The paper proposes an algorithm for the formation of a small training set, which ensures a reasonable quality of a surrogate machine learning model trained using this set. The algorithm uses multilayer perceptron to estimate heuristics and select the best next sample for the inclusion in a set. The paper tests the algorithm proposed applying it to the problem of deformation and breaking of a thin thread under the action of a transverse load pulse on it. The possibility to generalize the approach and apply it to building surrogate machine learning models for other physical problems is discussed.