SummaryIn this work, an alternative machine learning methodology is proposed, which utilizes nonlinear manifold learning techniques in the frame of surrogate modeling. Under the assumption that the solutions of a parametrized physical system lie on a low‐dimensional manifold embedded in a high‐dimensional Euclidean space, the goal is to unveil the manifold's intrinsic dimensionality and use it for the construction of a surrogate model, which will be used as a cost‐efficient emulator of the high‐dimensional physical system. To this purpose, a computational framework based on the diffusion maps algorithm is put forth herein, where a set of system solutions is used to identify the geometry of a low‐dimensional space called the diffusion maps space. This space is completely described by a low‐dimensional basis, which is constructed from the eigenvectors and eigenvalues of a diffusion operator on the data. The proposed approach exploits the diffusion maps space's reduced dimensionality for the construction of locally clustered interpolation schemes between the parameter space, the diffusion maps space, and the solution space, which are cheap to evaluate and highly accurate. This way, the need to formulate and solve the governing equations of the system is eliminated. In addition, a sampling methodology is proposed based on the metric of the diffusion maps space to efficiently sample the parameter space, thus ensuring the quality of the surrogate model. Even though it is exploited herein in the premises of uncertainty quantification, this methodology is applicable to any other problem type that depends on some parametric space (ie, optimization, sensitivity analysis, etc). In the numerical examples, it is shown that the proposed surrogate model is capable of high levels of accuracy, as well as significant computational gains.