Solving for detailed chemical kinetics remains one of the major bottlenecks for computational fluid dynamics simulations of reacting flows using a finite-rate-chemistry approach.This has motivated the use of neural ne...Solving for detailed chemical kinetics remains one of the major bottlenecks for computational fluid dynamics simulations of reacting flows using a finite-rate-chemistry approach.This has motivated the use of neural networks to predict stiff chemical source terms as functions of the thermochemical state of the combustion system.However,due to the nonlinearities and multi-scale nature of combustion,the predicted solution often diverges from the true solution when these machine learning models are coupled with a computational fluid dynamics solver.This is because these approaches minimize the error during training without guaranteeing successful integration with ordinary differential equation solvers.In the present work,a novel neural ordinary differential equations approach to modeling chemical kinetics,termed as ChemNODE,is developed.In this machine learning framework,the chemical source terms predicted by the neural networks are integrated during training,and by computing the required derivatives,the neural network weights are adjusted accordingly to minimize the difference between the predicted and ground-truth solution.A proof-of-concept study is performed with ChemNODE for homogeneous autoignition of hydrogen-air mixture over a range of composition and thermodynamic conditions.It is shown that ChemNODE accurately captures the chemical kinetic behavior and reproduces the results obtained using the detailed kinetic mechanism at a fraction of the computational cost.展开更多
There are vast constraint equations in conventional dynamics analysis of deployable structures,which lead to differential-algebraic equations(DAEs)solved hard.To reduce the difficulty of solving and the amount of equa...There are vast constraint equations in conventional dynamics analysis of deployable structures,which lead to differential-algebraic equations(DAEs)solved hard.To reduce the difficulty of solving and the amount of equations,a new flexible multibody dynamics analysis methodology of deployable structures with scissor-like elements(SLEs)is presented.Firstly,a precise model of a flexible bar of SLE is established by the higher order shear deformable beam element based on the absolute nodal coordinate formulation(ANCF),and the master/slave freedom method is used to obtain the dynamics equations of SLEs without constraint equations.Secondly,according to features of deployable structures,the specification matrix method(SMM)is proposed to eliminate the constraint equations among SLEs in the frame of ANCF.With this method,the inner and the boundary nodal coordinates of element characteristic matrices can be separated simply and efficiently,especially on condition that there are vast nodal coordinates.So the element characteristic matrices can be added end to end circularly.Thus,the dynamic model of deployable structure reduces dimension and can be assembled without any constraint equation.Next,a new iteration procedure for the generalized-a algorithm is presented to solve the ordinary differential equations(ODEs)of deployable structure.Finally,the proposed methodology is used to analyze the flexible multi-body dynamics of a planar linear array deployable structure based on three scissor-like elements.The simulation results show that flexibility has a significant influence on the deployment motion of the deployable structure.The proposed methodology indeed reduce the difficulty of solving and the amount of equations by eliminating redundant degrees of freedom and the constraint equations in scissor-like elements and among scissor-like elements.展开更多
Deep learning performs as a powerful paradigm in many real-world applications;however,its mechanism remains much of a mystery.To gain insights about nonlinear hierarchical deep networks,we theoretically describe the c...Deep learning performs as a powerful paradigm in many real-world applications;however,its mechanism remains much of a mystery.To gain insights about nonlinear hierarchical deep networks,we theoretically describe the coupled nonlinear learning dynamic of the two-layer neural network with quadratic activations,extending existing results from the linear case.The quadratic activation,although rarely used in practice,shares convexity with the widely used ReLU activation,thus producing similar dynamics.In this work,we focus on the case of a canonical regression problem under the standard normal distribution and use a coupled dynamical system to mimic the gradient descent method in the sense of a continuous-time limit,then use the high order moment tensor of the normal distribution to simplify these ordinary differential equations.The simplified system yields unexpected fixed points.The existence of these non-global-optimal stable points leads to the existence of saddle points in the loss surface of the quadratic networks.Our analysis shows there are conserved quantities during the training of the quadratic networks.Such quantities might result in a failed learning process if the network is initialized improperly.Finally,We illustrate the comparison between the numerical learning curves and the theoretical one,which reveals the two alternately appearing stages of the learning process.展开更多
Cancer is a fetal and complex disease.Individual differences of the same cancer type or the same patient at different stages of cancer development may require distinct treatments.Pathological differences are reflected...Cancer is a fetal and complex disease.Individual differences of the same cancer type or the same patient at different stages of cancer development may require distinct treatments.Pathological differences are reflected in tissues,cells and gene levels etc.The interactions between the cancer cells and nearby microenvironments can also influence the cancer progression and metastasis.It is a huge challenge to understand all of these mechanistically and quantitatively.Researchers applied pattern recognition algorithms such as machine learning or data mining to predict cancer types or classifications.With the rapidly growing and available computing powers,researchers begin to integrate huge data sets,multi-dimensional data types and information.The cells are controlled by the gene expressions determined by the promoter sequences and transcription regulators.For example,the changes in the gene expression through these underlying mechanisms can modify cell progressing in the cell-cycle.Such molecular activities can be governed by the gene regulations through the underlying gene regulatory networks,which are essential for cancer study when the information and gene regulations are clear and available.In this review,we briefly introduce several machine learning methods of cancer prediction and classification which include Artificial Neural Networks(ANNs),Decision Trees(DTs),Support Vector Machine(SVM)and naive Bayes.Then we describe a few typical models for building up gene regulatory networks such as Correlation,Regression and Bayes methods based on available data.These methods can help on cancer diagnosis such as susceptibility,recurrence,survival etc.At last,we summarize and compare the modeling methods to analyze the development and progression of cancer through gene regulatory networks.These models can provide possible physical strategies to analyze cancer progression in a systematic and quantitative way.展开更多
基金This work was supported by the U.S.Department of Energy,Office of Science under contract DE-AC02-06CH11357The research work was funded by Argonne’s Laboratory Directed Research and Development(LDRD)Innovate project#2020-0203.The authors acknowledge the computing resources available via Bebop,a high-performance computing cluster operated by the Laboratory Computing Resource Center(LCRC)at Argonne National Laboratory.
