不确定性量化的主要目标是刻画数学建模中的不确定性，以便更准确地进行模型

The main goal of uncertainty quantification is to characterize the uncertainty in mathematical modeling in order to make model predictions more accurately. Therefore, related papers cover a wide range of professional fields. From the perspective of system calibration, they can be roughly divided into: <br>1) Model calibration. The input parameters of the mathematical model usually contain some fixed but unknown parameters. The purpose of calibration is to determine the value of the calibration parameter, so that the output of the mathematical model and the actual measurement result are as consistent as possible, and the uncertainty is reduced, so as to realize the simulation of the mathematical model more accurately. Forecast function. The principle of the Bayesian calibration method is: first establish the Gaussian process a priori for the mathematical model, and carry out a limited number of runs on the Gaussian model and the physical experiment through a suitable experimental design method, and apply the Bayesian principle to the running results to get the best The previous uncertainty information is the posterior distribution of the Gaussian model, and then the estimated value of the calibration parameter can be obtained. The general Bayesian model calibration can be innovated in more accurate calculation of the posterior [73]. There are different mathematical models for research in specific fields, so there are different priors. For example, the priors of the coarse-grained (molecular dynamics) force field are composed of random weights corresponding to the orthogonal basis functions after the force spectrum is decomposed [74], and then Calculate the corresponding likelihood function and posterior. <br>2) Instead of calibration. For example, it does not require calibration to directly use the hierarchical Bayesian model to consider the uncertainty propagation to predict the degree of deterioration of the outdoor performance of the alloy, so as to solve the problem of instability in the prediction caused by the change of calibration over time in the traditional method [75]; regional groundwater flow model When dealing with covariate measurement errors, the Bayesian method is used for correction instead of regression calibration. It has statistical advantages, strong feasibility, and more flexible handling of missing data [76]; the thermal properties of materials can be determined by Bayesian method to speed up the speed [77] . <br>3) No calibration is required. Some uncertainty quantification is for data quality assessment and does not require calibration. For example, using Bayesian method to calculate the posterior of CT image AUC to quantify uncertainty [78]. The Bayesian method is used to quantify the parameters of deep learning and the final prediction results [79].

The main goal of uncertainty quantification is to depict uncertainty in mathematical modeling in order to make model predictions more accurately. Therefore, the relevant papers cover a wide range of areas of expertise. From the point of view of system calibration, they are roughly divided into:<br>1) Model calibration. Mathematical model input parameters usually contain some fixed but unknown parameters, the purpose of calibration is to determine the value of calibration parameters, so that the mathematical model output and the actual measurement results as consistent as possible, reduce uncertainty, so as to more accurately realize the mathematical model simulation, prediction function. The principle of Bayesian calibration method is: first of all, to establish Gaussian process a priori for mathematical models, through suitable experimental design methods, to run Gaussian models and physical experiments on a limited number of times, to apply Bayesian principles to the operating results, you can get the previous uncertainty information, that is, Gaussian model post-test distribution, and then you can get the estimate of calibration parameters. Universal Bayes model calibration can be innovated on more accurate post-calculation tests. Studies in specific fields have different mathematical models, so there are different a priori, such as coarse granulation (molecular dynamics) force field, which consists of random weights corresponding to orthosectial base functions after force spectrometum decomposition, and then calculates the corresponding aditional functions and post-tests.<br>2) Instead of calibration. For example, there is no need for calibration to directly use the hierarchical Bayesian model to consider uncertainty propagation to predict the degree of performance decline of the alloy outdoors in order to solve the problem of predictive instability caused by the calibration over time in traditional methods;<br>3) Calibration is not required. Some uncertainty quantification is for data quality assessment and does not require calibration. For example, the Bayes method is used to calculate the agency of CT images for uncertainty quantification. The parameters of deep learning and the final prediction results are quantified by Bayes method.

The main goal of uncertainty quantification is to describe the uncertainty in mathematical modeling so as to predict the model more accurately. Therefore, the related papers involve a wide range of professional fields. From the point of view of system calibration, they are roughly divided into three parts<br>1) Model calibration. The input parameters of mathematical model usually contain some fixed but unknown parameters. The purpose of calibration is to determine the value of calibration parameters, make the output of mathematical model consistent with the actual measurement results as much as possible, reduce the uncertainty, so as to realize the simulation and prediction function of mathematical model more accurately. The principle of Bayesian calibration method is as follows: firstly, the prior of Gaussian process is established for the mathematical model, and the Gaussian model and physical experiment are respectively run for a limited number of times through the appropriate experimental design method. The Bayesian principle is applied to the running results to obtain the prior uncertainty information, that is, the posterior distribution of Gaussian model, and then the estimated values of calibration parameters can be obtained. The general Bayesian model calibration can be innovated on more accurate posterior calculation [73]. There are different mathematical models in specific fields, so there are different priors. For example, the priors of coarse graining (molecular dynamics) force field are composed of random weights corresponding to orthogonal basis function after force spectrum decomposition [74], and then the corresponding likelihood function and a posteriori are calculated.<br>2) Instead of calibration. For example, without calibration, hierarchical Bayesian model is directly used to predict the degradation degree of alloy outdoor performance by considering uncertainty propagation, so as to solve the problem of unstable prediction caused by time-varying calibration in traditional methods [75]; Bayesian method is used to correct covariate measurement error instead of regression calibration in regional groundwater flow model, which has statistical advantages and feasibility It is more flexible to deal with missing data [76]; it can speed up the determination of thermal properties of materials by Bayesian method [77].<br>3) Calibration is not required. Some uncertainty quantification is for data quality evaluation and does not need calibration. For example, Bayesian method is used to calculate the posterior AUC of CT image to quantify the uncertainty [78]. Bayesian method is used to quantify the uncertainty of parameters and final prediction results of deep learning [79].<br>