@Aep93

Your number of simulations (N=2700) for d=44 dimensions is not so low, so you should be able to build a good polynomial chaos expansion surrogate model. I’m not sure you used the right options though, especially in terms of *sparse* PCE:

- you should use ‘LARS’ as solver
- you can specify a range of maximal degrees, say
`3:10`

instead of a single one: LARS will test all of them and keep the best.
- for this high dimension, you should use a
*q-norm truncation scheme*, which allows you to select a much smaller candidate basis before LARS is run.

I suggest something like this:

```
MetaOpts.Method = 'LARS';
MetaOpts.Degree = 3:10;
Metaopts.TruncOptions.qNorm = 0.3:0.1:0.8;
MetaOpts.ExpDesign.X = ; % your experimental design (X)
MetaOpts.ExpDesign.Y = ; % your experimental design (Y)
myPCE_LARS = uq_createModel(MetaOpts);
```

You can also limit the interactions terms in your polynomial basis (somehow similar effect as a low q=0.3 or so, depending on the dimension) wit ` MetaOpts.TruncOptions.MaxInteraction = 2;`

. In most cases there are only low interaction, but you need much higher univariate degrees to get a good accuracy.

From the obtained PCE, you can easily get the Sobol indices:

```
SobolOpts.Type = 'Sensitivity';
SobolOpts.Method = 'Sobol';
SobolFromPCE = uq_createAnalysis(SobolOpts);
% if you put this right after creating the PCE, the latter is used
% to compute Sobol' indices analytically.
```

I hope it will solve your problem. Regarding the data: the nice thing is that you could post *anonymized data* easily: what is needed a N \times d array of input parameters and the corresponding outputs. We don’t need to know what the parameters stand for (call them X_1, \dots , X_{44}). If the inputs are uniform distributions, they could be easily normalized to [0,1]. This way you can get targeted help from the community !

Best regards

Bruno