# How to solve multidimensional input variables in Sobol (M \> 20)? **URL:** \ **Category:** Community Q&A and How To\ **Tags:** sensitivity, input, metamodeling\ **Created:** [December 5, 2021, 7:08am UTC](https://uqworld.org/t/how-to-solve-multidimensional-input-variables-in-sobol-m-20/1400 "2021-12-05T07:08:13Z")\ **Posts on this page:** 2\ **Page:** 1
**Author:** ![FANFAN](https://uqworld.org/letter_avatar_proxy/v4/letter/f/45deac/32.png) [@FANFAN](https://uqworld.org/u/FANFAN)\ **Post date:** [December 5, 2021, 7:08am UTC](https://uqworld.org/t/how-to-solve-multidimensional-input-variables-in-sobol-m-20/1400/1 "2021-12-05T07:08:13Z")
Hello all, Recently, I am working on a practical case based on Sobol sensitivity analysis, The response model and probability input model are as follows: Y=((-X1+X19-8_X24-X13+450_(X11+X17)+8\*(X12+X6+X18)-X7).^2+(-X2+X20+200_X24-X14+450_(X10+X16)+400\*(X12+X6+X18)-X8).^2+(X21+8_X22-200_X23-X3-X15-8\*(X10+X4+X16)-400\*(X11+X5+X17)-X9).^2).^(0.5); InputOpts.Marginals(1).Name = ‘X1’; InputOpts.Marginals(1).Type = ‘uniform’; InputOpts.Marginals(1).Parameters = [0 0.029206]; InputOpts.Marginals(2).Name = ‘X2’; InputOpts.Marginals(2).Type = ‘uniform’; InputOpts.Marginals(2).Parameters = [0 0.0364]; InputOpts.Marginals(3).Name = ‘X3’; InputOpts.Marginals(3).Type = ‘uniform’; InputOpts.Marginals(3).Parameters = [0 0.011321]; InputOpts.Marginals(4).Name = ‘X4’; InputOpts.Marginals(4).Type = ‘uniform’; InputOpts.Marginals(4).Parameters = [0 6.0629E-5]; InputOpts.Marginals(5).Name = ‘X5’; InputOpts.Marginals(5).Type = ‘uniform’; InputOpts.Marginals(5).Parameters = [0 3.052E-5]; InputOpts.Marginals(6).Name = ‘X6’; InputOpts.Marginals(6).Type = ‘uniform’; InputOpts.Marginals(6).Parameters = [0 4.5717E-5]; InputOpts.Marginals(7).Name = ‘X7’; InputOpts.Marginals(7).Type = ‘uniform’; InputOpts.Marginals(7).Parameters = [0 0.020339]; InputOpts.Marginals(8).Name = ‘X8’; InputOpts.Marginals(8).Type = ‘uniform’; InputOpts.Marginals(8).Parameters = [0 0.048608]; InputOpts.Marginals(9).Name = ‘X9’; InputOpts.Marginals(9).Type = ‘uniform’; InputOpts.Marginals(9).Parameters = [0 0.011826]; InputOpts.Marginals(10).Name = ‘X10’; InputOpts.Marginals(10).Type = ‘uniform’; InputOpts.Marginals(10).Parameters = [0 6.3456E-5]; InputOpts.Marginals(11).Name = ‘X11’; InputOpts.Marginals(11).Type = ‘uniform’; InputOpts.Marginals(11).Parameters = [0 4.31E-5]; InputOpts.Marginals(12).Name = ‘X12’; InputOpts.Marginals(12).Type = ‘uniform’; InputOpts.Marginals(12).Parameters = [0 5.7912E-5]; InputOpts.Marginals(13).Name = ‘X13’; InputOpts.Marginals(13).Type = ‘uniform’; InputOpts.Marginals(13).Parameters = [0 0.013859]; InputOpts.Marginals(14).Name = ‘X14’; InputOpts.Marginals(14).Type = ‘uniform’; InputOpts.Marginals(14).Parameters = [0 0.047617]; InputOpts.Marginals(15).Name = ‘X15’; InputOpts.Marginals(15).Type = ‘uniform’; InputOpts.Marginals(15).Parameters = [0 0.010174]; InputOpts.Marginals(16).Name = ‘X16’; InputOpts.Marginals(16).Type = ‘uniform’; InputOpts.Marginals(16).Parameters = [0 5.8166E-5]; InputOpts.Marginals(17).Name = ‘X17’; InputOpts.Marginals(17).Type = ‘uniform’; InputOpts.Marginals(17).Parameters = [0 3.4953E-5]; InputOpts.Marginals(18).Name = ‘X18’; InputOpts.Marginals(18).Type = ‘uniform’; InputOpts.Marginals(18).Parameters = [0 5.6287E-5]; InputOpts.Marginals(19).Name = ‘X19’; InputOpts.Marginals(19).Type = ‘uniform’; InputOpts.Marginals(19).Parameters = [0 0.014194]; InputOpts.Marginals(20).Name = ‘X20’; InputOpts.Marginals(20).Type = ‘uniform’; InputOpts.Marginals(20).Parameters = [0 0.025789]; InputOpts.Marginals(21).Name = ‘X21’; InputOpts.Marginals(21).Type = ‘uniform’; InputOpts.Marginals(21).Parameters = [0 0.048935]; InputOpts.Marginals(22).Name = ‘X22’; InputOpts.Marginals(22).Type = ‘uniform’; InputOpts.Marginals(22).Parameters = [0 5.662E-5]; InputOpts.Marginals(23).Name = ‘X23’; InputOpts.Marginals(23).Type = ‘uniform’; InputOpts.Marginals(23).Parameters = [0 4.6306E-5]; InputOpts.Marginals(24).Name = ‘X24’; InputOpts.Marginals(24).Type = ‘uniform’; InputOpts.Marginals(24).Parameters = [0 4.4639E-5]; **The analysis results show some errors:** (a) The estimation of PCE coefficients stopped at polynomial degree 5 and qNorm 1.00 for output variable 1 Final LOO error estimate: 4.281862e-01 (b) Warning: LRA based indices can’t be efficiently computed for large dimensional problems (M\>20) switching back to MCS Sobol indices estimators… However, I have 24 input variables. How can I solve this problem? In addition, I don’t quite understand metaopts.expdesign, sampling type: the default option is MC. If I want to change to Sobol sequence sampling, which file should I modify? I hope to hear from you at your convenience! Best regards FANFAN ---
**Author:** ![giansteve](https://uqworld.org/user_avatar/uqworld.org/giansteve/32/973_2.png) [@giansteve](https://uqworld.org/u/giansteve)\ **Post date:** [December 6, 2021, 2:46pm UTC](https://uqworld.org/t/how-to-solve-multidimensional-input-variables-in-sobol-m-20/1400/2 "2021-12-06T14:46:49Z")
Hi @FANFAN, I will try to answer your questions regarding the PCE. I am not so practical with the LRA 🙂 **The estimation of PCE coefficients stopped at polynomial degree 5 and qNorm 1.00 for output variable 1** : you can set the metamodel such that it will not stop at the first degree with a lower LOO error. You can set this as ```matlab metaOpts.DegreeEarlyStop = false; ``` By default, the value is set to `true`, and it will stop the search at the local minimum of the error. If you need more support, maybe you can paste part of your code. **The experimental design** : once you define your input, as you wrote in your question, you need to specify the input object ```matlab myInput = uq_createInput(InputOpts); ``` and then you can collect a sample from it, with the sampling technique you prefer, as ```matlab X = uq_getSample(myInput,); % where : 'mc','lhs','Sobol', or 'Halton' ``` I hope it was helpful 🙂