# PCE: can the output PDF be bounded? **URL:** \ **Category:** Community Q&A and How To\ **Tags:** pce, metamodeling\ **Created:** [March 10, 2022, 8:10am UTC](https://uqworld.org/t/pce-can-the-output-pdf-be-bounded/1518 "2022-03-10T08:10:23Z")\ **Posts on this page:** 1\ **Page:** 1
**Author:** ![giansteve](https://uqworld.org/user_avatar/uqworld.org/giansteve/32/973_2.png) [@giansteve](https://uqworld.org/u/giansteve)\ **Post date:** [March 10, 2022, 8:10am UTC](https://uqworld.org/t/pce-can-the-output-pdf-be-bounded/1518/1 "2022-03-10T08:10:23Z")
Dear all UQ people I have a “silly” question for you 🙃 I am building a PCE for 2 model outputs, namely H/S(t) and L/S(t), and they are computed in 7 time steps. The PCE is built using LARS method, and with the following characteristics: - number of simulation N\_{sim}=7000 - `DegreeEarlyStop = false` - `metamodel.TruncOptions.qNorm = [0.9 0.95 0.975]` - `metamodel.Degree = 6:11;` - Input dimension M=7 After the PCE finds the best qNorm, the best Degree, I get my 2 PCEs. Successively, I create a new sample set, say N\_{sample}=10000 samples, to evaluate the created PCE and check the validity of the surrogates. In other words, I want to check how accurately they approximate my model. To check this, I evaluate the PCE, and plot the PDF functions of both the model’s outputs (H/S(t) and L/S(t)) and the surrogate’s outputs (\widehat{H/S}(t) and \widehat{L/S}(t)). You can see the results in the following picture. Model’s outputs are on the top row, and surrogate’s ones are on the bottom. ![ModOut_SurrOut_prob](https://uqworld.org/uploads/default/original/2X/8/86407efdaffd38accb970608928759e0a869f76c.jpeg) The PCEs errors (LOO, ModLOO, and NormEmpErrr) are reported here for outputs H/S before and L/S after. ```matlab % ::::::::: H/S ::::::::: LOO ModifiedLOO normEmpErr 0 0 0 0.0090583273425265 0.0129604505985762 0.00617285424918898 0.0224145486882809 0.0299271425113136 0.0159058780792346 0.0256757113910335 0.0352438072675073 0.0171982084514020 0.0218081098264392 0.0303681327153788 0.0145129841068436 0.0364352216699990 0.0514145886913357 0.0234572158255180 0.0446097448909121 0.0602193012041774 0.0296089961441069 % ::::::::: L/S ::::::::: LOO ModifiedLOO normEmpErr 0 0 0 0.0226401481139822 0.0288834103586079 0.0175835159153482 0.0520955801100249 0.0686993448933377 0.0385835562524133 0.0526829843782030 0.0648190913371306 0.0425621568554726 0.0555146490807771 0.0695122989997526 0.0451366872767112 0.0565982366525505 0.0673343001096283 0.0476579480569029 0.0488834208272997 0.0618057542342229 0.0389684913850232 ``` As you may notice, the model’s outputs are bounded to the upper limits H/S=1 and L/S=26. However, the PCE is not able to model these bounded results. I know that by nature, the PCE has a hard time modeling this particular behavior due to the nature of the Askey basis polynomials. However, I wonder if there is a way to “adjust” this somehow. Considering the model output H/S, for example, there is no physical meaning for H/S\>1. However, the PCE evaluates this because there is no imposed bound on some basis polynomial. Do you have any idea how I can treat this? Thank you in advance and all the best Gianni