Research On Image-Driven Modeling Methods And Design Platform For Complex Problems

According to the dependence of the governing equation on time,problems can be divided into time-independent and time-dependent ones.Traditional surrogate models have shortcomings in some problems and applications.First,they usually define statistical values(such as peak values,mean values,etc.)of the physical field as an objective function,which might lead to insufficient modeling accuracy.Besides,because of the abstract objective function,inverse problems might be ill-posed.Moreover,they are usually applied to time-independent problems,and the objective function is difficult to describe the time-dependent information of time-dependent problems.Thus,for timedependent problems,traditional methods usually approximate them as timeindependent ones.Compared with a scalar value,the contour map contains more physical information,can construct high-accurate models,and meet diversified design needs.Therefore,for time-independent and time-dependent cases,respectively,image-driven modeling methods are proposed and a design platform is constructed.The main content contains four aspects:(1)“Space transformation”-based “Image is Model”.Based on contour maps,“Image is Model(IIM)” is proposed to improve modeling accuracy.In some cases,modeling accuracy might be difficult to be improved even the number of samples is significantly increased.Therefore,the Global Sensitivity Analysis(GSA)is widely applied to reduce the design space.Nevertheless,it requires resampling after the GSA for modeling.Besides,the commonly applied space reduction method is not suitable for lowdimensional problems.Therefore,a surrogate model based on the “space transformation” is introduced.Based on images,a manifold space that is more sensitive to the objective function can be constructed.(2)Image-driven generative inverse method.Based on contour maps,the Generative Inverse Net(GIN)that handles the ill-posed inverse problem is proposed.One of the key factors resulting in illposed inverse problems is multi-solution.In our opinion,one of the reasons for multi-solution is the abstract definition of the objective function,which causes the same objective function to appear in different physical fields.Therefore,ff the contour map can be employed as the objective function,the mentioned problem can be handled.In this way,based on the IIM,GIN is further proposed.Besides,for some special issues,e.g.,sheet forming,the engineering and softwareization of the “image is model” can be realized without the simulation.Evaluation of the design can be directly realized based on images for high efficiency.For these problems,the Virtual Sample-based GIN,(VSGIN)is proposed.Through testing,the GIN effectively handles the ill-posed problems caused by the definition of the objective function.Compared with the GIN,the VSGIN is more efficient,while the GIN is more flexible with fewer application limitations.(3)Image-driven reconstructive method for time-dependent problems.Based on images,a reconstructive method is introduced for timedependent problems to improve modeling efficiency.For time-dependent problems,the solver commonly asks for hundreds of thousands of iterations,while only limited iterations can be sampled for evaluation.Limited iterative results must affect the accuracy of the time-dependent objective function.Therefore,an image-driven reconstructive method is proposed.Timedependent problems are classified as time-weak coupling problems and timestrong coupling ones.The time-weak coupling means the objective function changes smoothly over time.For these problems,a Re Constructive Neural Network(Re Con NN)is proposed.Through testing,a fine time-dependent process can be reconstructed based on limited samples.However,for timestrong coupling problems whose objective function changes drastically over time,the Re Con NN is powerless.In this way,an enhanced method is proposed.It can transform the time-strong coupling problem to the time-weak coupling one in manifold space.(4)Image-driven “Image Wizard” softwareBased on the research of the manuscript,an image-driven software “Image Wizard(Imard)” is developed,which applies research to actual problems.Imard is developed with image data,uses Graphical User Interface(GUI),and asks for less theoretical knowledge background.