文摘Solving for detailed chemical kinetics remains one of the major bottlenecks for computational fluid dynamics simulations of reacting flows using a finite-rate-chemistry approach.This has motivated the use of neural networks to predict stiff chemical source terms as functions of the thermochemical state of the combustion system.However,due to the nonlinearities and multi-scale nature of combustion,the predicted solution often diverges from the true solution when these machine learning models are coupled with a computational fluid dynamics solver.This is because these approaches minimize the error during training without guaranteeing successful integration with ordinary differential equation solvers.In the present work,a novel neural ordinary differential equations approach to modeling chemical kinetics,termed as ChemNODE,is developed.In this machine learning framework,the chemical source terms predicted by the neural networks are integrated during training,and by computing the required derivatives,the neural network weights are adjusted accordingly to minimize the difference between the predicted and ground-truth solution.A proof-of-concept study is performed with ChemNODE for homogeneous autoignition of hydrogen-air mixture over a range of composition and thermodynamic conditions.It is shown that ChemNODE accurately captures the chemical kinetic behavior and reproduces the results obtained using the detailed kinetic mechanism at a fraction of the computational cost.
基金Supported by National Natural Science Foundation of China(Grant No.51175422)
文摘There are vast constraint equations in conventional dynamics analysis of deployable structures,which lead to differential-algebraic equations(DAEs)solved hard.To reduce the difficulty of solving and the amount of equations,a new flexible multibody dynamics analysis methodology of deployable structures with scissor-like elements(SLEs)is presented.Firstly,a precise model of a flexible bar of SLE is established by the higher order shear deformable beam element based on the absolute nodal coordinate formulation(ANCF),and the master/slave freedom method is used to obtain the dynamics equations of SLEs without constraint equations.Secondly,according to features of deployable structures,the specification matrix method(SMM)is proposed to eliminate the constraint equations among SLEs in the frame of ANCF.With this method,the inner and the boundary nodal coordinates of element characteristic matrices can be separated simply and efficiently,especially on condition that there are vast nodal coordinates.So the element characteristic matrices can be added end to end circularly.Thus,the dynamic model of deployable structure reduces dimension and can be assembled without any constraint equation.Next,a new iteration procedure for the generalized-a algorithm is presented to solve the ordinary differential equations(ODEs)of deployable structure.Finally,the proposed methodology is used to analyze the flexible multi-body dynamics of a planar linear array deployable structure based on three scissor-like elements.The simulation results show that flexibility has a significant influence on the deployment motion of the deployable structure.The proposed methodology indeed reduce the difficulty of solving and the amount of equations by eliminating redundant degrees of freedom and the constraint equations in scissor-like elements and among scissor-like elements.
基金The authors would like to thank the support from National Natural Science Foundation of China(Grant No.61672281).
文摘Deep learning performs as a powerful paradigm in many real-world applications;however,its mechanism remains much of a mystery.To gain insights about nonlinear hierarchical deep networks,we theoretically describe the coupled nonlinear learning dynamic of the two-layer neural network with quadratic activations,extending existing results from the linear case.The quadratic activation,although rarely used in practice,shares convexity with the widely used ReLU activation,thus producing similar dynamics.In this work,we focus on the case of a canonical regression problem under the standard normal distribution and use a coupled dynamical system to mimic the gradient descent method in the sense of a continuous-time limit,then use the high order moment tensor of the normal distribution to simplify these ordinary differential equations.The simplified system yields unexpected fixed points.The existence of these non-global-optimal stable points leads to the existence of saddle points in the loss surface of the quadratic networks.Our analysis shows there are conserved quantities during the training of the quadratic networks.Such quantities might result in a failed learning process if the network is initialized improperly.Finally,We illustrate the comparison between the numerical learning curves and the theoretical one,which reveals the two alternately appearing stages of the learning process.
基金supported by National Nature Science Foundation of China Grants No.21721003.
文摘Cancer is a fetal and complex disease.Individual differences of the same cancer type or the same patient at different stages of cancer development may require distinct treatments.Pathological differences are reflected in tissues,cells and gene levels etc.The interactions between the cancer cells and nearby microenvironments can also influence the cancer progression and metastasis.It is a huge challenge to understand all of these mechanistically and quantitatively.Researchers applied pattern recognition algorithms such as machine learning or data mining to predict cancer types or classifications.With the rapidly growing and available computing powers,researchers begin to integrate huge data sets,multi-dimensional data types and information.The cells are controlled by the gene expressions determined by the promoter sequences and transcription regulators.For example,the changes in the gene expression through these underlying mechanisms can modify cell progressing in the cell-cycle.Such molecular activities can be governed by the gene regulations through the underlying gene regulatory networks,which are essential for cancer study when the information and gene regulations are clear and available.In this review,we briefly introduce several machine learning methods of cancer prediction and classification which include Artificial Neural Networks(ANNs),Decision Trees(DTs),Support Vector Machine(SVM)and naive Bayes.Then we describe a few typical models for building up gene regulatory networks such as Correlation,Regression and Bayes methods based on available data.These methods can help on cancer diagnosis such as susceptibility,recurrence,survival etc.At last,we summarize and compare the modeling methods to analyze the development and progression of cancer through gene regulatory networks.These models can provide possible physical strategies to analyze cancer progression in a systematic and quantitative way.
