Machine-learned augmentations to turbulence models can be advantageous for flows within the training dataset but can often cause harm outside.This lack of generalizability arises because the constants(as well as the f...Machine-learned augmentations to turbulence models can be advantageous for flows within the training dataset but can often cause harm outside.This lack of generalizability arises because the constants(as well as the functions)in a Reynolds-averaged Navier–Stokes(RANS)model are coupled,and un-constrained re-calibration of these constants(and functions)can disrupt the calibrations of the baseline model,the preservation of which is critical to the model's generalizability.To safeguard the behaviors of the baseline model beyond the training dataset,machine learning must be constrained such that basic calibrations like the law of the wall are kept intact.This letter aims to identify such constraints in two-equation RANS models so that future machine learning work can be performed without violating these constraints.We demonstrate that the identified constraints are not limiting.Furthermore,they help preserve the generalizability of the baseline model.展开更多
Dear Editor, We developed a GPU-based analytical method, named as SHEsisEpi, which purely focuses on risk epistasis in a genome-wide association study （GWAS） of complex traits, excluding the contamination of margin...Dear Editor, We developed a GPU-based analytical method, named as SHEsisEpi, which purely focuses on risk epistasis in a genome-wide association study （GWAS） of complex traits, excluding the contamination of marginal effects caused by single-locus association. We analyzed the Wellcome Trust Case Control Consortium＇s （WTCCC） GWAS data of bipolar disorder （BPD） with 500K SNPs.展开更多
Numerical approximation for a linearized time fractional KdV equation with initial singularity using L1 scheme on graded mesh is considered.It is proved that the L1 scheme can attain order 2−αconvergence rate with ap...Numerical approximation for a linearized time fractional KdV equation with initial singularity using L1 scheme on graded mesh is considered.It is proved that the L1 scheme can attain order 2−αconvergence rate with appropriate choice of the grading parameter,whereα(0<α<1)is the order of temporal Caputo fractional derivative.A fully discrete spectral scheme is constructed combing a Petrov-Galerkin spectral method for the spatial discretization,and its stability and convergence are theoretically proved.Some numerical results are provided to verify the theoretical analysis and demonstrated the sharpness of the error analysis.展开更多
基金supported by the Air Force Office of Scientific Research(Grant No.FA9550-23-1-0272)the National Natural Science Foundation of China(Grant Nos.11988102 and 91752202).
文摘Machine-learned augmentations to turbulence models can be advantageous for flows within the training dataset but can often cause harm outside.This lack of generalizability arises because the constants(as well as the functions)in a Reynolds-averaged Navier–Stokes(RANS)model are coupled,and un-constrained re-calibration of these constants(and functions)can disrupt the calibrations of the baseline model,the preservation of which is critical to the model's generalizability.To safeguard the behaviors of the baseline model beyond the training dataset,machine learning must be constrained such that basic calibrations like the law of the wall are kept intact.This letter aims to identify such constraints in two-equation RANS models so that future machine learning work can be performed without violating these constraints.We demonstrate that the identified constraints are not limiting.Furthermore,they help preserve the generalizability of the baseline model.
文摘Dear Editor, We developed a GPU-based analytical method, named as SHEsisEpi, which purely focuses on risk epistasis in a genome-wide association study （GWAS） of complex traits, excluding the contamination of marginal effects caused by single-locus association. We analyzed the Wellcome Trust Case Control Consortium＇s （WTCCC） GWAS data of bipolar disorder （BPD） with 500K SNPs.
基金The work of Hu Chen is supported in part by NSF of China(No.11801026)and China Postdoctoral Science Foundation Under No.2018M631316the work of Xiaohan Hu and Yifa Tang is supported in part by NSF of China(No.11771438)+3 种基金the work of Jincheng Ren is supported in part by NSF of China(No.11601119)sponsored by Program for HASTIT(No.18HASTIT027)Young talents Fund of HUELthe work of Tao Sun is supported in part by NSF of China(No.11401380).
文摘Numerical approximation for a linearized time fractional KdV equation with initial singularity using L1 scheme on graded mesh is considered.It is proved that the L1 scheme can attain order 2−αconvergence rate with appropriate choice of the grading parameter,whereα(0<α<1)is the order of temporal Caputo fractional derivative.A fully discrete spectral scheme is constructed combing a Petrov-Galerkin spectral method for the spatial discretization,and its stability and convergence are theoretically proved.Some numerical results are provided to verify the theoretical analysis and demonstrated the sharpness of the error analysis.
