityBeijing 100871China

In this paper,we propose an explicit symplectic Fourier pseudospectral method for solving the Klein-Gordon-Schr odinger *** 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 *** 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 *** canonical Hamiltonian form of the resulted ODEs is presented and the new derived scheme is proved strictly to be *** new scheme is totally explicitwhereas symplectic scheme are generally implicit or *** stability analysis is carried and a necessary Courant-Friedrichs-Lewy condition is *** numerical results are reported to test the accuracy and efficiency of the proposed method in long-term computing.

关键词： Klein-Gordon-Schr odinger equation Fourier pseudospectral method symplectic scheme explicit scheme

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

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Advances in Atmospheric Sciences 2019年第10期36卷 1156-1170页

作者： haochen li Chen YU Jiangjiang XIA Yingchun WANG Jiang ZHU Pingwen ZHANG School of Mathematical Sciences Peking University School of Science Beijing University of Posts and Telecommunications Institute of Atmospheric Physics Chinese Academy of Sciences Beijing Meteorological Service

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.

关键词： temperature forecasts MOS machine learning multiple linear regression Random Forest weather consultation feature engineering data structures

NeoHunter:Flexible software for systematically detecting neoantigens from sequencing data

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Quantitative Biology 2024年第1期12卷 70-84页

作者： Tianxing Ma Zetong Zhao haochen li Lei Wei Xuegong Zhang MOE Key Lab of Bioinformatics Bioinformatics Division of BNRIST and Department of AutomationTsinghua UniversityBeijingChina School of Medicine Tsinghua UniversityBeijingChina School of life Sciences Tsinghua UniversityBeijingChina

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

关键词： cancer vaccine molecular alteration neoantigen neoantigen prioritization

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

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Communications in Computational Physics 2022年第1期31卷 131-153页

作者： Wenjia Kong haochen li Chen Yu Jiangjiang Xia Yanyan Kang Pingwen Zhang Academy for Advanced Interdisciplinary Studies Peking UniversityBeijing 100871China School of Mathematical Sciences Peking UniversityBeijing 100871China School of Science Beijing University of Posts and TelecommunicationsBeijing 100876China Institute of Atmospheric Physics Chinese Academy of SciencesBeijing 100029China Beijing Weather Forecast Center Beijing 100089China

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.

关键词： Weather forecasting post-processing spatio-temporal modeling deep learning

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

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Chinese Chemical Letters 2020年第10期31卷 2678-2682页

作者： Tao Chen Yao lin haochen li Rui Yang Xiandeng Hou Baozhan Zheng Chengbin Zheng Key Laboratory of Green Chemistry and Technology Ministry of EducationCollege of ChemistrySichuan UniversityChengdu 610064China Chengdu No.7 High School Chengdu 610041China Analytical&Testing Center Sichuan UniversityChengdu 610064China

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 *** 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 ***,a3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide(MTT)assay showed that the r-CDs were nontoxic to wildlife and human ***,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/*** 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 *** accuracy of the proposed method was validated by the analysis of a certified reference material and several water samples with satisfactory results.

关键词： Mercury analysis Reduction Carbon dots Cold vapor generation