I have a model with 130 parameters and measure 18 outputs. I ran the Sobol analysis for the 2nd-order indices because there is a significant difference between the total indices and 1st-order, so I guess there are higher-order interactions. The output is a tensor (130, 130, 18). How could I interpret the output? I also observed that each layer is an upper triangular matrix.

So the 130x130 matrix is basically the s_{ij} i.e. the second order sensitivity wrt to the ith and jth parameters, of each of the output f(x)[k]. I hope that clarifies!

Thank you for the answer! It clarifies it. About the upper triangular matrix, is it problem specific or general way to express the higher-order interactions?