In this article, we introduce a novel data-driven variable selection approach in a multivariate nonparametric regression model designed to capture only the variables on which the regression function depends. The core concept of our method consists in approximating the underlying function by a linear combination of B-splines of order M and their pairwise interactions. The coefficients of this linear combination are estimated by minimizing the standard least-squares criterion penalized by the sum of the l2-norms of the partial derivatives with respect to the different variables on which the function depends. We demonstrate that our proposed method can be formulated as a Group Lasso problem, aiming to discard irrelevant variables for which the corresponding coefficients are close to zero. We validate our approach through numerical experiments varying the number of observations, the noise level and the total number of variables and compared it to two other state-ofthe-art methods. An application to a geochemical system based on calcite precipitation is also explored. In these different contexts, our approach exhibits better performance than the others. Our completely data-driven method is implemented in the absorber R package which is available on the Comprehensive R Archive Network (CRAN).